4260b17fba
Introduce a new, uniform way to create and solve games. Games can now be created directly from specification using creat_game, uniformly solved using solve_game and transformed into a strategy using create_strategy. Strategy are mealy machines, which can be minimized. * bin/ltlsynt.cc: Minor adaption * spot/twaalgos/game.cc: solve_game, setters and getters for named properties * spot/twaalgos/game.hh: Here too * spot/twaalgos/mealy_machine.cc: Minor adaption * spot/twaalgos/synthesis.cc: create_game, create_strategy and minimize_strategy * spot/twaalgos/synthesis.hh: Here too * tests/core/ltlsynt.test: Adapting * tests/python/aiger.py , tests/python/games.ipynb , tests/python/mealy.py , tests/python/parity.py , tests/python/split.py: Adapting
3571 lines
234 KiB
Text
3571 lines
234 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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],
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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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{
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"cell_type": "markdown",
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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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{
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"cell_type": "code",
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"execution_count": 3,
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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, False, True, False, True, True, True, False, False)"
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]
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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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"True"
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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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},
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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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"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",
|
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"\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 28 states, and 53 edges.\n",
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"output propositions are ('o0',)\n"
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]
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},
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"</g>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-631.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
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"<text text-anchor=\"start\" x=\"108\" y=\"-616.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
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"<!-- 0 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
|
|
"<title>0</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"333.33\" cy=\"-762.22\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"333.33\" y=\"-758.52\" font-family=\"Lato\" font-size=\"14.00\">0</text>\n",
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"<title>10</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"478.33,-826.22 448.16,-808.22 478.33,-790.22 508.49,-808.22 478.33,-826.22\"/>\n",
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"<text text-anchor=\"middle\" x=\"478.33\" y=\"-804.52\" font-family=\"Lato\" font-size=\"14.00\">10</text>\n",
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"</g>\n",
|
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"<!-- 0->10 -->\n",
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"<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=\"M338.49,-779.57C343.17,-794.86 352.44,-816.21 369.33,-826.22 396.12,-842.1 432.85,-830.29 455.82,-819.72\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"393.66\" y=\"-852.02\" font-family=\"Lato\" font-size=\"14.00\">i1</text>\n",
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"<text text-anchor=\"start\" x=\"391.66\" y=\"-837.02\" 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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"</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=\"M336,-744.36C339.68,-709.53 349.72,-634.61 369.33,-619.22 392.84,-600.77 428.9,-606.83 452.79,-614.04\"/>\n",
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"<g id=\"edge32\" class=\"edge\">\n",
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"<title>10->0</title>\n",
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"<text text-anchor=\"start\" x=\"391.16\" y=\"-811.02\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
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"<!-- 1 -->\n",
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"<title>1</title>\n",
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"<text text-anchor=\"middle\" x=\"583.66\" y=\"-658.52\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 12 -->\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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"</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=\"715.99,-523.22 685.82,-505.22 715.99,-487.22 746.16,-505.22 715.99,-523.22\"/>\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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"<text text-anchor=\"start\" x=\"635.66\" y=\"-525.02\" font-family=\"Lato\" font-size=\"14.00\">!i1</text>\n",
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"</g>\n",
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"<!-- 12->0 -->\n",
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"<g id=\"edge34\" class=\"edge\">\n",
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"<title>12->0</title>\n",
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"</g>\n",
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"<!-- 13->1 -->\n",
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"<g id=\"edge35\" class=\"edge\">\n",
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"<title>13->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M714.16,-522.35C711.79,-551.44 702.68,-610.42 667.66,-642.22 659.12,-649.98 630.28,-655.7 608.98,-658.99\"/>\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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"<text text-anchor=\"middle\" x=\"817.32\" y=\"-600.52\" font-family=\"Lato\" font-size=\"14.00\">2</text>\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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"</g>\n",
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"<g id=\"node11\" class=\"node\">\n",
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"</g>\n",
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"<!-- 2->15 -->\n",
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"<g id=\"edge7\" class=\"edge\">\n",
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"<title>2->15</title>\n",
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"</g>\n",
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"<g id=\"edge36\" class=\"edge\">\n",
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"<title>15->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M936.81,-588.82C927.79,-596.13 914.69,-605.24 901.32,-609.22 882.01,-614.99 859.07,-612.97 842.21,-609.96\"/>\n",
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"</g>\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=\"583.66\" y=\"-870.52\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
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"</g>\n",
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"<g id=\"edge8\" class=\"edge\">\n",
|
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"<title>3->12</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M597.22,-862.16C603.58,-856.5 611.64,-849.97 619.66,-845.22 639.4,-833.54 651.17,-842.18 667.66,-826.22 691.98,-802.69 704.56,-764.56 710.47,-740.21\"/>\n",
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"</g>\n",
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"</g>\n",
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"<!-- 3->16 -->\n",
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"<g id=\"edge9\" class=\"edge\">\n",
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"<title>3->16</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M601.26,-878.52C618.3,-882.18 645.39,-885.87 667.66,-879.22 678.31,-876.05 688.79,-869.62 697.17,-863.44\"/>\n",
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"</g>\n",
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"<!-- 16->2 -->\n",
|
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"<g id=\"edge37\" class=\"edge\">\n",
|
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"<title>16->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M722.76,-834.05C739.25,-793.54 786.7,-676.99 806.96,-627.21\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"809.64,-620.64 809.92,-628.31 808.32,-623.89 807,-627.13 807,-627.13 807,-627.13 808.32,-623.89 804.08,-625.94 809.64,-620.64 809.64,-620.64\"/>\n",
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"</g>\n",
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"<!-- 16->3 -->\n",
|
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"<g id=\"edge38\" class=\"edge\">\n",
|
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"<title>16->3</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M709.77,-862.55C702.93,-878.94 689.2,-904.97 667.66,-916.22 648.75,-926.1 638.98,-925.27 619.66,-916.22 610.48,-911.92 602.87,-903.9 597.11,-896.02\"/>\n",
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"<text text-anchor=\"start\" x=\"633.16\" y=\"-942.02\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
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"<text text-anchor=\"start\" x=\"635.66\" y=\"-927.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
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"<!-- 4 -->\n",
|
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"<g id=\"node14\" class=\"node\">\n",
|
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"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"817.32\" cy=\"-121.22\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"817.32\" y=\"-117.52\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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|
"</g>\n",
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|
"<!-- 4->14 -->\n",
|
|
"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>4->14</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M819.86,-139.05C823.53,-177.82 833.99,-268.2 853.32,-291.22 868.08,-308.79 884.83,-294.27 901.32,-310.22 914.37,-322.85 931.86,-369.68 941.51,-397.68\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"943.79,-404.36 938.55,-398.75 942.66,-401.05 941.53,-397.73 941.53,-397.73 941.53,-397.73 942.66,-401.05 944.51,-396.72 943.79,-404.36 943.79,-404.36\"/>\n",
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"<text text-anchor=\"start\" x=\"871.32\" y=\"-329.02\" font-family=\"Lato\" font-size=\"14.00\">i0</text>\n",
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"<text text-anchor=\"start\" x=\"869.32\" y=\"-314.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 17 -->\n",
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"<g id=\"node15\" class=\"node\">\n",
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"<title>17</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"949.65,-172.22 919.49,-154.22 949.65,-136.22 979.82,-154.22 949.65,-172.22\"/>\n",
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"<text text-anchor=\"middle\" x=\"949.65\" y=\"-150.52\" font-family=\"Lato\" font-size=\"14.00\">17</text>\n",
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|
"</g>\n",
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"<!-- 4->17 -->\n",
|
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"<g id=\"edge11\" class=\"edge\">\n",
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"<title>4->17</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M834.63,-126.64C840.49,-128.51 847.18,-130.55 853.32,-132.22 875.56,-138.27 901,-144.09 920,-148.22\"/>\n",
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"<text text-anchor=\"start\" x=\"869.32\" y=\"-163.02\" font-family=\"Lato\" font-size=\"14.00\">!i0</text>\n",
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"</g>\n",
|
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"<!-- 17->4 -->\n",
|
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"<g id=\"edge39\" class=\"edge\">\n",
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"<title>17->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M941.76,-140.63C934.01,-127.02 920.03,-106.91 901.32,-98.22 881.97,-89.24 873.76,-92.11 853.32,-98.22 847.84,-99.86 842.41,-102.67 837.53,-105.77\"/>\n",
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"<text text-anchor=\"start\" x=\"872.82\" y=\"-117.02\" font-family=\"Lato\" font-size=\"14.00\">1</text>\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=\"817.32\" cy=\"-366.22\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"817.32\" y=\"-362.52\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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"</g>\n",
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"<!-- 5->14 -->\n",
|
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"<g id=\"edge12\" class=\"edge\">\n",
|
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"<title>5->14</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M830.13,-379.4C836.43,-385.67 844.66,-392.76 853.32,-397.22 872.87,-407.3 897.03,-412.81 916.13,-415.79\"/>\n",
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"<text text-anchor=\"start\" x=\"857.32\" y=\"-431.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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"</g>\n",
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"<!-- 5->15 -->\n",
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"<g id=\"edge13\" class=\"edge\">\n",
|
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"<title>5->15</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M822.2,-383.85C826.89,-401.55 836.36,-428.67 853.32,-446.22 869.76,-463.24 884.91,-452.19 901.32,-469.22 924.8,-493.59 937.63,-531.48 943.81,-555.56\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"945.52,-562.56 940.8,-556.51 944.69,-559.16 943.86,-555.76 943.86,-555.76 943.86,-555.76 944.69,-559.16 946.92,-555.01 945.52,-562.56 945.52,-562.56\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"855.32\" y=\"-488.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"869.32\" y=\"-473.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->17 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
|
"<title>5->17</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M818.62,-347.94C819.94,-318.54 826.08,-260.01 853.32,-220.22 863.03,-206.04 902.2,-181.42 927.21,-166.59\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"933.54,-162.86 929.1,-169.13 930.52,-164.64 927.51,-166.41 927.51,-166.41 927.51,-166.41 930.52,-164.64 925.91,-163.7 933.54,-162.86 933.54,-162.86\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"855.32\" y=\"-239.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"869.32\" y=\"-224.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 18 -->\n",
|
|
"<g id=\"node17\" class=\"node\">\n",
|
|
"<title>18</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"949.65,-331.22 919.49,-313.22 949.65,-295.22 979.82,-313.22 949.65,-331.22\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"949.65\" y=\"-309.52\" font-family=\"Lato\" font-size=\"14.00\">18</text>\n",
|
|
"</g>\n",
|
|
"<!-- 5->18 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
|
"<title>5->18</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M835.39,-363.36C852.56,-360.1 879.54,-353.94 901.32,-344.22 911.19,-339.82 921.31,-333.48 929.65,-327.68\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"935.65,-323.39 931.79,-330.03 932.8,-325.43 929.95,-327.47 929.95,-327.47 929.95,-327.47 932.8,-325.43 928.12,-324.9 935.65,-323.39 935.65,-323.39\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"853.32\" y=\"-378.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"869.32\" y=\"-363.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 18->5 -->\n",
|
|
"<g id=\"edge40\" class=\"edge\">\n",
|
|
"<title>18->5</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M941.21,-300.1C933.21,-287.46 919.19,-269.12 901.32,-261.22 881.81,-252.6 870.63,-248.75 853.32,-261.22 828.32,-279.25 820.91,-315.91 818.86,-340.77\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"818.38,-348.08 815.69,-340.89 818.61,-344.59 818.84,-341.09 818.84,-341.09 818.84,-341.09 818.61,-344.59 821.98,-341.3 818.38,-348.08 818.38,-348.08\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"872.82\" y=\"-280.02\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"869.32\" y=\"-265.02\" 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=\"333.33\" cy=\"-260.22\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"333.33\" y=\"-256.52\" 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=\"M334.89,-278.21C337.44,-355.65 348.64,-658.4 369.33,-695.22 385.64,-724.26 406.75,-715.36 429.99,-739.22 444.58,-754.2 457.73,-774.15 466.45,-788.75\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"470.13,-795.04 463.87,-790.59 468.36,-792.02 466.59,-789 466.59,-789 466.59,-789 468.36,-792.02 469.31,-787.41 470.13,-795.04 470.13,-795.04\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"379.66\" y=\"-758.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"391.66\" y=\"-743.02\" 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=\"M341.49,-276.48C357.85,-313.8 398.94,-408.61 429.99,-489.22 445.15,-528.58 461.17,-575.12 470.14,-601.7\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"472.48,-608.65 467.26,-603.02 471.36,-605.33 470.24,-602.02 470.24,-602.02 470.24,-602.02 471.36,-605.33 473.23,-601.01 472.48,-608.65 472.48,-608.65\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"377.66\" y=\"-508.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"391.66\" y=\"-493.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19 -->\n",
|
|
"<g id=\"node19\" class=\"node\">\n",
|
|
"<title>19</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"478.33,-127.22 448.16,-109.22 478.33,-91.22 508.49,-109.22 478.33,-127.22\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"478.33\" y=\"-105.52\" font-family=\"Lato\" font-size=\"14.00\">19</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->19 -->\n",
|
|
"<g id=\"edge18\" class=\"edge\">\n",
|
|
"<title>6->19</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M335.8,-242.34C339.18,-206.24 348.82,-126.65 369.33,-110.22 392.14,-91.95 427.21,-95.56 451.16,-101.18\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"458.2,-102.96 450.64,-104.3 454.81,-102.1 451.42,-101.24 451.42,-101.24 451.42,-101.24 454.81,-102.1 452.19,-98.19 458.2,-102.96 458.2,-102.96\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"377.66\" y=\"-129.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"391.66\" y=\"-114.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20 -->\n",
|
|
"<g id=\"node20\" class=\"node\">\n",
|
|
"<title>20</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"478.33,-225.22 448.16,-207.22 478.33,-189.22 508.49,-207.22 478.33,-225.22\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"478.33\" y=\"-203.52\" font-family=\"Lato\" font-size=\"14.00\">20</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->20 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
|
"<title>6->20</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M342.47,-244.41C348.48,-234.51 357.62,-222.48 369.33,-216.22 392.98,-203.58 423.79,-202.22 446.44,-203.51\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"453.49,-204.01 446.28,-206.66 450,-203.76 446.51,-203.51 446.51,-203.51 446.51,-203.51 450,-203.76 446.73,-200.37 453.49,-204.01 453.49,-204.01\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"375.66\" y=\"-235.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"391.66\" y=\"-220.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->4 -->\n",
|
|
"<g id=\"edge41\" class=\"edge\">\n",
|
|
"<title>19->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M485.9,-95.66C493.75,-80.74 508.15,-56.94 526.66,-42.22 577.46,-1.83 603.6,6.2 667.66,-4.22 720.23,-12.78 741.92,-6.38 781.32,-42.22 797.05,-56.53 806.09,-79.22 811.03,-96.61\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"812.9,-103.71 808.07,-97.74 812.01,-100.32 811.11,-96.94 811.11,-96.94 811.11,-96.94 812.01,-100.32 814.16,-96.13 812.9,-103.71 812.9,-103.71\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"633.16\" y=\"-23.02\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-8.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->6 -->\n",
|
|
"<g id=\"edge42\" class=\"edge\">\n",
|
|
"<title>19->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M463.96,-118.67C454.64,-125.08 441.8,-133.57 429.99,-140.22 403.95,-154.89 389.61,-147.28 369.33,-169.22 352.24,-187.71 343.19,-215.43 338.61,-235.42\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"337.12,-242.4 335.5,-234.9 337.85,-238.98 338.58,-235.56 338.58,-235.56 338.58,-235.56 337.85,-238.98 341.67,-236.22 337.12,-242.4 337.12,-242.4\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"391.16\" y=\"-188.02\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"391.66\" y=\"-173.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->4 -->\n",
|
|
"<g id=\"edge43\" class=\"edge\">\n",
|
|
"<title>20->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M487.48,-194.11C506.41,-165.08 556.59,-95.9 619.66,-70.22 681.47,-45.05 759.35,-84.96 795.78,-107.49\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"802.08,-111.47 794.48,-110.39 799.12,-109.6 796.16,-107.73 796.16,-107.73 796.16,-107.73 799.12,-109.6 797.85,-105.07 802.08,-111.47 802.08,-111.47\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"633.16\" y=\"-89.02\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-74.02\" 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=\"583.66\" cy=\"-211.22\" rx=\"18\" ry=\"18\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"583.66\" y=\"-207.52\" 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=\"M508.6,-207.2C520.7,-207.3 534.86,-207.58 547.66,-208.22 551.13,-208.4 554.79,-208.64 558.38,-208.92\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"565.58,-209.52 558.35,-212.08 562.1,-209.23 558.61,-208.94 558.61,-208.94 558.61,-208.94 562.1,-209.23 558.87,-205.8 565.58,-209.52 565.58,-209.52\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"528.66\" y=\"-227.02\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"529.16\" y=\"-212.02\" 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=\"M585.53,-229.4C588.77,-294.24 600.97,-511.67 619.66,-536.22 633.55,-554.48 652.2,-538.27 667.66,-555.22 702.89,-593.88 712,-657.39 714.29,-692.3\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"714.7,-699.71 711.17,-692.89 714.51,-696.21 714.31,-692.72 714.31,-692.72 714.31,-692.72 714.51,-696.21 717.46,-692.54 714.7,-699.71 714.7,-699.71\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"623.66\" y=\"-574.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-559.02\" 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=\"M586.31,-229.2C590.15,-267.38 600.81,-354.88 619.66,-377.22 634.45,-394.76 651.17,-380.27 667.66,-396.22 691.98,-419.76 704.56,-457.88 710.47,-482.24\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"712.09,-489.33 707.46,-483.21 711.31,-485.91 710.53,-482.5 710.53,-482.5 710.53,-482.5 711.31,-485.91 713.6,-481.8 712.09,-489.33 712.09,-489.33\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"621.66\" y=\"-415.02\" font-family=\"Lato\" font-size=\"14.00\">i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-400.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21 -->\n",
|
|
"<g id=\"node22\" class=\"node\">\n",
|
|
"<title>21</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"715.99,-260.22 685.82,-242.22 715.99,-224.22 746.16,-242.22 715.99,-260.22\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"715.99\" y=\"-238.52\" font-family=\"Lato\" font-size=\"14.00\">21</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->21 -->\n",
|
|
"<g id=\"edge22\" class=\"edge\">\n",
|
|
"<title>7->21</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M601.88,-210.09C618.93,-209.47 645.61,-209.85 667.66,-216.22 677.42,-219.04 687.4,-224.14 695.66,-229.07\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"701.61,-232.77 694.01,-231.75 698.64,-230.92 695.67,-229.08 695.67,-229.08 695.67,-229.08 698.64,-230.92 697.33,-226.4 701.61,-232.77 701.61,-232.77\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"621.66\" y=\"-235.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-220.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 22 -->\n",
|
|
"<g id=\"node23\" class=\"node\">\n",
|
|
"<title>22</title>\n",
|
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"715.99,-139.22 685.82,-121.22 715.99,-103.22 746.16,-121.22 715.99,-139.22\"/>\n",
|
|
"<text text-anchor=\"middle\" x=\"715.99\" y=\"-117.52\" font-family=\"Lato\" font-size=\"14.00\">22</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->22 -->\n",
|
|
"<g id=\"edge23\" class=\"edge\">\n",
|
|
"<title>7->22</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M596.23,-198.08C602.73,-191.12 611.2,-182.71 619.66,-176.22 642.81,-158.46 672.27,-142.32 692.27,-132.18\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"698.67,-128.98 693.82,-134.93 695.54,-130.55 692.41,-132.11 692.41,-132.11 692.41,-132.11 695.54,-130.55 691,-129.3 698.67,-128.98 698.67,-128.98\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"619.66\" y=\"-195.02\" font-family=\"Lato\" font-size=\"14.00\">!i0 & !i1</text>\n",
|
|
"<text text-anchor=\"start\" x=\"635.66\" y=\"-180.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21->4 -->\n",
|
|
"<g id=\"edge45\" class=\"edge\">\n",
|
|
"<title>21->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M726.88,-230.18C744.14,-209.15 779.91,-165.58 800.6,-140.37\"/>\n",
|
|
"<polygon fill=\"black\" stroke=\"black\" points=\"805.27,-134.69 803.26,-142.09 803.05,-137.39 800.83,-140.1 800.83,-140.1 800.83,-140.1 803.05,-137.39 798.39,-138.1 805.27,-134.69 805.27,-134.69\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"764.32\" y=\"-201.02\" font-family=\"Lato\" font-size=\"14.00\">o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"764.82\" y=\"-186.02\" 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=\"M689.46,-244.58C682.4,-245.18 674.74,-245.78 667.66,-246.22 552,-253.54 413.51,-257.97 358.53,-259.56\"/>\n",
|
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"<polygon fill=\"black\" stroke=\"black\" points=\"351.34,-259.76 358.25,-256.41 354.84,-259.66 358.34,-259.56 358.34,-259.56 358.34,-259.56 354.84,-259.66 358.43,-262.71 351.34,-259.76 351.34,-259.76\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"526.66\" y=\"-273.02\" font-family=\"Lato\" font-size=\"14.00\">!o0</text>\n",
|
|
"<text text-anchor=\"start\" x=\"529.16\" y=\"-258.02\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 22->4 -->\n",
|
|
"<g id=\"edge47\" class=\"edge\">\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 0x7f7249801c30> >"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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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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{
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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",
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"output_type": "stream",
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"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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"<text text-anchor=\"start\" x=\"92\" y=\"-385.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 27 -->\n",
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"<g id=\"node29\" class=\"node\">\n",
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"<title>27</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"235,-409.88 204.83,-391.88 235,-373.88 265.16,-391.88 235,-409.88\"/>\n",
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"</g>\n",
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"<!-- 9->27 -->\n",
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"<g id=\"edge31\" class=\"edge\">\n",
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"<title>9->27</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M73.65,-437.17C104.31,-428.51 169.93,-409.98 207.02,-399.5\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"214.04,-397.52 208.16,-402.45 210.67,-398.47 207.3,-399.42 207.3,-399.42 207.3,-399.42 210.67,-398.47 206.45,-396.39 214.04,-397.52 214.04,-397.52\"/>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-435.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 0 -->\n",
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"<g id=\"node3\" class=\"node\">\n",
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"<title>0</title>\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=\"#33a02c\" stroke-width=\"2\" points=\"446.33,-613.88 416.16,-595.88 446.33,-577.88 476.49,-595.88 446.33,-613.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"446.33\" y=\"-592.18\" font-family=\"Lato\" font-size=\"14.00\">10</text>\n",
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"</g>\n",
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"<!-- 0->10 -->\n",
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"<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=\"M309.12,-566.33C314.8,-577.75 324.13,-592.09 337.33,-598.88 362.61,-611.89 395.82,-608.44 418.7,-603.46\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"425.75,-601.81 419.65,-606.47 422.34,-602.61 418.93,-603.41 418.93,-603.41 418.93,-603.41 422.34,-602.61 418.21,-600.34 425.75,-601.81 425.75,-601.81\"/>\n",
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-611.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 11 -->\n",
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"<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=\"446.33,-458.88 416.16,-440.88 446.33,-422.88 476.49,-440.88 446.33,-458.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"446.33\" y=\"-437.18\" 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=\"M301.88,-531.71C302.36,-505.77 307.57,-458.81 337.33,-436.88 361.14,-419.32 396.6,-424.91 420.31,-431.79\"/>\n",
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-440.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 10->0 -->\n",
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"<g id=\"edge32\" class=\"edge\">\n",
|
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"<title>10->0</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M426.47,-589.4C417.81,-586.45 407.4,-582.94 397.99,-579.88 371.13,-571.13 364.29,-569.34 337.33,-560.88 333.53,-559.69 329.5,-558.42 325.58,-557.19\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"318.71,-555.03 326.33,-554.12 322.2,-555.6 325.54,-556.65 325.39,-557.13 325.24,-557.61 321.9,-556.56 324.44,-560.13 318.71,-555.03 318.71,-555.03\"/>\n",
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-583.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
|
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"<!-- 1 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
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"<title>1</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"546.66\" cy=\"-467.88\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"546.66\" y=\"-464.18\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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"<!-- 11->1 -->\n",
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"<g id=\"edge33\" class=\"edge\">\n",
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"<title>11->1</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M467.7,-446.47C483.65,-450.85 505.84,-456.94 522.46,-461.51\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"529.22,-463.36 521.63,-464.55 525.71,-462.92 522.33,-461.99 522.47,-461.51 522.6,-461.03 525.97,-461.95 523.3,-458.47 529.22,-463.36 529.22,-463.36\"/>\n",
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"<text text-anchor=\"start\" x=\"494.66\" y=\"-460.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\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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"<title>12</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"646.99,-537.88 616.82,-519.88 646.99,-501.88 677.16,-519.88 646.99,-537.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"646.99\" y=\"-516.18\" font-family=\"Lato\" font-size=\"14.00\">12</text>\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=\"M560.07,-480.53C566.39,-486.43 574.47,-493.17 582.66,-497.88 593.69,-504.22 606.85,-509.15 618.3,-512.73\"/>\n",
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-508.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 13 -->\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=\"#33a02c\" stroke-width=\"2\" points=\"646.99,-385.88 616.82,-367.88 646.99,-349.88 677.16,-367.88 646.99,-385.88\"/>\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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"<path fill=\"none\" stroke=\"black\" d=\"M548.2,-449.61C549.99,-426.48 556.9,-387.4 582.66,-368.88 592.79,-361.59 606.38,-360.57 618.37,-361.69\"/>\n",
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-372.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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"<!-- 12->0 -->\n",
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"<g id=\"edge34\" class=\"edge\">\n",
|
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"<title>12->0</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M620.35,-522.12C556.13,-527.72 389.06,-542.31 326.47,-547.77\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"319.37,-548.39 326.07,-544.64 322.81,-547.59 326.3,-547.28 326.34,-547.78 326.39,-548.28 322.9,-548.58 326.62,-550.92 319.37,-548.39 319.37,-548.39\"/>\n",
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"<text text-anchor=\"start\" x=\"494.66\" y=\"-535.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
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"<!-- 13->1 -->\n",
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"<g id=\"edge35\" class=\"edge\">\n",
|
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"<title>13->1</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M642.61,-383.44C637.19,-404.41 624.43,-441.26 598.66,-459.88 590.98,-465.43 580.94,-467.76 571.8,-468.58\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"564.73,-468.95 571.56,-465.44 568.2,-468.27 571.7,-468.09 571.72,-468.59 571.75,-469.08 568.25,-469.27 571.89,-471.73 564.73,-468.95 564.73,-468.95\"/>\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=\"#e31a1c\" stroke-width=\"2\" cx=\"747.32\" cy=\"-438.88\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"747.32\" y=\"-435.18\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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"</g>\n",
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"<!-- 14 -->\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=\"#e31a1c\" stroke-width=\"2\" points=\"847.65,-323.88 817.49,-305.88 847.65,-287.88 877.82,-305.88 847.65,-323.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"847.65\" y=\"-302.18\" font-family=\"Lato\" font-size=\"14.00\">14</text>\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=\"#e31a1c\" stroke-width=\"2\" d=\"M758.85,-424.64C776.9,-400.22 813.74,-350.39 833.48,-323.7\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"837.65,-318.06 836.02,-325.56 835.97,-321.17 833.89,-323.99 833.48,-323.69 833.08,-323.39 835.16,-320.58 830.95,-321.82 837.65,-318.06 837.65,-318.06\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-391.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
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"<!-- 15 -->\n",
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"<g id=\"node11\" class=\"node\">\n",
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"<title>15</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"847.65,-437.88 817.49,-419.88 847.65,-401.88 877.82,-419.88 847.65,-437.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"847.65\" y=\"-416.18\" font-family=\"Lato\" font-size=\"14.00\">15</text>\n",
|
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"</g>\n",
|
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"<!-- 2->15 -->\n",
|
|
"<g id=\"edge7\" class=\"edge\">\n",
|
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"<title>2->15</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M763.05,-429.39C769.09,-426.03 776.3,-422.64 783.32,-420.88 793.11,-418.43 804.01,-417.6 813.98,-417.56\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"821.04,-417.65 814,-420.71 817.54,-417.6 814.04,-417.56 814.04,-417.56 814.04,-417.56 817.54,-417.6 814.08,-414.41 821.04,-417.65 821.04,-417.65\"/>\n",
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|
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"</g>\n",
|
|
"<!-- 15->2 -->\n",
|
|
"<g id=\"edge36\" class=\"edge\">\n",
|
|
"<title>15->2</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M828.98,-427.11C820.21,-430.37 809.37,-433.92 799.32,-435.88 790.7,-437.56 781.12,-438.39 772.61,-438.77\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"765.46,-439.01 772.36,-435.63 768.96,-438.89 772.46,-438.78 772.46,-438.78 772.46,-438.78 768.96,-438.89 772.56,-441.92 765.46,-439.01 765.46,-439.01\"/>\n",
|
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-441.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
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"</g>\n",
|
|
"<!-- 3 -->\n",
|
|
"<g id=\"node12\" class=\"node\">\n",
|
|
"<title>3</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"546.66\" cy=\"-639.88\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"546.66\" y=\"-636.18\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
|
|
"</g>\n",
|
|
"<!-- 3->12 -->\n",
|
|
"<g id=\"edge8\" class=\"edge\">\n",
|
|
"<title>3->12</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M562.23,-630.28C573.12,-622.64 587.91,-611.21 598.66,-598.88 614.42,-580.79 627.97,-556.76 636.48,-539.97\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"639.6,-533.7 639.3,-541.37 638.04,-536.83 636.48,-539.96 636.48,-539.96 636.48,-539.96 638.04,-536.83 633.66,-538.56 639.6,-533.7 639.6,-533.7\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-617.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
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"<!-- 16 -->\n",
|
|
"<g id=\"node13\" class=\"node\">\n",
|
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"<title>16</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"646.99,-638.88 616.82,-620.88 646.99,-602.88 677.16,-620.88 646.99,-638.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"646.99\" y=\"-617.18\" font-family=\"Lato\" font-size=\"14.00\">16</text>\n",
|
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"</g>\n",
|
|
"<!-- 3->16 -->\n",
|
|
"<g id=\"edge9\" class=\"edge\">\n",
|
|
"<title>3->16</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M564.8,-640.01C574.76,-639.8 587.51,-639.05 598.66,-636.88 606.19,-635.41 614.17,-633.05 621.39,-630.58\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-642.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
|
"<!-- 16->2 -->\n",
|
|
"<g id=\"edge37\" class=\"edge\">\n",
|
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"<title>16->2</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M655.22,-607.5C672.08,-576.3 714.1,-498.52 734.64,-460.5\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"737.98,-454.31 737.43,-461.97 736.32,-457.39 734.66,-460.47 734.66,-460.47 734.66,-460.47 736.32,-457.39 731.88,-458.97 737.98,-454.31 737.98,-454.31\"/>\n",
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"<text text-anchor=\"start\" x=\"695.32\" y=\"-533.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
|
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"<!-- 16->3 -->\n",
|
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"<g id=\"edge38\" class=\"edge\">\n",
|
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"<title>16->3</title>\n",
|
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M635.62,-632.39C626.79,-641.27 613.25,-652.85 598.66,-657.88 588.66,-661.32 577.58,-658.25 568.31,-653.73\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"561.93,-650.25 569.58,-650.83 565.24,-651.49 568.31,-653.16 568.08,-653.6 567.84,-654.04 564.76,-652.37 566.57,-656.37 561.93,-650.25 561.93,-650.25\"/>\n",
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-662.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 4 -->\n",
|
|
"<g id=\"node14\" class=\"node\">\n",
|
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"<title>4</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"747.32\" cy=\"-92.88\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"747.32\" y=\"-89.18\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
|
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"<!-- 4->14 -->\n",
|
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"<g id=\"edge10\" class=\"edge\">\n",
|
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"<title>4->14</title>\n",
|
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"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M751.38,-110.49C755.93,-133.83 765.89,-175.79 783.32,-207.88 788.59,-217.58 792.91,-217.89 799.32,-226.88 813.14,-246.24 826.88,-269.77 835.97,-286.09\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"839.56,-292.61 833.42,-288 837.44,-289.79 835.74,-286.72 836.18,-286.48 836.62,-286.24 838.31,-289.31 838.94,-284.96 839.56,-292.61 839.56,-292.61\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-230.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 17 -->\n",
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"<g id=\"node15\" class=\"node\">\n",
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"<title>17</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"847.65,-133.88 817.49,-115.88 847.65,-97.88 877.82,-115.88 847.65,-133.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"847.65\" y=\"-112.18\" font-family=\"Lato\" font-size=\"14.00\">17</text>\n",
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"</g>\n",
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"<!-- 4->17 -->\n",
|
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"<g id=\"edge11\" class=\"edge\">\n",
|
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"<title>4->17</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M765,-96.78C779.58,-100.19 801.05,-105.21 818.31,-109.25\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"825.42,-110.91 817.89,-112.39 822.02,-110.12 818.61,-109.32 818.61,-109.32 818.61,-109.32 822.02,-110.12 819.32,-106.25 825.42,-110.91 825.42,-110.91\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-108.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
|
"<!-- 17->4 -->\n",
|
|
"<g id=\"edge39\" class=\"edge\">\n",
|
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"<title>17->4</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M835.3,-104.94C826.34,-97.1 813.08,-87.2 799.32,-82.88 790.22,-80.02 779.94,-81.23 771,-83.63\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-86.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\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=\"#e31a1c\" stroke-width=\"2\" cx=\"747.32\" cy=\"-267.88\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"747.32\" y=\"-264.18\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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"</g>\n",
|
|
"<!-- 5->14 -->\n",
|
|
"<g id=\"edge12\" class=\"edge\">\n",
|
|
"<title>5->14</title>\n",
|
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"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M763.87,-275.37C769.89,-278.17 776.87,-281.29 783.32,-283.88 795.49,-288.76 809.21,-293.6 820.76,-297.5\"/>\n",
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"827.64,-299.79 820,-300.57 824.16,-299.16 820.84,-298.05 821,-297.58 821.16,-297.1 824.48,-298.21 821.99,-294.59 827.64,-299.79 827.64,-299.79\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-293.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 5->15 -->\n",
|
|
"<g id=\"edge13\" class=\"edge\">\n",
|
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"<title>5->15</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M757.93,-282.73C775.89,-310.49 814.51,-370.19 834.34,-400.85\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"838.28,-406.93 831.83,-402.76 836.38,-403.99 834.48,-401.05 834.48,-401.05 834.48,-401.05 836.38,-403.99 837.12,-399.34 838.28,-406.93 838.28,-406.93\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-347.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
|
"<!-- 5->17 -->\n",
|
|
"<g id=\"edge14\" class=\"edge\">\n",
|
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"<title>5->17</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M751.86,-250.17C756.56,-229.71 766.31,-195.69 783.32,-170.88 794.82,-154.11 812.61,-139.27 826.42,-129.25\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"832.44,-124.99 828.54,-131.6 829.58,-127.01 826.72,-129.03 826.72,-129.03 826.72,-129.03 829.58,-127.01 824.91,-126.46 832.44,-124.99 832.44,-124.99\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-174.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 18 -->\n",
|
|
"<g id=\"node17\" class=\"node\">\n",
|
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"<title>18</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"847.65,-239.88 817.49,-221.88 847.65,-203.88 877.82,-221.88 847.65,-239.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"847.65\" y=\"-218.18\" font-family=\"Lato\" font-size=\"14.00\">18</text>\n",
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"</g>\n",
|
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"<!-- 5->18 -->\n",
|
|
"<g id=\"edge15\" class=\"edge\">\n",
|
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"<title>5->18</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M764.51,-261.2C774.6,-256.96 787.8,-251.28 799.32,-245.88 807.66,-241.97 816.71,-237.45 824.64,-233.4\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"831,-230.12 826.22,-236.13 827.89,-231.73 824.77,-233.33 824.77,-233.33 824.77,-233.33 827.89,-231.73 823.33,-230.53 831,-230.12 831,-230.12\"/>\n",
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"</g>\n",
|
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"<!-- 18->5 -->\n",
|
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"<g id=\"edge40\" class=\"edge\">\n",
|
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"<title>18->5</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M835.89,-210.52C822.9,-198.25 800.66,-181.83 783.32,-192.88 766.14,-203.82 757.26,-225.64 752.75,-242.94\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"751.07,-250.03 749.62,-242.49 751.88,-246.62 752.68,-243.21 752.68,-243.21 752.68,-243.21 751.88,-246.62 755.75,-243.94 751.07,-250.03 751.07,-250.03\"/>\n",
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"<text text-anchor=\"start\" x=\"783.32\" y=\"-196.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
|
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"<!-- 6 -->\n",
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"<g id=\"node18\" class=\"node\">\n",
|
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"<title>6</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"301.33\" cy=\"-182.88\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"301.33\" y=\"-179.18\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
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"</g>\n",
|
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"<!-- 6->10 -->\n",
|
|
"<g id=\"edge16\" class=\"edge\">\n",
|
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"<title>6->10</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M302.45,-201.01C303.13,-260.19 307.65,-446.87 337.33,-497.88 354.08,-526.67 373.38,-519.44 397.99,-541.88 410.12,-552.93 422.29,-566.9 431.25,-577.85\"/>\n",
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"</g>\n",
|
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"<!-- 6->11 -->\n",
|
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"<g id=\"edge17\" class=\"edge\">\n",
|
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"<title>6->11</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M312.09,-197.83C330.01,-225.53 368.99,-286.93 397.99,-340.88 412.46,-367.78 427.21,-399.85 436.32,-420.28\"/>\n",
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"</g>\n",
|
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"<!-- 19 -->\n",
|
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"<g id=\"node19\" class=\"node\">\n",
|
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"<title>19</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"446.33,-94.88 416.16,-76.88 446.33,-58.88 476.49,-76.88 446.33,-94.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"446.33\" y=\"-73.18\" font-family=\"Lato\" font-size=\"14.00\">19</text>\n",
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"</g>\n",
|
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"<!-- 6->19 -->\n",
|
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"<g id=\"edge18\" class=\"edge\">\n",
|
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"<title>6->19</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M302.41,-164.77C303.63,-140.43 309.83,-97.89 337.33,-77.88 360.82,-60.78 395.45,-64.02 419.12,-69.23\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-81.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
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"<!-- 20 -->\n",
|
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"<g id=\"node20\" class=\"node\">\n",
|
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"<title>20</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"446.33,-154.88 416.16,-136.88 446.33,-118.88 476.49,-136.88 446.33,-154.88\"/>\n",
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"<text text-anchor=\"middle\" x=\"446.33\" y=\"-133.18\" font-family=\"Lato\" font-size=\"14.00\">20</text>\n",
|
|
"</g>\n",
|
|
"<!-- 6->20 -->\n",
|
|
"<g id=\"edge19\" class=\"edge\">\n",
|
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"<title>6->20</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M314.48,-170.02C320.74,-164.17 328.84,-157.71 337.33,-153.88 360.02,-143.63 387.81,-139.43 409.52,-137.76\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"416.63,-137.28 409.86,-140.89 413.14,-137.51 409.65,-137.75 409.65,-137.75 409.65,-137.75 413.14,-137.51 409.44,-134.6 416.63,-137.28 416.63,-137.28\"/>\n",
|
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-157.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->4 -->\n",
|
|
"<g id=\"edge41\" class=\"edge\">\n",
|
|
"<title>19->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M455.57,-64.24C463.99,-52.33 478.15,-34.86 494.66,-24.88 535.16,-0.38 551.56,2.88 598.66,-1.88 649.5,-7.02 670.59,5.99 711.32,-24.88 725.51,-35.63 734.44,-53.77 739.72,-68.61\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"742.03,-75.58 736.84,-69.93 740.93,-72.26 739.83,-68.94 739.83,-68.94 739.83,-68.94 740.93,-72.26 742.82,-67.95 742.03,-75.58 742.03,-75.58\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-5.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 19->6 -->\n",
|
|
"<g id=\"edge42\" class=\"edge\">\n",
|
|
"<title>19->6</title>\n",
|
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M427.1,-83.55C398.2,-94.25 344.39,-114.66 337.33,-120.88 325.48,-131.31 316.74,-146.77 310.96,-159.64\"/>\n",
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|
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-124.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
|
|
"</g>\n",
|
|
"<!-- 20->4 -->\n",
|
|
"<g id=\"edge43\" class=\"edge\">\n",
|
|
"<title>20->4</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M461.48,-127.5C489.61,-109.69 555.13,-72.15 616.66,-65.88 643.48,-63.15 650.83,-60.88 677.32,-65.88 693.68,-68.97 711.14,-75.83 724.4,-81.87\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"730.92,-84.93 723.25,-84.81 727.75,-83.44 724.59,-81.96 724.59,-81.96 724.59,-81.96 727.75,-83.44 725.92,-79.1 730.92,-84.93 730.92,-84.93\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-76.68\" 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",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"546.66\" cy=\"-136.88\" rx=\"18\" ry=\"18\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"546.66\" y=\"-133.18\" 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=\"M476.56,-136.88C490.8,-136.88 507.71,-136.88 521.25,-136.88\"/>\n",
|
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"528.38,-136.88 521.38,-140.03 524.88,-137.38 521.38,-137.38 521.38,-136.88 521.38,-136.38 524.88,-136.38 521.38,-133.73 528.38,-136.88 528.38,-136.88\"/>\n",
|
|
"<text text-anchor=\"start\" x=\"494.66\" y=\"-140.68\" 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=\"M546.89,-155.18C545.82,-197.46 547.13,-304.4 582.66,-383.88 587.16,-393.96 592.96,-393.42 598.66,-402.88 617.39,-433.97 631.69,-473.81 639.46,-498.06\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"641.57,-504.76 636.47,-499.03 640.52,-501.43 639.47,-498.09 639.47,-498.09 639.47,-498.09 640.52,-501.43 642.48,-497.14 641.57,-504.76 641.57,-504.76\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-406.68\" 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=\"M550.49,-154.69C555.05,-180.78 565.31,-230.56 582.66,-269.88 584.51,-274.08 615.56,-321.56 633.48,-348.86\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"637.51,-355 631.04,-350.88 635.59,-352.07 633.67,-349.15 633.67,-349.15 633.67,-349.15 635.59,-352.07 636.3,-347.42 637.51,-355 637.51,-355\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-297.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
|
"</g>\n",
|
|
"<!-- 21 -->\n",
|
|
"<g id=\"node22\" class=\"node\">\n",
|
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"<title>21</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"646.99,-189.88 616.82,-171.88 646.99,-153.88 677.16,-171.88 646.99,-189.88\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"646.99\" y=\"-168.18\" font-family=\"Lato\" font-size=\"14.00\">21</text>\n",
|
|
"</g>\n",
|
|
"<!-- 7->21 -->\n",
|
|
"<g id=\"edge22\" class=\"edge\">\n",
|
|
"<title>7->21</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M564.25,-142.22C574.26,-145.48 587.23,-149.8 598.66,-153.88 605.99,-156.49 613.9,-159.45 621.13,-162.2\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"628.07,-164.86 620.41,-165.3 624.81,-163.61 621.54,-162.36 621.54,-162.36 621.54,-162.36 624.81,-163.61 622.67,-159.42 628.07,-164.86 628.07,-164.86\"/>\n",
|
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-157.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
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"<!-- 22 -->\n",
|
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"<g id=\"node23\" class=\"node\">\n",
|
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"<title>22</title>\n",
|
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"646.99,-110.88 616.82,-92.88 646.99,-74.88 677.16,-92.88 646.99,-110.88\"/>\n",
|
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"<text text-anchor=\"middle\" x=\"646.99\" y=\"-89.18\" font-family=\"Lato\" font-size=\"14.00\">22</text>\n",
|
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"</g>\n",
|
|
"<!-- 7->22 -->\n",
|
|
"<g id=\"edge23\" class=\"edge\">\n",
|
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"<title>7->22</title>\n",
|
|
"<path fill=\"none\" stroke=\"black\" d=\"M563.46,-129.81C579.51,-122.63 604.55,-111.42 622.84,-103.24\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"629.24,-100.37 624.14,-106.11 626.05,-101.8 622.85,-103.23 622.85,-103.23 622.85,-103.23 626.05,-101.8 621.57,-100.36 629.24,-100.37 629.24,-100.37\"/>\n",
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-124.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
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"</g>\n",
|
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"<!-- 21->4 -->\n",
|
|
"<g id=\"edge45\" class=\"edge\">\n",
|
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"<title>21->4</title>\n",
|
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"<path fill=\"none\" stroke=\"black\" d=\"M660.44,-161.87C677.28,-148.34 707.47,-124.09 727.2,-108.24\"/>\n",
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"<text text-anchor=\"start\" x=\"695.32\" y=\"-136.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
|
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"<!-- 21->6 -->\n",
|
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"<g id=\"edge46\" class=\"edge\">\n",
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"<title>21->6</title>\n",
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"</g>\n",
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"<!-- 22->4 -->\n",
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"<title>22->4</title>\n",
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"<text text-anchor=\"start\" x=\"695.32\" y=\"-96.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
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"</g>\n",
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"<!-- 22->7 -->\n",
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"<g id=\"edge48\" class=\"edge\">\n",
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"<title>22->7</title>\n",
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"</g>\n",
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"<!-- 8 -->\n",
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"<g id=\"node24\" class=\"node\">\n",
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"</g>\n",
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"<!-- 8->12 -->\n",
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"<g id=\"edge24\" class=\"edge\">\n",
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"<title>8->12</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M555.87,-377.62C562.56,-390 572.51,-407.49 582.66,-421.88 589.02,-430.9 592.24,-431.89 598.66,-440.88 612.47,-460.24 626.21,-483.77 635.3,-500.09\"/>\n",
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"</g>\n",
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"<!-- 8->16 -->\n",
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"<g id=\"edge25\" class=\"edge\">\n",
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"<title>8->16</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M551.45,-379.47C560.47,-421.34 582.48,-523.46 582.66,-523.88 595.19,-553.89 617.16,-584.69 631.65,-603.31\"/>\n",
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"<text text-anchor=\"start\" x=\"582.66\" y=\"-558.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
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"<!-- 8->21 -->\n",
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"<g id=\"edge26\" class=\"edge\">\n",
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"<title>8->21</title>\n",
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|
"</g>\n",
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"<!-- 23 -->\n",
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"<g id=\"node25\" class=\"node\">\n",
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"</g>\n",
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"<!-- 8->23 -->\n",
|
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"<g id=\"edge27\" class=\"edge\">\n",
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"<title>8->23</title>\n",
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"</g>\n",
|
|
"<!-- 23->5 -->\n",
|
|
"<g id=\"edge49\" class=\"edge\">\n",
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"<title>23->5</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M677.23,-267.88C691.46,-267.88 708.38,-267.88 721.91,-267.88\"/>\n",
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"</g>\n",
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"<!-- 23->8 -->\n",
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"<g id=\"edge50\" class=\"edge\">\n",
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"<title>23->8</title>\n",
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"</g>\n",
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"<!-- 24->0 -->\n",
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"<g id=\"edge51\" class=\"edge\">\n",
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"<title>24->0</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M180.63,-531.46C206.96,-535.51 249.62,-542.08 276.26,-546.18\"/>\n",
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"</g>\n",
|
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"<!-- 25->3 -->\n",
|
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"<g id=\"edge52\" class=\"edge\">\n",
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"<title>25->3</title>\n",
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"</g>\n",
|
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"<!-- 26->6 -->\n",
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"<g id=\"edge53\" class=\"edge\">\n",
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"<title>26->6</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M169.52,-292.65C194.47,-271.71 251.5,-223.85 281.34,-198.81\"/>\n",
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"</g>\n",
|
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"<!-- 27->8 -->\n",
|
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"<g id=\"edge54\" class=\"edge\">\n",
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"<title>27->8</title>\n",
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"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M261.34,-389.42C319.81,-383.76 463.56,-369.83 521.18,-364.25\"/>\n",
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"<text text-anchor=\"start\" x=\"359.66\" y=\"-384.68\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\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.jupyter.SVG object>"
|
|
]
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|
},
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"#Solve the game\n",
|
|
"print(\"Found a solution: \", spot.solve_game(game))\n",
|
|
"spot.highlight_strategy(game)\n",
|
|
"game.show('.g')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"minimization lvl 0\n"
|
|
]
|
|
},
|
|
{
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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=\"729pt\" height=\"302pt\"\n",
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" viewBox=\"0.00 0.00 729.00 302.14\" 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(0.8264462809917356 0.8264462809917356) rotate(0) translate(4 363)\">\n",
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"<!-- I -->\n",
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"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\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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"</g>\n",
|
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"<!-- 1 -->\n",
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"<title>1</title>\n",
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"</g>\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"<text text-anchor=\"start\" x=\"320\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\">i0 & i1</text>\n",
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|
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"<g id=\"node4\" class=\"node\">\n",
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|
"<title>2</title>\n",
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"<text text-anchor=\"middle\" x=\"340\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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"</g>\n",
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"<!-- 0->2 -->\n",
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|
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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=\"-223\" rx=\"18\" ry=\"18\"/>\n",
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"</g>\n",
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"<!-- 0->3 -->\n",
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"<g id=\"edge4\" class=\"edge\">\n",
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"<title>0->3</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M68.51,-121.48C85.81,-140.76 120.51,-175.79 158,-193 210.29,-217.01 278.92,-222.07 314.78,-222.97\"/>\n",
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"<!-- 4 -->\n",
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"<g id=\"node6\" class=\"node\">\n",
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"<title>4</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"180\" cy=\"-133\" rx=\"18\" ry=\"18\"/>\n",
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"</g>\n",
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"<!-- 0->4 -->\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>0->4</title>\n",
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"<g id=\"edge6\" class=\"edge\">\n",
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"<title>1->1</title>\n",
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"</g>\n",
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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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"# 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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"## 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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"text/plain": [
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"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f724981b2d0> >"
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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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"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": 12,
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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: 11\n",
|
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"Start: 0\n",
|
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"AP: 2 \"b\" \"a\"\n",
|
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"acc-name: parity max odd 3\n",
|
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"Acceptance: 3 Fin(2) & (Inf(1) | Fin(0))\n",
|
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"properties: trans-labels explicit-labels trans-acc colored complete\n",
|
|
"properties: deterministic\n",
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"spot-state-player: 0 1 1 0 0 0 1 1 1 0 1\n",
|
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"--BODY--\n",
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"State: 0\n",
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"[!1] 1 {1}\n",
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"[1] 2 {1}\n",
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"State: 1\n",
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"[!0] 3 {1}\n",
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"[0] 4 {1}\n",
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"State: 2\n",
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"[!0] 5 {1}\n",
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"[0] 4 {1}\n",
|
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"State: 3\n",
|
|
"[!1] 6 {1}\n",
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"[1] 7 {2}\n",
|
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"State: 4\n",
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"[t] 8 {2}\n",
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"State: 5\n",
|
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"[!1] 6 {1}\n",
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"[1] 7 {2}\n",
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"State: 6\n",
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"[t] 3 {1}\n",
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"State: 7\n",
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"[t] 5 {2}\n",
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"State: 8\n",
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"[!0] 9 {1}\n",
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"[0] 4 {2}\n",
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"State: 9\n",
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"[t] 10 {1}\n",
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"State: 10\n",
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"[t] 9 {1}\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": 13,
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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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"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": 14,
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"metadata": {},
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"outputs": [
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"text/plain": [
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]
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},
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"execution_count": 14,
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"metadata": {},
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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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"source": [
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"<h2>Reading an aiger-file</h2>\n",
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"\n",
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"<p>Read an aiger file. Note that we do not support the full \n",
|
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" <a href=\"http://fmv.jku.at/aiger/FORMAT.aiger\">syntax</a>, but are restricted to:\n",
|
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" <ul>\n",
|
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" <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",
|
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" <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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"name": "stdout",
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"text": [
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"2\n",
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|
"i0 a\n",
|
|
"i1 b\n",
|
|
"o0 c\n",
|
|
"o1 d\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"#aiger file \n",
|
|
"aag_txt = \"\"\"aag 5 2 0 2 3\n",
|
|
"2\n",
|
|
"4\n",
|
|
"10\n",
|
|
"6\n",
|
|
"6 2 4\n",
|
|
"8 3 5\n",
|
|
"10 7 9\n",
|
|
"i0 a\n",
|
|
"i1 b\n",
|
|
"o0 c\n",
|
|
"o1 d\n",
|
|
"\"\"\"\n",
|
|
"print(aag_txt)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"this_aig = spot.aiger_circuit(aag_txt)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
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"data": {
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"</g>\n",
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"<!-- 10 -->\n",
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"<g id=\"node5\" class=\"node\">\n",
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"<title>10</title>\n",
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"</g>\n",
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"<g id=\"edge5\" class=\"edge\">\n",
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"<title>6->10</title>\n",
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"<ellipse fill=\"black\" stroke=\"black\" cx=\"82.29\" cy=\"-155.79\" rx=\"4\" ry=\"4\"/>\n",
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"</g>\n",
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"<title>6->o1o1:s</title>\n",
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"<title>8->10</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M65.2,-118.34C65.2,-126.54 65.2,-136.58 65.2,-145.95\"/>\n",
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"<ellipse fill=\"black\" stroke=\"black\" cx=\"65.2\" cy=\"-149.95\" rx=\"4\" ry=\"4\"/>\n",
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"</g>\n",
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"<!-- o0o0 -->\n",
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"<title>o0o0</title>\n",
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"</g>\n",
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"<!-- 10->o0o0 -->\n",
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"<title>10->o0o0:s</title>\n",
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"</svg>\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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"metadata": {},
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"output_type": "display_data"
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}
|
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],
|
|
"source": [
|
|
"display(this_aig.show())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"aag 5 2 0 2 3\n",
|
|
"2\n",
|
|
"4\n",
|
|
"10\n",
|
|
"6\n",
|
|
"6 2 4\n",
|
|
"8 3 5\n",
|
|
"10 7 9\n",
|
|
"i0 i0\n",
|
|
"i1 i1\n",
|
|
"o0 o0\n",
|
|
"o1 o1\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(this_aig.to_str())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"((2, 4), (3, 5), (7, 9))\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(this_aig.gates())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h2>Verifying an implementation</h2>\n",
|
|
"\n",
|
|
"<p>\n",
|
|
" 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",
|
|
"</p>"
|
|
]
|
|
},
|
|
{
|
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"cell_type": "code",
|
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"execution_count": 20,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
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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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" \"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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" viewBox=\"0.00 0.00 535.00 115.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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"<text text-anchor=\"start\" x=\"252.5\" y=\"-76.8\" font-family=\"Lato\" font-size=\"14.00\">[all]</text>\n",
|
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"<!-- I -->\n",
|
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"<!-- 0 -->\n",
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"<g id=\"node2\" class=\"node\">\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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"</g>\n",
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"<!-- 0->0 -->\n",
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"<title>0->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M257.12,-35.04C255.82,-44.86 257.95,-54 263.5,-54 267.67,-54 269.9,-48.86 270.21,-42.14\"/>\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.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f72497abfc0> >"
|
|
]
|
|
},
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"metadata": {},
|
|
"output_type": "display_data"
|
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}
|
|
],
|
|
"source": [
|
|
"aigasmon = this_aig.as_automaton()\n",
|
|
"display(aigasmon)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
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"source": []
|
|
}
|
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],
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}
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