634dd28379
* spot/twa/twagraph.cc: Implement it. * spot/twa/twagraph.hh, NEWS: Document it. * tests/python/mergedge.py: Test it. * tests/core/ltlsynt.test, tests/python/games.ipynb: Adjust expectations.
1299 lines
77 KiB
Text
1299 lines
77 KiB
Text
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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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"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": "execute_result"
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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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"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, False, True, False, True, True, True, False, False)"
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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.get_state_players(game)"
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]
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},
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"cell_type": "code",
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"execution_count": 4,
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"1"
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]
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"metadata": {},
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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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"execution_count": 5,
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"# Solving a game\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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]
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"source": [
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]
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"source": [
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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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"## 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 0x7fa3979355d0> >"
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]
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},
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"execution_count": 8,
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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",
|
|
"\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": 9,
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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",
|
|
"acc-name: parity max odd 3\n",
|
|
"Acceptance: 3 Fin(2) & (Inf(1) | Fin(0))\n",
|
|
"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",
|
|
"[0] 4 {1}\n",
|
|
"State: 3\n",
|
|
"[!1] 6 {1}\n",
|
|
"[1] 7 {2}\n",
|
|
"State: 4\n",
|
|
"[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": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 10,
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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": 11,
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"metadata": {},
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"outputs": [
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{
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]
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