0ac5bbc05d
* bin/ltlsynt.cc: Implement the new option, and make it default to bisimulation with output assignment (a.k.a. bwoa). * NEWS, bin/spot-x.cc, doc/org/ltlsynt.org: Update the documentation. * spot/twaalgos/game.hh: Make bwoa the default. * tests/core/ltlsynt.test: Add and adjust test cases. * tests/python/games.ipynb: Adjust.
4373 lines
292 KiB
Text
4373 lines
292 KiB
Text
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"metadata": {},
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"source": [
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"import spot\n",
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"from buddy import bddtrue\n",
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"spot.setup()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Support for games\n",
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"\n",
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"The support for games is currently quite rudimentary, as Spot currently only uses those games in `ltlsynt`.\n",
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"\n",
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"In essence, agame is just an ω-automaton with a property named `state-player` that stores the player owning each state. The players are named 0 and 1. The player owning a state can decide what the next transition from this state should be. The goal for player 1 is to force the play to be infinite and to satisfy the acceptance condition of the automaton, while the goal for player 0 is to prevent it by either forcing a finite play, or forcing an infinite play that does not satisfy the acceptance condition.\n",
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"\n",
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"The support is currently restricted to games that use:\n",
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"- `t` acceptance: all infinite run are accepting, and player 0 can only win if it manages to force a finite play (this requires reaching states without successors).\n",
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"- max odd parity acceptance: player 0 can win if the maximal value seen infinitely often is even"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Creating games from scratch\n",
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"\n",
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"Games can be [created like any automaton](https://spot.lrde.epita.fr/tut22.html). \n",
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"Using `set_state_players()` will fix the state owners."
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]
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},
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]
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},
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}
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],
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"source": [
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"bdict = spot.make_bdd_dict();\n",
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"game = spot.make_twa_graph(bdict)\n",
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"game.new_states(9)\n",
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"for (s, d) in ((0,1), (0, 3), \n",
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" (1, 0), (1, 2),\n",
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" (2, 1), (2, 5),\n",
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" (3, 2), (3, 4), (3, 6),\n",
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" (6, 7),\n",
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" (7, 6), (7, 8),\n",
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" (8, 5)):\n",
|
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" game.new_edge(s, d, bddtrue)\n",
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"spot.set_state_players(game, [True, False, True, False, True, True, True, False, False])\n",
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"game.show('.g') # Use \"g\" to hide the irrelevant edge labels."
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]
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},
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"metadata": {},
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"source": [
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"The `set_state_players()` function takes a list of owner for each of the states in the automaton. In the output,\n",
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"states from player 0 use circles, ellispes, or rectangle with rounded corners (mnemonic: 0 is round) while states from player 1 have a losanse shape (1 has only straight lines). \n",
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"\n",
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"\n",
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"State ownership can also be manipulated by the following functions:"
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]
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},
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"(True, False, True, False, True, True, True, False, False)"
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]
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"source": [
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"spot.get_state_players(game)"
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]
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],
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"source": [
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"spot.get_state_player(game, 4)"
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]
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"# Solving a game - The \"old\" way\n",
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"\n",
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"Solving a game is done my calling `solve_safety_game()` or `solve_parity_game()`. This will attach two additional vectors into the game automaton: one vector stores the winner of each state, and one vector stores (memory-less) strategy for each state, i.e., the transition that should always be taken by the owner of this state in order to win. \n",
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"\n",
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"The return value of those function is simply the winner for the initial state."
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]
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"source": [
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]
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},
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"Calling the `highlight_strategy()` function can be used to decorate the `game` automaton using the winning regions and strategies. Below, green represent the winning region/strategy for player 1 and red those for player 0."
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]
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},
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"</g>\n",
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],
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"text/plain": [
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"spot.highlight_strategy(game)\n",
|
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"game.show('.g')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"# Solving a game - The new interface\n",
|
|
"\n",
|
|
"A strategy/control circuit can now be derived more conveniently from a LTL/PSL specification.\n",
|
|
"The process is decomposed in to three steps:\n",
|
|
"- Creating the game\n",
|
|
"- Solving the game\n",
|
|
"- Obtaining the strategy\n",
|
|
"\n",
|
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"Each of these steps is parametrized by the same options structure called game_info."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"game has 29 states, and 55 edges.\n",
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"output propositions are ('o0',)\n"
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]
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},
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"<text text-anchor=\"start\" x=\"247\" y=\"-936.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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"<text text-anchor=\"start\" x=\"259\" y=\"-921.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>0</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1098.65\" cy=\"-757.33\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1098.65\" y=\"-753.63\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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|
"</g>\n",
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"<!-- 10 -->\n",
|
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"<g id=\"node4\" class=\"node\">\n",
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"<title>10</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1230.98,-598.33 1200.82,-580.33 1230.98,-562.33 1261.15,-580.33 1230.98,-598.33\"/>\n",
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"<text text-anchor=\"middle\" x=\"1230.98\" y=\"-576.63\" font-family=\"Lato\" font-size=\"14.00\">10</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->10 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
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"<title>0->10</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1111.68,-744.74C1128.54,-726.78 1159.7,-692.42 1182.65,-660.33 1196.74,-640.63 1210.58,-616.54 1219.62,-599.97\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-737.13\" font-family=\"Lato\" font-size=\"14.00\">!i1</text>\n",
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-722.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<text text-anchor=\"middle\" x=\"1230.98\" y=\"-753.63\" font-family=\"Lato\" font-size=\"14.00\">11</text>\n",
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"</g>\n",
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"<!-- 0->11 -->\n",
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"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->11</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1116.69,-757.33C1136.09,-757.33 1168.36,-757.33 1193.51,-757.33\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1200.73,-757.33 1193.73,-760.48 1197.23,-757.33 1193.73,-757.33 1193.73,-757.33 1193.73,-757.33 1197.23,-757.33 1193.73,-754.18 1200.73,-757.33 1200.73,-757.33\"/>\n",
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"<title>10->1</title>\n",
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"</g>\n",
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"<!-- 11->0 -->\n",
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"<g id=\"edge33\" class=\"edge\">\n",
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"<title>11->0</title>\n",
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"</g>\n",
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"<!-- 12 -->\n",
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"<g id=\"node7\" class=\"node\">\n",
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"</g>\n",
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"<!-- 1->12 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->12</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1349.43,-638.53C1356.54,-644.85 1365.86,-652.28 1375.21,-657.33 1387.7,-664.08 1402.61,-669.17 1415.3,-672.76\"/>\n",
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"</g>\n",
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"<g id=\"node8\" class=\"node\">\n",
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"<title>13</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"993.32,-745.33 963.15,-727.33 993.32,-709.33 1023.48,-727.33 993.32,-745.33\"/>\n",
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"</g>\n",
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"<!-- 1->13 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>1->13</title>\n",
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"</g>\n",
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"<!-- 12->1 -->\n",
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"<g id=\"edge34\" class=\"edge\">\n",
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"<title>12->1</title>\n",
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"<text text-anchor=\"start\" x=\"1375.21\" y=\"-642.13\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
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"<text text-anchor=\"start\" x=\"1377.71\" y=\"-627.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
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"<!-- 13->0 -->\n",
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"<g id=\"edge35\" class=\"edge\">\n",
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"<title>13->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1014.24,-733.12C1031.43,-738.11 1056.27,-745.32 1074.37,-750.57\"/>\n",
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"<text text-anchor=\"start\" x=\"1041.65\" y=\"-765.13\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
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"</g>\n",
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"<!-- 2 -->\n",
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"<g id=\"node9\" class=\"node\">\n",
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"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1098.65\" cy=\"-509.33\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"1098.65\" y=\"-505.63\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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"</g>\n",
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"<g id=\"node10\" class=\"node\">\n",
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"<title>14</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1230.98,-184.33 1200.82,-166.33 1230.98,-148.33 1261.15,-166.33 1230.98,-184.33\"/>\n",
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"</g>\n",
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"<!-- 2->14 -->\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->14</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1105.52,-492.52C1111.26,-477.81 1121.12,-456.48 1134.65,-441.33 1151.73,-422.21 1169.34,-431.24 1182.65,-409.33 1220.73,-346.67 1183.76,-316.69 1200.65,-245.33 1205.47,-224.96 1214.07,-202.68 1220.71,-186.99\"/>\n",
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"<text text-anchor=\"start\" x=\"1152.65\" y=\"-460.13\" font-family=\"Lato\" font-size=\"14.00\">i1</text>\n",
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-445.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 16 -->\n",
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"<g id=\"node11\" class=\"node\">\n",
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"<title>16</title>\n",
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"</g>\n",
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"<!-- 2->16 -->\n",
|
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>2->16</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1116.25,-513.94C1133.28,-517.89 1160.36,-521.98 1182.65,-515.33 1193.3,-512.15 1203.78,-505.73 1212.17,-499.55\"/>\n",
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"</g>\n",
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"<!-- 15 -->\n",
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"<g id=\"node30\" class=\"node\">\n",
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"<title>15</title>\n",
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"</g>\n",
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"<!-- 14->15 -->\n",
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"<g id=\"edge36\" class=\"edge\">\n",
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"<title>14->15</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1244.58,-156.12C1257.4,-147.01 1277.93,-135.88 1296.32,-141.33 1302.46,-143.15 1308.54,-146.3 1313.99,-149.76\"/>\n",
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"</g>\n",
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"<!-- 16->2 -->\n",
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"<g id=\"edge38\" class=\"edge\">\n",
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"<title>16->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1208.87,-479.4C1189.09,-475.77 1159.03,-472.78 1134.65,-481.33 1128.29,-483.56 1122.22,-487.49 1116.98,-491.71\"/>\n",
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"</g>\n",
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"<!-- 3 -->\n",
|
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"<g id=\"node12\" class=\"node\">\n",
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"<title>3</title>\n",
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"<text text-anchor=\"middle\" x=\"860.99\" y=\"-821.63\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
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"</g>\n",
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"<!-- 3->13 -->\n",
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"<g id=\"edge8\" class=\"edge\">\n",
|
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"<title>3->13</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M878.68,-821.91C896.52,-817.6 924.95,-808.83 944.99,-793.33 960.95,-780.99 973.85,-761.82 982.13,-747.32\"/>\n",
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"<text text-anchor=\"start\" x=\"914.99\" y=\"-835.13\" font-family=\"Lato\" font-size=\"14.00\">i1</text>\n",
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"</g>\n",
|
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"<!-- 17 -->\n",
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"<g id=\"node13\" class=\"node\">\n",
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"<title>17</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"755.65,-795.33 725.49,-777.33 755.65,-759.33 785.82,-777.33 755.65,-795.33\"/>\n",
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"<text text-anchor=\"middle\" x=\"755.65\" y=\"-773.63\" font-family=\"Lato\" font-size=\"14.00\">17</text>\n",
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"</g>\n",
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"<!-- 3->17 -->\n",
|
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"<g id=\"edge9\" class=\"edge\">\n",
|
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"<title>3->17</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M842.76,-822.76C831.38,-820.65 816.35,-817.06 803.99,-811.33 793.39,-806.42 782.74,-799.03 774.22,-792.4\"/>\n",
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"<text text-anchor=\"start\" x=\"806.49\" y=\"-837.13\" font-family=\"Lato\" font-size=\"14.00\">!i1</text>\n",
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"<text text-anchor=\"start\" x=\"806.49\" y=\"-822.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
|
|
"<!-- 17->2 -->\n",
|
|
"<g id=\"edge39\" class=\"edge\">\n",
|
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"<title>17->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M777.68,-772.38C820.81,-761.95 917.54,-737.05 944.99,-717.33 963.56,-703.98 1049.69,-579.51 1083.74,-529.75\"/>\n",
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"<text text-anchor=\"start\" x=\"912.99\" y=\"-742.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 17->3 -->\n",
|
|
"<g id=\"edge40\" class=\"edge\">\n",
|
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"<title>17->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M777.83,-772.56C791.95,-770.48 810.5,-769.97 824.99,-777.33 835.54,-782.7 843.67,-792.91 849.43,-802.54\"/>\n",
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|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
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"<g id=\"node14\" class=\"node\">\n",
|
|
"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1098.65\" cy=\"-330.33\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"1098.65\" y=\"-326.63\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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|
"</g>\n",
|
|
"<!-- 4->14 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>4->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1100.66,-312.24C1103.27,-272.97 1111.71,-181.96 1134.65,-163.33 1154.17,-147.48 1184.07,-151.49 1205.17,-157.37\"/>\n",
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"<text text-anchor=\"start\" x=\"1152.65\" y=\"-182.13\" font-family=\"Lato\" font-size=\"14.00\">i0</text>\n",
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-167.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
|
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"<!-- 18 -->\n",
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"<g id=\"node15\" class=\"node\">\n",
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"<title>18</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1230.98,-290.33 1200.82,-272.33 1230.98,-254.33 1261.15,-272.33 1230.98,-290.33\"/>\n",
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|
"</g>\n",
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"<!-- 4->18 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
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"<title>4->18</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M1104.99,-313.25C1110.21,-299.77 1119.59,-281.86 1134.65,-273.33 1155.05,-261.78 1182.05,-262.7 1202.11,-265.83\"/>\n",
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-292.13\" font-family=\"Lato\" font-size=\"14.00\">!i0</text>\n",
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"</g>\n",
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"<!-- 18->4 -->\n",
|
|
"<g id=\"edge41\" class=\"edge\">\n",
|
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"<title>18->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1216.88,-282.28C1207.67,-288.92 1194.87,-297.47 1182.65,-303.33 1163.4,-312.56 1140.2,-319.81 1123.23,-324.46\"/>\n",
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"</g>\n",
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"<!-- 5 -->\n",
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"<g id=\"node16\" class=\"node\">\n",
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"<title>5</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1098.65\" cy=\"-166.33\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"1098.65\" y=\"-162.63\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
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"<!-- 5->14 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1105.83,-149.66C1111.34,-137.44 1120.72,-121.75 1134.65,-114.33 1153.48,-104.31 1163.14,-105.71 1182.65,-114.33 1197.86,-121.06 1210.29,-135.35 1218.59,-147.26\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1222.54,-153.21 1216.05,-149.12 1220.61,-150.29 1218.67,-147.38 1218.67,-147.38 1218.67,-147.38 1220.61,-150.29 1221.29,-145.64 1222.54,-153.21 1222.54,-153.21\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1138.65\" y=\"-133.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-118.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->16 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>5->16</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1101,-184.3C1104.44,-225.91 1114.7,-327.38 1134.65,-354.33 1148.96,-373.66 1166.13,-361.85 1182.65,-379.33 1204.96,-402.94 1218.01,-438.86 1224.57,-461.96\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1226.48,-468.98 1221.61,-463.05 1225.56,-465.6 1224.65,-462.23 1224.65,-462.23 1224.65,-462.23 1225.56,-465.6 1227.69,-461.4 1226.48,-468.98 1226.48,-468.98\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1136.65\" y=\"-398.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
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"<text text-anchor=\"start\" x=\"1150.65\" y=\"-383.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->18 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>5->18</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1112.29,-178.2C1118.81,-184.15 1126.98,-191.33 1134.65,-197.33 1155.05,-213.28 1162.26,-214.38 1182.65,-230.33 1193.25,-238.63 1204.55,-248.61 1213.45,-256.76\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1218.66,-261.56 1211.38,-259.13 1216.08,-259.19 1213.51,-256.81 1213.51,-256.81 1213.51,-256.81 1216.08,-259.19 1215.65,-254.5 1218.66,-261.56 1218.66,-261.56\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1136.65\" y=\"-249.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1150.65\" y=\"-234.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19 -->\n",
|
|
"<g id=\"node17\" class=\"node\">\n",
|
|
"<title>19</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1230.98,-52.33 1200.82,-34.33 1230.98,-16.33 1261.15,-34.33 1230.98,-52.33\"/>\n",
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"<text text-anchor=\"middle\" x=\"1230.98\" y=\"-30.63\" font-family=\"Lato\" font-size=\"14.00\">19</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->19 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>5->19</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1100.89,-148.36C1103.88,-110.74 1112.96,-25.74 1134.65,-8.33 1156.84,9.48 1190.29,-6.7 1211.1,-20.3\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1217.12,-24.4 1209.56,-23.07 1214.23,-22.43 1211.33,-20.46 1211.33,-20.46 1211.33,-20.46 1214.23,-22.43 1213.1,-17.86 1217.12,-24.4 1217.12,-24.4\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1134.65\" y=\"-27.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1150.65\" y=\"-12.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->5 -->\n",
|
|
"<g id=\"edge42\" class=\"edge\">\n",
|
|
"<title>19->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1207.02,-38.29C1185.64,-43.09 1154.22,-53.2 1134.65,-73.33 1116.58,-91.92 1107.66,-120.73 1103.38,-141.36\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1102.05,-148.29 1100.28,-140.82 1102.71,-144.85 1103.37,-141.41 1103.37,-141.41 1103.37,-141.41 1102.71,-144.85 1106.47,-142.01 1102.05,-148.29 1102.05,-148.29\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1154.15\" y=\"-92.13\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1150.65\" y=\"-77.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6 -->\n",
|
|
"<g id=\"node18\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"623.32\" cy=\"-501.33\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"623.32\" y=\"-497.63\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->10 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
|
"<title>6->10</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M636.73,-513.35C643.06,-518.91 651.13,-525.18 659.32,-529.33 718.72,-559.43 738.1,-558.66 803.99,-568.33 878.66,-579.29 1104.86,-580.4 1193.66,-580.4\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1200.81,-580.4 1193.81,-583.55 1197.31,-580.4 1193.81,-580.4 1193.81,-580.4 1193.81,-580.4 1197.31,-580.4 1193.81,-577.25 1200.81,-580.4 1200.81,-580.4\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"898.99\" y=\"-595.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-580.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->11 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>6->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M631.61,-517.57C637.54,-529.08 646.96,-544.06 659.32,-553.33 683.95,-571.79 695.66,-566.11 725.32,-574.33 775.71,-588.29 1139.98,-655.11 1182.65,-685.33 1200.7,-698.12 1213.69,-720.16 1221.45,-736.49\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1224.45,-743.1 1218.68,-738.03 1223,-739.91 1221.55,-736.73 1221.55,-736.73 1221.55,-736.73 1223,-739.91 1224.42,-735.42 1224.45,-743.1 1224.45,-743.1\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"900.99\" y=\"-639.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-624.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20 -->\n",
|
|
"<g id=\"node19\" class=\"node\">\n",
|
|
"<title>20</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"755.65,-499.33 725.49,-481.33 755.65,-463.33 785.82,-481.33 755.65,-499.33\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"755.65\" y=\"-477.63\" font-family=\"Lato\" font-size=\"14.00\">20</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->20 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>6->20</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M641.36,-498.72C662.43,-495.48 698.65,-489.93 724.47,-485.96\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"731.45,-484.89 725.01,-489.07 727.99,-485.42 724.53,-485.95 724.53,-485.95 724.53,-485.95 727.99,-485.42 724.06,-482.84 731.45,-484.89 731.45,-484.89\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"659.32\" y=\"-514.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"675.32\" y=\"-499.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21 -->\n",
|
|
"<g id=\"node20\" class=\"node\">\n",
|
|
"<title>21</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"755.65,-413.33 725.49,-395.33 755.65,-377.33 785.82,-395.33 755.65,-413.33\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"755.65\" y=\"-391.63\" font-family=\"Lato\" font-size=\"14.00\">21</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->21 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>6->21</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M633.38,-486.11C639.77,-476.24 649.01,-463.55 659.32,-454.33 677.74,-437.87 686.32,-439.32 707.32,-426.33 716.38,-420.73 726.25,-414.32 734.62,-408.78\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"740.69,-404.75 736.6,-411.24 737.78,-406.68 734.86,-408.62 734.86,-408.62 734.86,-408.62 737.78,-406.68 733.12,-406 740.69,-404.75 740.69,-404.75\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"661.32\" y=\"-473.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"675.32\" y=\"-458.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->4 -->\n",
|
|
"<g id=\"edge43\" class=\"edge\">\n",
|
|
"<title>20->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M769.46,-471.21C793.3,-452.8 846.64,-413.6 896.99,-390.33 929.1,-375.49 1028.33,-348.54 1074.09,-336.47\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"1080.96,-334.66 1074.99,-339.49 1077.58,-335.56 1074.19,-336.45 1074.19,-336.45 1074.19,-336.45 1077.58,-335.56 1073.39,-333.4 1080.96,-334.66 1080.96,-334.66\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"910.49\" y=\"-409.13\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-394.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g id=\"node21\" class=\"node\">\n",
|
|
"<title>7</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"860.99\" cy=\"-488.33\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"860.99\" y=\"-484.63\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->7 -->\n",
|
|
"<g id=\"edge44\" class=\"edge\">\n",
|
|
"<title>20->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M784.97,-480.76C797.28,-480.77 811.87,-481.12 824.99,-482.33 828.58,-482.66 832.36,-483.16 836.05,-483.72\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"842.97,-484.87 835.55,-486.83 839.51,-484.3 836.06,-483.72 836.06,-483.72 836.06,-483.72 839.51,-484.3 836.58,-480.62 842.97,-484.87 842.97,-484.87\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"805.99\" y=\"-501.13\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"806.49\" y=\"-486.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21->4 -->\n",
|
|
"<g id=\"edge45\" class=\"edge\">\n",
|
|
"<title>21->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M770.65,-386.26C795.07,-371.07 847.61,-341.16 896.99,-331.33 959.61,-318.87 1035.42,-323.74 1073.43,-327.51\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"1080.52,-328.25 1073.23,-330.66 1077.04,-327.88 1073.56,-327.52 1073.56,-327.52 1073.56,-327.52 1077.04,-327.88 1073.88,-324.39 1080.52,-328.25 1080.52,-328.25\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"910.49\" y=\"-350.13\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-335.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21->6 -->\n",
|
|
"<g id=\"edge46\" class=\"edge\">\n",
|
|
"<title>21->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M736.57,-388.7C715.83,-382.36 681.8,-375.94 659.32,-392.33 633.3,-411.3 626.2,-449.92 624.49,-475.71\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"624.13,-482.95 621.33,-475.8 624.3,-479.45 624.48,-475.95 624.48,-475.95 624.48,-475.95 624.3,-479.45 627.62,-476.11 624.13,-482.95 624.13,-482.95\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"674.82\" y=\"-411.13\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"675.32\" y=\"-396.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->12 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>7->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M862.46,-506.73C864.46,-576.8 873.16,-824.31 896.99,-849.33 926.51,-880.35 949.49,-863.33 992.32,-863.33 992.32,-863.33 992.32,-863.33 1336.76,-863.33 1410.01,-863.33 1433.85,-752.91 1440.88,-703.15\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"1441.83,-695.98 1444.03,-703.34 1441.37,-699.45 1440.91,-702.92 1440.91,-702.92 1440.91,-702.92 1441.37,-699.45 1437.79,-702.51 1441.83,-695.98 1441.83,-695.98\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1136.65\" y=\"-882.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"1150.65\" y=\"-867.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->13 -->\n",
|
|
"<g id=\"edge21\" class=\"edge\">\n",
|
|
"<title>7->13</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M863.62,-506.26C867.48,-545.29 878.29,-636.36 896.99,-660.33 911.53,-678.99 925.43,-670.02 944.99,-683.33 956.51,-691.18 967.99,-701.77 976.76,-710.59\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"981.85,-715.82 974.71,-713 979.41,-713.31 976.97,-710.8 976.97,-710.8 976.97,-710.8 979.41,-713.31 979.22,-708.61 981.85,-715.82 981.85,-715.82\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"900.99\" y=\"-702.13\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-687.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 22 -->\n",
|
|
"<g id=\"node22\" class=\"node\">\n",
|
|
"<title>22</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"993.32,-454.33 963.15,-436.33 993.32,-418.33 1023.48,-436.33 993.32,-454.33\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"993.32\" y=\"-432.63\" font-family=\"Lato\" font-size=\"14.00\">22</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->22 -->\n",
|
|
"<g id=\"edge22\" class=\"edge\">\n",
|
|
"<title>7->22</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M879.06,-485.72C896.23,-482.71 923.21,-476.89 944.99,-467.33 955.02,-462.92 965.3,-456.47 973.7,-450.59\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"979.73,-446.25 975.89,-452.9 976.89,-448.3 974.05,-450.34 974.05,-450.34 974.05,-450.34 976.89,-448.3 972.21,-447.79 979.73,-446.25 979.73,-446.25\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"896.99\" y=\"-500.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"912.99\" y=\"-485.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 23 -->\n",
|
|
"<g id=\"node23\" class=\"node\">\n",
|
|
"<title>23</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"478.33,-623.33 448.16,-605.33 478.33,-587.33 508.49,-605.33 478.33,-623.33\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"478.33\" y=\"-601.63\" font-family=\"Lato\" font-size=\"14.00\">23</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->23 -->\n",
|
|
"<g id=\"edge23\" class=\"edge\">\n",
|
|
"<title>7->23</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M857.07,-506.19C853.12,-524.21 844.21,-551.32 824.99,-565.33 727.67,-636.24 572.35,-620.98 508.35,-610.75\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"501.36,-609.59 508.78,-607.62 504.81,-610.16 508.27,-610.73 508.27,-610.73 508.27,-610.73 504.81,-610.16 507.75,-613.84 501.36,-609.59 501.36,-609.59\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"661.32\" y=\"-636.13\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"675.32\" y=\"-621.13\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 22->4 -->\n",
|
|
"<g id=\"edge47\" class=\"edge\">\n",
|
|
"<title>22->4</title>\n",
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"</svg>\n"
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],
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"text/plain": [
|
|
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f0ddc16bd50> >"
|
|
]
|
|
},
|
|
"metadata": {},
|
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"output_type": "display_data"
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|
}
|
|
],
|
|
"source": [
|
|
"#Create the game\n",
|
|
"gi = spot.game_info()\n",
|
|
"gi.s = spot.game_info.solver_LAR #Use lar solver\n",
|
|
"\n",
|
|
"#Todo arena changes when executed multiple times\n",
|
|
"game = spot.create_game(\"G((F(i0) && F(i1))->(G(i1<->(X(o0)))))\", [\"o0\"], gi)\n",
|
|
"print(\"game has \", game.num_states(), \" states, and \", game.num_edges(), \" edges.\")\n",
|
|
"print(\"output propositions are \", spot.get_synthesis_output_aps(game))\n",
|
|
"display(game)"
|
|
]
|
|
},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
|
|
{
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|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
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"Found a solution: True\n"
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|
]
|
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},
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{
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"data": {
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|
"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"156.33,-523.02 126.17,-505.02 156.33,-487.02 186.5,-505.02 156.33,-523.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"156.33\" y=\"-501.32\" font-family=\"Lato\" font-size=\"14.00\">25</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->25 -->\n",
|
|
"<g id=\"edge28\" class=\"edge\">\n",
|
|
"<title>9->25</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M69.06,-594.51C86.85,-576.05 120.15,-541.51 139.77,-521.16\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"144.68,-516.07 142.09,-523.29 142.25,-518.59 139.82,-521.11 139.82,-521.11 139.82,-521.11 142.25,-518.59 137.55,-518.92 144.68,-516.07 144.68,-516.07\"/>\n",
|
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"<text text-anchor=\"start\" x=\"92\" y=\"-571.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 26 -->\n",
|
|
"<g id=\"node27\" class=\"node\">\n",
|
|
"<title>26</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"235,-647.02 204.83,-629.02 235,-611.02 265.16,-629.02 235,-647.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"235\" y=\"-625.32\" font-family=\"Lato\" font-size=\"14.00\">26</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->26 -->\n",
|
|
"<g id=\"edge29\" class=\"edge\">\n",
|
|
"<title>9->26</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M73.97,-609.13C103.58,-612.81 165.09,-620.45 202.63,-625.12\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"209.81,-626.01 202.47,-628.27 206.33,-625.58 202.86,-625.15 202.86,-625.15 202.86,-625.15 206.33,-625.58 203.25,-622.02 209.81,-626.01 209.81,-626.01\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-615.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 27 -->\n",
|
|
"<g id=\"node28\" class=\"node\">\n",
|
|
"<title>27</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"367.66,-388.02 337.5,-370.02 367.66,-352.02 397.83,-370.02 367.66,-388.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"367.66\" y=\"-366.32\" font-family=\"Lato\" font-size=\"14.00\">27</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->27 -->\n",
|
|
"<g id=\"edge30\" class=\"edge\">\n",
|
|
"<title>9->27</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M60.92,-589.43C68.46,-559.48 87.74,-498.4 126,-463.02 186.96,-406.64 285.83,-383.14 335.74,-374.47\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"342.74,-373.3 336.36,-377.56 339.29,-373.88 335.84,-374.46 335.84,-374.46 335.84,-374.46 339.29,-373.88 335.32,-371.35 342.74,-373.3 342.74,-373.3\"/>\n",
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"<text text-anchor=\"start\" x=\"148.33\" y=\"-466.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 28 -->\n",
|
|
"<g id=\"node29\" class=\"node\">\n",
|
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"<title>28</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"524.99,-697.02 494.82,-679.02 524.99,-661.02 555.16,-679.02 524.99,-697.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"524.99\" y=\"-675.32\" font-family=\"Lato\" font-size=\"14.00\">28</text>\n",
|
|
"</g>\n",
|
|
"<!-- 9->28 -->\n",
|
|
"<g id=\"edge31\" class=\"edge\">\n",
|
|
"<title>9->28</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M67.25,-621.59C83.37,-642.63 116.82,-679.02 155.33,-679.02 155.33,-679.02 155.33,-679.02 368.66,-679.02 409.35,-679.02 456.04,-679.02 487.52,-679.02\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"494.79,-679.02 487.79,-682.17 491.29,-679.02 487.79,-679.02 487.79,-679.02 487.79,-679.02 491.29,-679.02 487.79,-675.87 494.79,-679.02 494.79,-679.02\"/>\n",
|
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"<text text-anchor=\"start\" x=\"227\" y=\"-682.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>0</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"992.65\" cy=\"-558.02\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"992.65\" y=\"-554.32\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 10 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
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"<title>10</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1092.98,-429.02 1062.82,-411.02 1092.98,-393.02 1123.15,-411.02 1092.98,-429.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-407.32\" font-family=\"Lato\" font-size=\"14.00\">10</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->10 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->10</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1003.44,-543.39C1021.49,-516.4 1059.97,-458.87 1079.73,-429.34\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1083.64,-423.48 1082.37,-431.05 1081.7,-426.39 1079.75,-429.3 1079.75,-429.3 1079.75,-429.3 1081.7,-426.39 1077.13,-427.55 1083.64,-423.48 1083.64,-423.48\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-504.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 11 -->\n",
|
|
"<g id=\"node5\" class=\"node\">\n",
|
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"<title>11</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1092.98,-576.02 1062.82,-558.02 1092.98,-540.02 1123.15,-558.02 1092.98,-576.02\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-554.32\" font-family=\"Lato\" font-size=\"14.00\">11</text>\n",
|
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"</g>\n",
|
|
"<!-- 0->11 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
|
"<title>0->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1010.78,-558.02C1023.07,-558.02 1040.1,-558.02 1055.39,-558.02\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1062.73,-558.02 1055.73,-561.17 1059.23,-558.02 1055.73,-558.02 1055.73,-558.02 1055.73,-558.02 1059.23,-558.02 1055.73,-554.87 1062.73,-558.02 1062.73,-558.02\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-561.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node6\" class=\"node\">\n",
|
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"<title>1</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"1196.76\" cy=\"-457.02\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1196.76\" y=\"-453.32\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 10->1 -->\n",
|
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"<g id=\"edge32\" class=\"edge\">\n",
|
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"<title>10->1</title>\n",
|
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M1116.72,-414.91C1129.13,-417.57 1144.53,-421.77 1157.32,-428.02 1164.19,-431.38 1171.06,-436.04 1177.05,-440.64\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1182.72,-445.18 1175.29,-443.26 1179.68,-443.38 1176.94,-441.19 1177.26,-440.8 1177.57,-440.41 1180.3,-442.6 1179.23,-438.35 1182.72,-445.18 1182.72,-445.18\"/>\n",
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"<text text-anchor=\"start\" x=\"1141.32\" y=\"-431.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
|
|
"<!-- 11->0 -->\n",
|
|
"<g id=\"edge33\" class=\"edge\">\n",
|
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"<title>11->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M1076.17,-566.18C1063.4,-571.76 1044.94,-577.57 1028.65,-574.02 1024.2,-573.05 1019.63,-571.46 1015.32,-569.65\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1008.83,-566.68 1016.51,-566.73 1012.23,-567.68 1015.41,-569.14 1015.2,-569.59 1014.99,-570.05 1011.81,-568.59 1013.89,-572.46 1008.83,-566.68 1008.83,-566.68\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-578.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 12 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
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"<title>12</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1300.54,-513.02 1270.38,-495.02 1300.54,-477.02 1330.71,-495.02 1300.54,-513.02\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1300.54\" y=\"-491.32\" font-family=\"Lato\" font-size=\"14.00\">12</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->12 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>1->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1213.76,-463.93C1220.64,-466.83 1228.78,-470.18 1236.21,-473.02 1248.46,-477.69 1262.19,-482.51 1273.73,-486.44\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1280.59,-488.77 1272.95,-489.51 1277.28,-487.64 1273.96,-486.52 1273.96,-486.52 1273.96,-486.52 1277.28,-487.64 1274.97,-483.54 1280.59,-488.77 1280.59,-488.77\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1236.21\" y=\"-481.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 13 -->\n",
|
|
"<g id=\"node8\" class=\"node\">\n",
|
|
"<title>13</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"892.32,-554.02 862.15,-536.02 892.32,-518.02 922.48,-536.02 892.32,-554.02\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"892.32\" y=\"-532.32\" font-family=\"Lato\" font-size=\"14.00\">13</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->13 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>1->13</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1178.79,-455.45C1148.16,-453.15 1081.9,-450.54 1028.65,-465.02 984.28,-477.08 937.96,-505.35 912.67,-522.36\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"906.7,-526.42 910.71,-519.88 909.6,-524.45 912.49,-522.48 912.49,-522.48 912.49,-522.48 909.6,-524.45 914.26,-525.08 906.7,-526.42 906.7,-526.42\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-468.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 12->1 -->\n",
|
|
"<g id=\"edge34\" class=\"edge\">\n",
|
|
"<title>12->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M1290.12,-483.08C1281.48,-473.16 1267.69,-459.79 1252.21,-454.02 1242.6,-450.43 1231.37,-450.42 1221.61,-451.6\"/>\n",
|
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"1214.49,-452.69 1220.93,-448.52 1217.87,-451.67 1221.33,-451.14 1221.4,-451.63 1221.48,-452.13 1218.02,-452.66 1221.88,-454.74 1214.49,-452.69 1214.49,-452.69\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1236.21\" y=\"-457.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 13->0 -->\n",
|
|
"<g id=\"edge35\" class=\"edge\">\n",
|
|
"<title>13->0</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M914.66,-540.79C930.33,-544.3 951.63,-549.06 967.86,-552.69\"/>\n",
|
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"974.91,-554.27 967.4,-555.82 971.39,-554 967.97,-553.23 968.08,-552.75 968.19,-552.26 971.61,-553.02 968.77,-549.67 974.91,-554.27 974.91,-554.27\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"940.65\" y=\"-552.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g id=\"node9\" class=\"node\">\n",
|
|
"<title>2</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"992.65\" cy=\"-357.02\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"992.65\" y=\"-353.32\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
|
|
"</g>\n",
|
|
"<!-- 14 -->\n",
|
|
"<g id=\"node10\" class=\"node\">\n",
|
|
"<title>14</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1092.98,-136.02 1062.82,-118.02 1092.98,-100.02 1123.15,-118.02 1092.98,-136.02\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-114.32\" font-family=\"Lato\" font-size=\"14.00\">14</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->14 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>2->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M1005.93,-344.04C1017.86,-330.62 1035.5,-308.51 1044.65,-286.02 1064.81,-236.47 1044.57,-217.36 1062.65,-167.02 1066.53,-156.21 1072.91,-145.14 1078.73,-136.27\"/>\n",
|
|
"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1082.82,-130.23 1081.5,-137.79 1081.27,-133.41 1079.31,-136.31 1078.89,-136.03 1078.48,-135.75 1080.44,-132.85 1076.29,-134.26 1082.82,-130.23 1082.82,-130.23\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1028.65\" y=\"-316.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 16 -->\n",
|
|
"<g id=\"node11\" class=\"node\">\n",
|
|
"<title>16</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1092.98,-364.02 1062.82,-346.02 1092.98,-328.02 1123.15,-346.02 1092.98,-364.02\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-342.32\" font-family=\"Lato\" font-size=\"14.00\">16</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2->16 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>2->16</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1010.69,-359.95C1016.38,-360.79 1022.77,-361.6 1028.65,-362.02 1035.74,-362.52 1037.63,-363.17 1044.65,-362.02 1052.35,-360.75 1060.49,-358.4 1067.8,-355.88\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1074.8,-353.34 1069.29,-358.69 1071.51,-354.53 1068.22,-355.73 1068.22,-355.73 1068.22,-355.73 1071.51,-354.53 1067.14,-352.77 1074.8,-353.34 1074.8,-353.34\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1028.65\" y=\"-365.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 15 -->\n",
|
|
"<g id=\"node30\" class=\"node\">\n",
|
|
"<title>15</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"1196.76\" cy=\"-118.02\" rx=\"21.4\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1196.76\" y=\"-114.32\" font-family=\"Lato\" font-size=\"14.00\">15</text>\n",
|
|
"</g>\n",
|
|
"<!-- 14->15 -->\n",
|
|
"<g id=\"edge36\" class=\"edge\">\n",
|
|
"<title>14->15</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1108.96,-109.4C1121.71,-103.11 1140.58,-96.29 1157.32,-100.02 1162.36,-101.14 1167.53,-103 1172.37,-105.11\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1178.73,-108.09 1171.05,-107.97 1175.56,-106.6 1172.39,-105.12 1172.39,-105.12 1172.39,-105.12 1175.56,-106.6 1173.73,-102.26 1178.73,-108.09 1178.73,-108.09\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1141.32\" y=\"-103.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
|
"</g>\n",
|
|
"<!-- 16->2 -->\n",
|
|
"<g id=\"edge38\" class=\"edge\">\n",
|
|
"<title>16->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1068.93,-342.33C1056.84,-341.04 1041.84,-340.48 1028.65,-343.02 1024.45,-343.83 1020.12,-345.14 1015.99,-346.63\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1009.29,-349.29 1014.64,-343.78 1012.55,-348 1015.8,-346.71 1015.8,-346.71 1015.8,-346.71 1012.55,-348 1016.96,-349.64 1009.29,-349.29 1009.29,-349.29\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-346.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3 -->\n",
|
|
"<g id=\"node12\" class=\"node\">\n",
|
|
"<title>3</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"791.99\" cy=\"-605.02\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"791.99\" y=\"-601.32\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->13 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>3->13</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M807.91,-595.78C818.19,-589.32 832.08,-580.38 843.99,-572.02 853.73,-565.17 864.31,-557.19 872.99,-550.48\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"878.66,-546.06 875.07,-552.85 875.89,-548.21 873.13,-550.36 873.13,-550.36 873.13,-550.36 875.89,-548.21 871.2,-547.88 878.66,-546.06 878.66,-546.06\"/>\n",
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"<text text-anchor=\"start\" x=\"827.99\" y=\"-585.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
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"<!-- 17 -->\n",
|
|
"<g id=\"node13\" class=\"node\">\n",
|
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"<title>17</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"691.65,-585.02 661.49,-567.02 691.65,-549.02 721.82,-567.02 691.65,-585.02\"/>\n",
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"<text text-anchor=\"middle\" x=\"691.65\" y=\"-563.32\" font-family=\"Lato\" font-size=\"14.00\">17</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->17 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->17</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M774.26,-600.37C764.21,-597.43 751.24,-593.38 739.99,-589.02 731.83,-585.86 723.11,-581.96 715.39,-578.32\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"708.64,-575.09 716.31,-575.27 711.79,-576.6 714.95,-578.11 714.95,-578.11 714.95,-578.11 711.79,-576.6 713.59,-580.95 708.64,-575.09 708.64,-575.09\"/>\n",
|
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"<text text-anchor=\"start\" x=\"739.99\" y=\"-597.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 17->2 -->\n",
|
|
"<g id=\"edge39\" class=\"edge\">\n",
|
|
"<title>17->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M713.01,-561.69C743.32,-553.14 801.28,-534.4 843.99,-506.02 899.72,-468.98 951.52,-408.35 976.32,-377.07\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"980.92,-371.23 979.07,-378.68 978.75,-373.98 976.59,-376.73 976.59,-376.73 976.59,-376.73 978.75,-373.98 974.11,-374.78 980.92,-371.23 980.92,-371.23\"/>\n",
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"<text text-anchor=\"start\" x=\"827.99\" y=\"-518.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 17->3 -->\n",
|
|
"<g id=\"edge40\" class=\"edge\">\n",
|
|
"<title>17->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M717.06,-564.14C729.23,-563.68 743.91,-564.68 755.99,-570.02 763.57,-573.37 770.41,-579.17 775.98,-585.09\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"780.74,-590.5 773.75,-587.32 778.05,-588.2 775.74,-585.57 776.12,-585.24 776.49,-584.91 778.8,-587.54 778.48,-583.16 780.74,-590.5 780.74,-590.5\"/>\n",
|
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"<text text-anchor=\"start\" x=\"739.99\" y=\"-573.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node14\" class=\"node\">\n",
|
|
"<title>4</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"992.65\" cy=\"-232.02\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"992.65\" y=\"-228.32\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->14 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>4->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M994.3,-213.83C996.18,-190.23 1003.18,-149.53 1028.65,-128.02 1036.87,-121.07 1047.92,-117.95 1058.48,-116.75\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1065.68,-116.2 1058.94,-119.87 1062.22,-116.96 1058.73,-117.23 1058.7,-116.73 1058.66,-116.23 1062.15,-115.97 1058.46,-113.59 1065.68,-116.2 1065.68,-116.2\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-131.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 18 -->\n",
|
|
"<g id=\"node15\" class=\"node\">\n",
|
|
"<title>18</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1092.98,-212.02 1062.82,-194.02 1092.98,-176.02 1123.15,-194.02 1092.98,-212.02\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-190.32\" font-family=\"Lato\" font-size=\"14.00\">18</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->18 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
|
"<title>4->18</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1003.09,-217.32C1009.27,-209.12 1018.13,-199.65 1028.65,-195.02 1038.87,-190.52 1050.95,-189.43 1061.81,-189.76\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1069.09,-190.19 1061.92,-192.92 1065.59,-189.98 1062.1,-189.78 1062.1,-189.78 1062.1,-189.78 1065.59,-189.98 1062.28,-186.63 1069.09,-190.19 1069.09,-190.19\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-198.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 18->4 -->\n",
|
|
"<g id=\"edge41\" class=\"edge\">\n",
|
|
"<title>18->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1074.05,-200.95C1057.89,-207.19 1034.03,-216.41 1016.5,-223.19\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1009.89,-225.74 1015.28,-220.28 1013.15,-224.48 1016.42,-223.22 1016.42,-223.22 1016.42,-223.22 1013.15,-224.48 1017.55,-226.16 1009.89,-225.74 1009.89,-225.74\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-221.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node16\" class=\"node\">\n",
|
|
"<title>5</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"992.65\" cy=\"-118.02\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"992.65\" y=\"-114.32\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->14 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M1003.07,-103.26C1009.23,-95.03 1018.09,-85.56 1028.65,-81.02 1035.18,-78.21 1037.93,-78.7 1044.65,-81.02 1056.51,-85.1 1067.67,-93.51 1076.17,-101.29\"/>\n",
|
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1081.61,-106.5 1074.38,-103.93 1078.74,-104.44 1076.21,-102.02 1076.56,-101.66 1076.91,-101.3 1079.43,-103.72 1078.74,-99.38 1081.61,-106.5 1081.61,-106.5\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-84.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->16 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>5->16</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M997.38,-135.42C1002.75,-159.01 1013.67,-202.2 1028.65,-237.02 1042.99,-270.36 1065.33,-306.25 1079.29,-327.39\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1083.33,-333.46 1076.83,-329.38 1081.39,-330.55 1079.45,-327.63 1079.45,-327.63 1079.45,-327.63 1081.39,-330.55 1082.07,-325.89 1083.33,-333.46 1083.33,-333.46\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-271.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->18 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>5->18</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1007.32,-128.59C1024.54,-141.89 1054.19,-164.81 1073.44,-179.68\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1079.05,-184.02 1071.59,-182.24 1076.28,-181.88 1073.51,-179.74 1073.51,-179.74 1073.51,-179.74 1076.28,-181.88 1075.44,-177.25 1079.05,-184.02 1079.05,-184.02\"/>\n",
|
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"<text text-anchor=\"start\" x=\"1028.65\" y=\"-159.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19 -->\n",
|
|
"<g id=\"node17\" class=\"node\">\n",
|
|
"<title>19</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"1092.98,-41.02 1062.82,-23.02 1092.98,-5.02 1123.15,-23.02 1092.98,-41.02\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"1092.98\" y=\"-19.32\" font-family=\"Lato\" font-size=\"14.00\">19</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->19 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>5->19</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M993.21,-99.85C993.68,-73.91 998.89,-26.95 1028.65,-5.02 1041.54,4.48 1059.29,-1.8 1072.71,-9.44\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1078.92,-13.24 1071.3,-12.27 1075.93,-11.41 1072.95,-9.59 1072.95,-9.59 1072.95,-9.59 1075.93,-11.41 1074.59,-6.9 1078.92,-13.24 1078.92,-13.24\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1028.65\" y=\"-8.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->5 -->\n",
|
|
"<g id=\"edge42\" class=\"edge\">\n",
|
|
"<title>19->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M1074.88,-30.47C1061.2,-37.05 1042.14,-47.67 1028.65,-61.02 1018.65,-70.92 1010.27,-84.22 1004.22,-95.49\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1000.94,-101.84 1001.35,-94.18 1002.54,-98.73 1004.15,-95.63 1004.15,-95.63 1004.15,-95.63 1002.54,-98.73 1006.95,-97.07 1000.94,-101.84 1000.94,-101.84\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"1028.65\" y=\"-64.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6 -->\n",
|
|
"<g id=\"node18\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"591.32\" cy=\"-329.02\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"591.32\" y=\"-325.32\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->10 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
|
"<title>6->10</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M607.02,-338.11C643.9,-360.04 743.92,-414.02 834.99,-414.02 834.99,-414.02 834.99,-414.02 993.65,-414.02 1014.91,-414.02 1038.74,-413.31 1057.62,-412.58\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1064.86,-412.29 1057.99,-415.72 1061.36,-412.43 1057.87,-412.57 1057.87,-412.57 1057.87,-412.57 1061.36,-412.43 1057.74,-409.42 1064.86,-412.29 1064.86,-412.29\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"827.99\" y=\"-417.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->11 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>6->11</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M603.1,-343.04C615.44,-358.02 637.1,-381.19 661.32,-393.02 820.37,-470.7 896.23,-404.58 1044.65,-501.02 1059.35,-510.57 1071.81,-526.1 1080.25,-538.54\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"1084.29,-544.71 1077.82,-540.58 1082.37,-541.78 1080.46,-538.86 1080.46,-538.86 1080.46,-538.86 1082.37,-541.78 1083.09,-537.13 1084.29,-544.71 1084.29,-544.71\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"827.99\" y=\"-441.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20 -->\n",
|
|
"<g id=\"node19\" class=\"node\">\n",
|
|
"<title>20</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"691.65,-335.02 661.49,-317.02 691.65,-299.02 721.82,-317.02 691.65,-335.02\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"691.65\" y=\"-313.32\" font-family=\"Lato\" font-size=\"14.00\">20</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->20 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>6->20</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M609.45,-326.93C623.1,-325.26 642.58,-322.89 659.04,-320.88\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"666.36,-319.98 659.79,-323.96 662.88,-320.41 659.41,-320.83 659.41,-320.83 659.41,-320.83 662.88,-320.41 659.03,-317.7 666.36,-319.98 666.36,-319.98\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"627.32\" y=\"-327.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21 -->\n",
|
|
"<g id=\"node20\" class=\"node\">\n",
|
|
"<title>21</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"691.65,-271.02 661.49,-253.02 691.65,-235.02 721.82,-253.02 691.65,-271.02\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"691.65\" y=\"-249.32\" font-family=\"Lato\" font-size=\"14.00\">21</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->21 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>6->21</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M605.99,-318.45C623.21,-305.14 652.86,-282.23 672.11,-267.35\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"677.72,-263.01 674.11,-269.79 674.95,-265.15 672.18,-267.29 672.18,-267.29 672.18,-267.29 674.95,-265.15 670.26,-264.8 677.72,-263.01 677.72,-263.01\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"627.32\" y=\"-303.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->4 -->\n",
|
|
"<g id=\"edge43\" class=\"edge\">\n",
|
|
"<title>20->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M710.41,-310.17C736.09,-300.43 785.21,-282.37 827.99,-270.02 877.02,-255.85 935.48,-243.3 967.58,-236.77\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"974.77,-235.32 968.53,-239.79 971.34,-236.01 967.91,-236.71 967.91,-236.71 967.91,-236.71 971.34,-236.01 967.29,-233.62 974.77,-235.32 974.77,-235.32\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"827.99\" y=\"-273.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7 -->\n",
|
|
"<g id=\"node21\" class=\"node\">\n",
|
|
"<title>7</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"791.99\" cy=\"-317.02\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"791.99\" y=\"-313.32\" font-family=\"Lato\" font-size=\"14.00\">7</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->7 -->\n",
|
|
"<g id=\"edge44\" class=\"edge\">\n",
|
|
"<title>20->7</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M721.89,-317.02C736.13,-317.02 753.04,-317.02 766.57,-317.02\"/>\n",
|
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"773.71,-317.02 766.71,-320.17 770.21,-317.52 766.71,-317.52 766.71,-317.02 766.71,-316.52 770.21,-316.52 766.71,-313.87 773.71,-317.02 773.71,-317.02\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"739.99\" y=\"-320.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21->4 -->\n",
|
|
"<g id=\"edge45\" class=\"edge\">\n",
|
|
"<title>21->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M711.66,-246.85C737.61,-238.79 785.73,-225.1 827.99,-220.02 877.48,-214.07 935.77,-221.86 967.72,-227.39\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"974.87,-228.66 967.43,-230.53 971.43,-228.05 967.98,-227.43 967.98,-227.43 967.98,-227.43 971.43,-228.05 968.54,-224.33 974.87,-228.66 974.87,-228.66\"/>\n",
|
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"<text text-anchor=\"start\" x=\"827.99\" y=\"-223.82\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21->6 -->\n",
|
|
"<g id=\"edge46\" class=\"edge\">\n",
|
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"<title>21->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M666.5,-256.04C653.82,-258.61 638.6,-263.34 627.32,-272.02 616.01,-280.72 607.5,-294.2 601.7,-305.87\"/>\n",
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"</g>\n",
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],
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"text/plain": [
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"<spot.jupyter.SVG object>"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
|
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"source": [
|
|
"#Solve the game\n",
|
|
"print(\"Found a solution: \", spot.solve_game(game))\n",
|
|
"spot.highlight_strategy(game)\n",
|
|
"game.show('.g')"
|
|
]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
|
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
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"minimization lvl 0\n"
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]
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},
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{
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"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-349.47 881.5,-349.47 881.5,4 -4,4\"/>\n",
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"<text text-anchor=\"start\" x=\"435.75\" y=\"-330.27\" font-family=\"Lato\" font-size=\"14.00\">t</text>\n",
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"<text text-anchor=\"start\" x=\"427.75\" y=\"-315.27\" font-family=\"Lato\" font-size=\"14.00\">[all]</text>\n",
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|
"<!-- I -->\n",
|
|
"<!-- 0 -->\n",
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|
"<g id=\"node2\" class=\"node\">\n",
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|
"<title>0</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"56\" cy=\"-208.47\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"56\" y=\"-204.77\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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"</g>\n",
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"<!-- I->0 -->\n",
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|
"<g id=\"edge1\" class=\"edge\">\n",
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|
"<title>I->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-208.47C2.79,-208.47 17.15,-208.47 30.63,-208.47\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-208.47 30.94,-211.62 34.44,-208.47 30.94,-208.47 30.94,-208.47 30.94,-208.47 34.44,-208.47 30.94,-205.32 37.94,-208.47 37.94,-208.47\"/>\n",
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|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>1</title>\n",
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|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"180\" cy=\"-143.47\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"180\" y=\"-139.77\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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|
"</g>\n",
|
|
"<!-- 0->1 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->1</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M72.45,-200.23C93.9,-188.8 132.81,-168.07 157.21,-155.08\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"163.67,-151.63 158.98,-157.7 160.59,-153.28 157.5,-154.92 157.5,-154.92 157.5,-154.92 160.59,-153.28 156.01,-152.14 163.67,-151.63 163.67,-151.63\"/>\n",
|
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"<text text-anchor=\"start\" x=\"92\" y=\"-192.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 2 -->\n",
|
|
"<g id=\"node4\" class=\"node\">\n",
|
|
"<title>2</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"340\" cy=\"-205.47\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"340\" y=\"-201.77\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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|
"</g>\n",
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"<!-- 0->2 -->\n",
|
|
"<g id=\"edge3\" class=\"edge\">\n",
|
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"<title>0->2</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M74.05,-211.08C114.08,-216.77 217.14,-228.81 302,-216.47 306.53,-215.81 311.27,-214.72 315.79,-213.47\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"322.65,-211.43 316.84,-216.45 319.3,-212.43 315.94,-213.43 315.94,-213.43 315.94,-213.43 319.3,-212.43 315.04,-210.41 322.65,-211.43 322.65,-211.43\"/>\n",
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"<text text-anchor=\"start\" x=\"158\" y=\"-225.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"</g>\n",
|
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"<!-- 3 -->\n",
|
|
"<g id=\"node5\" class=\"node\">\n",
|
|
"<title>3</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"340\" cy=\"-78.47\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"340\" y=\"-74.77\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->3 -->\n",
|
|
"<g id=\"edge4\" class=\"edge\">\n",
|
|
"<title>0->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M65.85,-193.3C81.09,-168.83 114.85,-121.36 158,-101.47 209.96,-77.5 278.72,-75.91 314.69,-77.04\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"321.86,-77.32 314.74,-80.2 318.36,-77.18 314.86,-77.05 314.86,-77.05 314.86,-77.05 318.36,-77.18 314.98,-73.9 321.86,-77.32 321.86,-77.32\"/>\n",
|
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"<text text-anchor=\"start\" x=\"158\" y=\"-105.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node6\" class=\"node\">\n",
|
|
"<title>4</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"707\" cy=\"-116.47\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"707\" y=\"-112.77\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->4 -->\n",
|
|
"<g id=\"edge5\" class=\"edge\">\n",
|
|
"<title>0->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M67.71,-222.71C87.06,-246.68 130.4,-292.47 179,-292.47 179,-292.47 179,-292.47 516,-292.47 605.54,-292.47 670.74,-185.97 695.29,-138.66\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"698.49,-132.39 698.11,-140.06 696.9,-135.51 695.31,-138.63 695.31,-138.63 695.31,-138.63 696.9,-135.51 692.5,-137.2 698.49,-132.39 698.49,-132.39\"/>\n",
|
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"<text text-anchor=\"start\" x=\"320\" y=\"-296.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->1 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>1->1</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M169.29,-158.26C165.81,-168.88 169.38,-179.47 180,-179.47 188.13,-179.47 192.13,-173.26 192,-165.59\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"190.71,-158.26 195.02,-164.61 191.31,-161.7 191.92,-165.15 191.92,-165.15 191.92,-165.15 191.31,-161.7 188.82,-165.7 190.71,-158.26 190.71,-158.26\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"137.5\" y=\"-183.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1 & !o0</text>\n",
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|
"</g>\n",
|
|
"<!-- 1->2 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>1->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M193.84,-155.42C201.06,-161.59 210.5,-168.77 220,-173.47 250.94,-188.76 290.13,-197.49 314.9,-201.85\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"322.1,-203.06 314.67,-205 318.65,-202.48 315.19,-201.9 315.19,-201.9 315.19,-201.9 318.65,-202.48 315.72,-198.79 322.1,-203.06 322.1,-203.06\"/>\n",
|
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"<text text-anchor=\"start\" x=\"220\" y=\"-202.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->3 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
|
"<title>1->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M197.62,-137.93C228.46,-127.61 292.32,-106.09 302,-101.47 307.59,-98.8 313.4,-95.48 318.7,-92.2\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"324.66,-88.42 320.44,-94.83 321.71,-90.3 318.75,-92.17 318.75,-92.17 318.75,-92.17 321.71,-90.3 317.06,-89.51 324.66,-88.42 324.66,-88.42\"/>\n",
|
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"<text text-anchor=\"start\" x=\"220\" y=\"-133.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1->4 -->\n",
|
|
"<g id=\"edge6\" class=\"edge\">\n",
|
|
"<title>1->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M198.08,-144.53C204.89,-144.91 212.82,-145.28 220,-145.47 256.43,-146.4 265.56,-146.25 302,-145.47 455.89,-142.13 495.59,-151.96 648,-130.47 659.5,-128.84 672.05,-125.96 682.53,-123.22\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"689.41,-121.37 683.47,-126.23 686.03,-122.28 682.65,-123.19 682.65,-123.19 682.65,-123.19 686.03,-122.28 681.84,-120.15 689.41,-121.37 689.41,-121.37\"/>\n",
|
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"<text text-anchor=\"start\" x=\"380\" y=\"-149.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1 & !o0</text>\n",
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|
"</g>\n",
|
|
"<!-- 2->2 -->\n",
|
|
"<g id=\"edge11\" class=\"edge\">\n",
|
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"<title>2->2</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M327.61,-218.76C322.31,-229.86 326.44,-241.47 340,-241.47 350.8,-241.47 355.62,-234.1 354.45,-225.49\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"352.39,-218.76 357.46,-224.53 353.42,-222.1 354.44,-225.45 354.44,-225.45 354.44,-225.45 353.42,-222.1 351.43,-226.37 352.39,-218.76 352.39,-218.76\"/>\n",
|
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"<text text-anchor=\"start\" x=\"313.5\" y=\"-245.27\" font-family=\"Lato\" font-size=\"14.00\">!i1 & !o0</text>\n",
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|
"</g>\n",
|
|
"<!-- 2->4 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
|
"<title>2->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M358,-207.45C406.18,-212.32 546.68,-221.2 648,-173.47 665.5,-165.22 680.88,-149.47 691.4,-136.62\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"695.88,-130.95 694.01,-138.39 693.71,-133.7 691.54,-136.44 691.54,-136.44 691.54,-136.44 693.71,-133.7 689.07,-134.49 695.88,-130.95 695.88,-130.95\"/>\n",
|
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"<text text-anchor=\"start\" x=\"490.5\" y=\"-213.27\" font-family=\"Lato\" font-size=\"14.00\">i1 & !o0</text>\n",
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|
"</g>\n",
|
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"<!-- 3->3 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>3->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M327.61,-91.76C322.31,-102.86 326.44,-114.47 340,-114.47 350.8,-114.47 355.62,-107.1 354.45,-98.49\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"352.39,-91.76 357.46,-97.53 353.42,-95.1 354.44,-98.45 354.44,-98.45 354.44,-98.45 353.42,-95.1 351.43,-99.37 352.39,-91.76 352.39,-91.76\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"301\" y=\"-118.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1 & o0</text>\n",
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|
"</g>\n",
|
|
"<!-- 3->4 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
|
"<title>3->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M356.9,-85.64C363.33,-88.23 370.89,-90.9 378,-92.47 489.29,-117.05 626.44,-117.89 681.47,-117.06\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"688.68,-116.94 681.73,-120.21 685.18,-117 681.68,-117.06 681.68,-117.06 681.68,-117.06 685.18,-117 681.62,-113.91 688.68,-116.94 688.68,-116.94\"/>\n",
|
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"<text text-anchor=\"start\" x=\"478\" y=\"-118.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1 & o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5 -->\n",
|
|
"<g id=\"node7\" class=\"node\">\n",
|
|
"<title>5</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"851\" cy=\"-47.47\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"851\" y=\"-43.77\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->5 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>3->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M347.24,-61.73C353.11,-48.4 363.22,-30.37 378,-20.47 415.51,4.68 433.02,-6.48 478,-2.47 610.04,9.32 767.59,-26.17 826.36,-41.14\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"833.35,-42.94 825.79,-44.25 829.97,-42.07 826.58,-41.2 826.58,-41.2 826.58,-41.2 829.97,-42.07 827.36,-38.15 833.35,-42.94 833.35,-42.94\"/>\n",
|
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"<text text-anchor=\"start\" x=\"570\" y=\"-11.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1 & o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6 -->\n",
|
|
"<g id=\"node8\" class=\"node\">\n",
|
|
"<title>6</title>\n",
|
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"515\" cy=\"-29.47\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"515\" y=\"-25.77\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->6 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>3->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M350.41,-63.59C356.96,-54.63 366.56,-43.92 378,-38.47 414.07,-21.25 461.75,-22.84 490.01,-25.91\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"497.1,-26.75 489.78,-29.05 493.63,-26.34 490.15,-25.92 490.15,-25.92 490.15,-25.92 493.63,-26.34 490.53,-22.79 497.1,-26.75 497.1,-26.75\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"378\" y=\"-42.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1 & o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->4 -->\n",
|
|
"<g id=\"edge17\" class=\"edge\">\n",
|
|
"<title>4->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M694.16,-129.38C688.31,-140.6 692.59,-152.47 707,-152.47 718.49,-152.47 723.54,-144.93 722.15,-136.19\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"719.84,-129.38 725.07,-135 720.96,-132.7 722.09,-136.01 722.09,-136.01 722.09,-136.01 720.96,-132.7 719.11,-137.03 719.84,-129.38 719.84,-129.38\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"684\" y=\"-156.27\" font-family=\"Lato\" font-size=\"14.00\">i1 & o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4->5 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
|
"<title>4->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M725.27,-115.88C747.6,-114.39 786.95,-109.21 815,-91.47 823.81,-85.89 831.36,-77.31 837.17,-69.21\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"841.26,-63.15 839.95,-70.72 839.3,-66.05 837.34,-68.95 837.34,-68.95 837.34,-68.95 839.3,-66.05 834.73,-67.19 841.26,-63.15 841.26,-63.15\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"766\" y=\"-114.27\" font-family=\"Lato\" font-size=\"14.00\">!i1 & o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->4 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>5->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M833.23,-50.59C815.78,-54.27 787.99,-61.32 766,-72.47 751.6,-79.76 737.13,-90.73 726.25,-99.89\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"720.9,-104.49 724.15,-97.54 723.55,-102.21 726.21,-99.93 726.21,-99.93 726.21,-99.93 723.55,-102.21 728.26,-102.32 720.9,-104.49 720.9,-104.49\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"766\" y=\"-76.27\" font-family=\"Lato\" font-size=\"14.00\">i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->5 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>5->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M840.85,-62.63C837.77,-73.13 841.16,-83.47 851,-83.47 858.54,-83.47 862.29,-77.41 862.25,-69.86\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"861.15,-62.63 865.32,-69.08 861.68,-66.09 862.2,-69.55 862.2,-69.55 862.2,-69.55 861.68,-66.09 859.09,-70.03 861.15,-62.63 861.15,-62.63\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"824.5\" y=\"-87.27\" font-family=\"Lato\" font-size=\"14.00\">!i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->3 -->\n",
|
|
"<g id=\"edge23\" class=\"edge\">\n",
|
|
"<title>6->3</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M498.74,-37.29C488.11,-42.48 473.47,-49.11 460,-53.47 427.78,-63.88 389.22,-71.06 364.91,-74.97\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"357.85,-76.08 364.27,-71.88 361.3,-75.53 364.76,-74.99 364.76,-74.99 364.76,-74.99 361.3,-75.53 365.25,-78.1 357.85,-76.08 357.85,-76.08\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"378\" y=\"-77.27\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->4 -->\n",
|
|
"<g id=\"edge21\" class=\"edge\">\n",
|
|
"<title>6->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M531.96,-36.18C556.9,-46.73 606.53,-68 648,-87.47 659.98,-93.09 673.2,-99.67 683.98,-105.13\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"690.35,-108.38 682.68,-108.01 687.23,-106.79 684.11,-105.2 684.11,-105.2 684.11,-105.2 687.23,-106.79 685.54,-102.39 690.35,-108.38 690.35,-108.38\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"570\" y=\"-91.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1 & !o0</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->5 -->\n",
|
|
"<g id=\"edge20\" class=\"edge\">\n",
|
|
"<title>6->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M533.02,-30.38C588.08,-33.35 761.48,-42.69 825.73,-46.16\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"833.01,-46.55 825.85,-49.32 829.52,-46.36 826.02,-46.17 826.02,-46.17 826.02,-46.17 829.52,-46.36 826.19,-43.03 833.01,-46.55 833.01,-46.55\"/>\n",
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"<text text-anchor=\"start\" x=\"666\" y=\"-46.27\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1 & !o0</text>\n",
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|
"</g>\n",
|
|
"<!-- 6->6 -->\n",
|
|
"<g id=\"edge22\" class=\"edge\">\n",
|
|
"<title>6->6</title>\n",
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"source": [
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"# Create the strategy\n",
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"# We have different strategies for minimization:\n",
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"# 0 : No minimizaiton\n",
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"# 1 : DFA minimization\n",
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"# 2 : Inclusion based minimization with output assignement\n",
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"# 3 : SAT based exact minimization\n",
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"# 4 : First 1 then 3 (exact)\n",
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"# 5 : First 2 then 3 (not exact)\n",
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"for i in range(6):\n",
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" print(\"minimization lvl \", i)\n",
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" gi.minimize_lvl = i #Use inclusion with output assignement to minimize the strategy\n",
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" strat = spot.create_strategy(game, gi)\n",
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" display(strat.show())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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"</g>\n",
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"<title>20->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M412.84,-325.05C393.23,-327.75 364.17,-329.72 339.92,-323 334.75,-321.57 329.58,-319.15 324.87,-316.45\"/>\n",
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"</g>\n",
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"<g id=\"edge11\" class=\"edge\">\n",
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"<title>3->13</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M559.71,-364.68C611.54,-365.86 769.06,-362.82 866.14,-289 887.57,-272.71 900.49,-243.81 907.29,-223.81\"/>\n",
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"</g>\n",
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"<!-- 3->19 -->\n",
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"<g id=\"edge12\" class=\"edge\">\n",
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"<title>3->19</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M523.46,-365.82C508.8,-367.38 487.27,-369.67 469.4,-371.58\"/>\n",
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"</g>\n",
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"<g id=\"node14\" class=\"node\">\n",
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"</g>\n",
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"<!-- 5->10 -->\n",
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"<g id=\"edge14\" class=\"edge\">\n",
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"<title>5->10</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M550.28,-144.91C556.19,-134.47 565.41,-121.61 577.58,-115 603.42,-100.95 614.18,-111.11 643.58,-110 820.74,-103.3 1033.07,-115.99 1113.79,-121.56\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1121.19,-122.08 1113.98,-124.73 1117.7,-121.83 1114.2,-121.59 1114.2,-121.59 1114.2,-121.59 1117.7,-121.83 1114.42,-118.45 1121.19,-122.08 1121.19,-122.08\"/>\n",
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"<text text-anchor=\"start\" x=\"820.14\" y=\"-113.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 11 -->\n",
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"<g id=\"node15\" class=\"node\">\n",
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"</g>\n",
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"<!-- 5->11 -->\n",
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"<g id=\"edge15\" class=\"edge\">\n",
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"<title>5->11</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M548.61,-144.13C554.14,-131.15 563.61,-113.81 577.58,-104 666.4,-41.64 947.84,-16.06 1055.81,-5 1075.26,-3.01 1080.42,-2.39 1099.81,-5 1107.03,-5.97 1114.7,-7.75 1121.73,-9.68\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"1128.49,-11.64 1120.89,-12.71 1125.13,-10.66 1121.77,-9.69 1121.77,-9.69 1121.77,-9.69 1125.13,-10.66 1122.64,-6.66 1128.49,-11.64 1128.49,-11.64\"/>\n",
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"<text text-anchor=\"start\" x=\"822.14\" y=\"-37.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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"</g>\n",
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"<!-- 15 -->\n",
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"<g id=\"node16\" class=\"node\">\n",
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"<title>15</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"673.91,-155 643.75,-137 673.91,-119 704.08,-137 673.91,-155\"/>\n",
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"</g>\n",
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"<!-- 5->15 -->\n",
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"<g id=\"edge16\" class=\"edge\">\n",
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"<title>5->15</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M552,-146.24C558.16,-138.02 567.02,-128.55 577.58,-124 600.64,-114.07 629.48,-120.28 649.36,-127.1\"/>\n",
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"<text text-anchor=\"start\" x=\"577.58\" y=\"-127.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 16 -->\n",
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"<g id=\"node17\" class=\"node\">\n",
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"</g>\n",
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"<!-- 5->16 -->\n",
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"<g id=\"edge17\" class=\"edge\">\n",
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"<title>5->16</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M557.9,-169.14C563.89,-172.02 570.92,-175.03 577.58,-177 597.69,-182.94 620.97,-186.42 639.48,-188.43\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"646.59,-189.15 639.3,-191.57 643.11,-188.79 639.62,-188.44 639.62,-188.44 639.62,-188.44 643.11,-188.79 639.94,-185.31 646.59,-189.15 646.59,-189.15\"/>\n",
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"<text text-anchor=\"start\" x=\"579.58\" y=\"-189.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
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"</g>\n",
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"<!-- 9 -->\n",
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"<g id=\"node19\" class=\"node\">\n",
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"<title>9</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"1249.47\" cy=\"-185\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"1249.47\" y=\"-181.3\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
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"</g>\n",
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"<!-- 10->9 -->\n",
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"<g id=\"edge24\" class=\"edge\">\n",
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"<title>10->9</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1164.08,-132.55C1177.2,-140.13 1196.74,-151.57 1213.47,-162 1218.14,-164.91 1223.1,-168.11 1227.78,-171.17\"/>\n",
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"</g>\n",
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"<!-- 11->7 -->\n",
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"<g id=\"edge25\" class=\"edge\">\n",
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"<title>11->7</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1127.24,-12.4C1108.02,-8.11 1078.57,-4.5 1055.81,-15 1046.73,-19.19 1039.14,-27.01 1033.37,-34.71\"/>\n",
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"</g>\n",
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"<g id=\"node21\" class=\"node\">\n",
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"<title>14</title>\n",
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"<text text-anchor=\"middle\" x=\"778.69\" y=\"-206.3\" font-family=\"Lato\" font-size=\"14.00\">14</text>\n",
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"</g>\n",
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"<!-- 15->14 -->\n",
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"<g id=\"edge32\" class=\"edge\">\n",
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"<title>15->14</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M688.35,-146.54C705.58,-158.78 735.69,-180.16 756.14,-194.69\"/>\n",
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"</g>\n",
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"<!-- 16->5 -->\n",
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"<g id=\"edge33\" class=\"edge\">\n",
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"<title>16->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M661.56,-180.06C652.6,-172.22 639.34,-162.32 625.58,-158 606.37,-151.97 583.43,-153.41 566.54,-155.96\"/>\n",
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"</g>\n",
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"<!-- 7->10 -->\n",
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"<g id=\"edge19\" class=\"edge\">\n",
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"<title>7->10</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1036.46,-63.21C1052.56,-70.75 1078.24,-83.1 1099.81,-95 1108.82,-99.97 1118.54,-105.84 1126.82,-110.99\"/>\n",
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"<text text-anchor=\"start\" x=\"1069.81\" y=\"-98.8\" font-family=\"Lato\" font-size=\"14.00\">!i1</text>\n",
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"</g>\n",
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"<!-- 7->11 -->\n",
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"<g id=\"edge20\" class=\"edge\">\n",
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"<title>7->11</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1037.53,-51.63C1053.57,-47.36 1078.44,-40.58 1099.81,-34 1107.02,-31.78 1114.79,-29.22 1121.92,-26.81\"/>\n",
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"</g>\n",
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"<g id=\"edge23\" class=\"edge\">\n",
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"<title>9->13</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1231.43,-185.87C1179.15,-188.54 1020.27,-196.65 949.79,-200.25\"/>\n",
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"</g>\n",
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"<g id=\"node20\" class=\"node\">\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"1354.8,-236 1324.64,-218 1354.8,-200 1384.97,-218 1354.8,-236\"/>\n",
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"<text text-anchor=\"middle\" x=\"1354.8\" y=\"-214.3\" font-family=\"Lato\" font-size=\"14.00\">12</text>\n",
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"</g>\n",
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"<!-- 9->12 -->\n",
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"<g id=\"edge22\" class=\"edge\">\n",
|
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"<title>9->12</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1267.07,-190.3C1283.53,-195.56 1308.99,-203.69 1328.07,-209.78\"/>\n",
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"<text text-anchor=\"start\" x=\"1287.97\" y=\"-205.8\" font-family=\"Lato\" font-size=\"14.00\">!i1</text>\n",
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|
"</g>\n",
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"<!-- 12->9 -->\n",
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"<g id=\"edge26\" class=\"edge\">\n",
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"<title>12->9</title>\n",
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|
"<path fill=\"none\" stroke=\"black\" d=\"M1344.38,-206.06C1335.74,-196.15 1321.95,-182.77 1306.47,-177 1296,-173.1 1283.78,-174.24 1273.43,-176.72\"/>\n",
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"<text text-anchor=\"start\" x=\"1285.47\" y=\"-180.8\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
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"</g>\n",
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"<!-- 14->13 -->\n",
|
|
"<g id=\"edge29\" class=\"edge\">\n",
|
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"<title>14->13</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M800.3,-208.77C821.38,-207.51 854.49,-205.53 879.46,-204.03\"/>\n",
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"<text text-anchor=\"start\" x=\"822.14\" y=\"-210.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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|
"</g>\n",
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"<!-- 14->18 -->\n",
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"<g id=\"edge31\" class=\"edge\">\n",
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"<title>14->18</title>\n",
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|
"<path fill=\"none\" stroke=\"black\" d=\"M757.46,-212.57C742.73,-214.36 722.28,-216.65 704.24,-218 621.57,-224.2 524.21,-227.1 472.95,-228.29\"/>\n",
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"<text text-anchor=\"start\" x=\"579.58\" y=\"-227.8\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
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"</g>\n",
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"<!-- 14->12 -->\n",
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"<g id=\"edge28\" class=\"edge\">\n",
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"<title>14->12</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M797.84,-218.62C823.14,-229.83 870.74,-248 913.47,-248 913.47,-248 913.47,-248 1250.47,-248 1279,-248 1310.27,-237.32 1330.85,-228.71\"/>\n",
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"<text text-anchor=\"start\" x=\"1055.81\" y=\"-251.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
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"</g>\n",
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"<!-- 17 -->\n",
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"</g>\n",
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"<!-- 14->17 -->\n",
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"<g id=\"edge30\" class=\"edge\">\n",
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"<title>14->17</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M783.49,-192.23C788.28,-174.72 798.4,-148.92 818.14,-137 839.64,-124.03 868.99,-129.16 889.42,-135.55\"/>\n",
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"<!-- 17->14 -->\n",
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"<title>17->14</title>\n",
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"</g>\n",
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f0ddc16b720> >"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"gi.minimize_lvl = 0\n",
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"spot.apply_strategy(game, False, False)\n"
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]
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},
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"## Input/Output\n",
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"\n",
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"An extension of the HOA format makes it possible to store the `state-player` property. This allows us to read the parity game constructed by `ltlsynt` using `spot.automaton()` like any other automaton."
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]
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},
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{
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"execution_count": 12,
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"outputs": [
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f0ddc16bf30> >"
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]
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},
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"execution_count": 12,
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"metadata": {},
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}
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],
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"source": [
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"game = spot.automaton(\"ltlsynt --ins=a --outs=b -f '!b & GFa <-> Gb' --print-game-hoa |\");\n",
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"game"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In the graphical output, player 0 is represented by circles (or ellipses or rounded rectangles depending on the situations), while player 1's states are diamond shaped. In the case of `ltlsynt`, player 0 plays the role of the environment, and player 1 plays the role of the controler.\n",
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"\n",
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"In the HOA output, a header `spot-state-player` (or `spot.state-player` in HOA 1.1) lists the owner of each state."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"HOA: v1\n",
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"States: 12\n",
|
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"Start: 4\n",
|
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"AP: 2 \"b\" \"a\"\n",
|
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"acc-name: parity max odd 5\n",
|
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"Acceptance: 5 Fin(4) & (Inf(3) | (Fin(2) & (Inf(1) | Fin(0))))\n",
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"properties: trans-labels explicit-labels trans-acc colored complete\n",
|
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"properties: deterministic\n",
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"spot-state-player: 0 0 0 0 0 1 1 1 1 1 1 1\n",
|
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"--BODY--\n",
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"State: 0\n",
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"[!1] 5 {1}\n",
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"[1] 6 {1}\n",
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"State: 1\n",
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"[1] 6 {1}\n",
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"[!1] 7 {1}\n",
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"State: 2\n",
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"[t] 8 {1}\n",
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"State: 3\n",
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"[t] 9 {1}\n",
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"State: 4\n",
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"[!1] 10 {1}\n",
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"[1] 11 {1}\n",
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"State: 5\n",
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"[t] 0 {3}\n",
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"State: 6\n",
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"[t] 1 {4}\n",
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"State: 7\n",
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"[t] 0 {4}\n",
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"State: 8\n",
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"[t] 2 {3}\n",
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"State: 9\n",
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"[!0] 2 {3}\n",
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"[0] 3 {4}\n",
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"State: 10\n",
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"[!0] 0 {3}\n",
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"[0] 3 {3}\n",
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"State: 11\n",
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"[!0] 1 {3}\n",
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"[0] 3 {3}\n",
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"--END--\n"
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]
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}
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],
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"source": [
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"print(game.to_str('hoa'))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here is the solution of this particular game."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"spot.solve_parity_game(game)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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]
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"spot.highlight_strategy(game)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h2>Reading an aiger-file</h2>\n",
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|
"\n",
|
|
"<p>Read an aiger file. Note that we do not support the full \n",
|
|
" <a href=\"http://fmv.jku.at/aiger/FORMAT.aiger\">syntax</a>, but are restricted to:\n",
|
|
" <ul>\n",
|
|
" <li>Input variables start at index 2 and are consecutively numbered.</li>\n",
|
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" <li>Latch variables start at index (1 + #inputs) * 2 and are consecutively numbered.</li>\n",
|
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" <li>If inputs or outputs are named in the comments, all of them have to be named.</li>\n",
|
|
" <li>Gate number $n$ can only have latches, inputs or previously defined gates ($<n$). </li>\n",
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" </ul>\n",
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"</p>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"aag 5 2 0 2 3\n",
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|
"2\n",
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|
"4\n",
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|
"10\n",
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|
"6\n",
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|
"6 2 4\n",
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|
"8 3 5\n",
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|
"10 7 9\n",
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"i0 a\n",
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"i1 b\n",
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"o0 c\n",
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|
"o1 d\n"
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]
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}
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],
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"source": [
|
|
"#aiger file \n",
|
|
"aag_txt = \"\"\"aag 5 2 0 2 3\n",
|
|
"2\n",
|
|
"4\n",
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|
"10\n",
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|
"6\n",
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"6 2 4\n",
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"8 3 5\n",
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"10 7 9\n",
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"i0 a\n",
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"i1 b\n",
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"o0 c\n",
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"o1 d\"\"\"\n",
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"print(aag_txt)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [],
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"source": [
|
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"this_aig = spot.aiger_circuit(aag_txt)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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"metadata": {},
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}
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],
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"source": [
|
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"display(this_aig.show())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"aag 5 2 0 2 3\n",
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"2\n",
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"4\n",
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"10\n",
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"6\n",
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"6 2 4\n",
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"8 3 5\n",
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"10 7 9\n",
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"i0 i0\n",
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"i1 i1\n",
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"o0 o0\n",
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"o1 o1\n"
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]
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}
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],
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"source": [
|
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"print(this_aig.to_str())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"((2, 4), (3, 5), (7, 9))\n"
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]
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}
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],
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"source": [
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"print(this_aig.gates())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h2>Verifying an implementation</h2>\n",
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"\n",
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"<p>\n",
|
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" An aiger circuit can be transformed into a monitor. If the aiger represents the implementation of a strategy in the context of active control, it can be check for correctness. This is done by computing the intersecting of the monitor and the negation of the specification.\n",
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"</p>"
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]
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},
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"text/plain": [
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]
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}
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],
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"source": [
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"aigasmon = this_aig.as_automaton()\n",
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"display(aigasmon)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h2>Incomplete circuit</h2>\n",
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"\n",
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"<p>\n",
|
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" It can happen that propositions declared as output are ommited in the aig circuit.\n",
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" This happens if the output does not appear in the strategy. Since it does not appear in the\n",
|
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" strategy it can take arbritrary values.\n",
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"</p>"
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]
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},
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"True\n"
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"</g>\n",
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"</g>\n",
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"</svg>\n"
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],
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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f0ddc26bea0> >"
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]
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
|
|
],
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"source": [
|
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"game = spot.create_game(\"o0\", [\"o0\", \"o1\"])\n",
|
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"print(spot.solve_game(game))\n",
|
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"spot.highlight_strategy(game)"
|
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]
|
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},
|
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{
|
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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"<!-- Generated by graphviz version 2.43.0 (0)\n",
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" -->\n",
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"<!-- Pages: 1 -->\n",
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"<svg width=\"96pt\" height=\"126pt\"\n",
|
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" viewBox=\"0.00 0.00 96.39 126.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 122)\">\n",
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"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-122 92.39,-122 92.39,4 -4,4\"/>\n",
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"<!-- o0o0 -->\n",
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"<g id=\"node1\" class=\"node\">\n",
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"<title>o0o0</title>\n",
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"<polygon fill=\"none\" stroke=\"black\" points=\"44.2,-72 88.59,-106.5 -0.2,-106.5 44.2,-72\"/>\n",
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"<text text-anchor=\"middle\" x=\"44.2\" y=\"-91.3\" font-family=\"Times,serif\" font-size=\"14.00\">o0</text>\n",
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"</g>\n",
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"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
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"<title>0</title>\n",
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"<polygon fill=\"none\" stroke=\"black\" points=\"15.2,0 73.2,0 73.2,-36 15.2,-36 15.2,0\"/>\n",
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"<text text-anchor=\"middle\" x=\"44.2\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Const</text>\n",
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"</g>\n",
|
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"<!-- 0->o0o0 -->\n",
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"<g id=\"edge1\" class=\"edge\">\n",
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"<title>0->o0o0:s</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M44.2,-36.19C44.2,-44.29 44.2,-54.29 44.2,-63.98\"/>\n",
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"<ellipse fill=\"black\" stroke=\"black\" cx=\"44.2\" cy=\"-68\" rx=\"4\" ry=\"4\"/>\n",
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"</g>\n",
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"</g>\n",
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"</svg>\n"
|
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],
|
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"text/plain": [
|
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"<spot.aig; proxy of <Swig Object of type 'spot::aig_ptr *' at 0x7f0ddc26b930> >"
|
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]
|
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},
|
|
"execution_count": 23,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"strat = spot.create_strategy(game)\n",
|
|
"aig = spot.strategy_to_aig(strat, \"isop\")\n",
|
|
"aig"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"By handing over the input and output propositions explicitly, you can force their occurrence in the propositions of the circuit"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
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|
"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
|
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"<!-- Generated by graphviz version 2.43.0 (0)\n",
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" -->\n",
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"<!-- Pages: 1 -->\n",
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"<svg width=\"202pt\" height=\"126pt\"\n",
|
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" viewBox=\"0.00 0.00 202.39 126.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<g id=\"graph0\" class=\"graph\" transform=\"scale(1.0 1.0) rotate(0) translate(4 122)\">\n",
|
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"<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-122 198.39,-122 198.39,4 -4,4\"/>\n",
|
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"<!-- o0o0 -->\n",
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"<g id=\"node1\" class=\"node\">\n",
|
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"<title>o0o0</title>\n",
|
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"<polygon fill=\"none\" stroke=\"black\" points=\"44.2,-72 88.59,-106.5 -0.2,-106.5 44.2,-72\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"44.2\" y=\"-91.3\" font-family=\"Times,serif\" font-size=\"14.00\">o0</text>\n",
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"</g>\n",
|
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"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\n",
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"<title>0</title>\n",
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"<polygon fill=\"none\" stroke=\"black\" points=\"68.2,0 126.2,0 126.2,-36 68.2,-36 68.2,0\"/>\n",
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"<text text-anchor=\"middle\" x=\"97.2\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Const</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->o0o0 -->\n",
|
|
"<g id=\"edge1\" class=\"edge\">\n",
|
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"<title>0->o0o0:s</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M67.91,-34.99C57.85,-42.36 48.34,-52.12 45.24,-63.94\"/>\n",
|
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"<ellipse fill=\"black\" stroke=\"black\" cx=\"44.71\" cy=\"-68.03\" rx=\"4\" ry=\"4\"/>\n",
|
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"</g>\n",
|
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"<!-- o1o1 -->\n",
|
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"<g id=\"node3\" class=\"node\">\n",
|
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"<title>o1o1</title>\n",
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"<polygon fill=\"none\" stroke=\"black\" points=\"150.2,-72 194.59,-106.5 105.8,-106.5 150.2,-72\"/>\n",
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"<text text-anchor=\"middle\" x=\"150.2\" y=\"-91.3\" font-family=\"Times,serif\" font-size=\"14.00\">o1</text>\n",
|
|
"</g>\n",
|
|
"<!-- 0->o1o1 -->\n",
|
|
"<g id=\"edge2\" class=\"edge\">\n",
|
|
"<title>0->o1o1:s</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M126.49,-34.99C135.97,-41.94 144.97,-51.01 148.56,-61.94\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"145.13,-62.69 150.2,-72 152.04,-61.57 145.13,-62.69\"/>\n",
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"</g>\n",
|
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"</g>\n",
|
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"</svg>\n"
|
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],
|
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"text/plain": [
|
|
"<spot.aig; proxy of <Swig Object of type 'spot::aig_ptr *' at 0x7f0ddc26be70> >"
|
|
]
|
|
},
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"aig2 = spot.strategy_to_aig(strat, \"isop\", [], [\"o0\", \"o1\"])\n",
|
|
"aig2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
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"display_name": "Python 3",
|
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"language": "python",
|
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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