python: add some parity-game bindings
* python/spot/impl.i: Process game.hh. * spot/misc/game.cc, spot/misc/game.hh: Make the output of parity_game_solve() a solved_game object for easier manipulation in Python. * bin/ltlsynt.cc: Adjust usage. * tests/python/paritygame.ipynb: New file. * tests/Makefile.am, doc/org/tut.org: Add it. * NEWS: Mention these bindings.
This commit is contained in:
Alexandre Duret-Lutz
parent
9e8a842975
commit
760bde093b
8 changed files with 1040 additions and 16 deletions
5
NEWS
5
NEWS
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@ -79,6 +79,11 @@ New in spot 2.9.4.dev (not yet released)
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- print_dot() will display states from player 1 using a diamond
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- print_dot() will display states from player 1 using a diamond
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shape.
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shape.
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Python:
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- Bindings for functions related to parity games.
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See https://spot.lrde.epita.fr/ipynb/paritygame.html for examples.
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New in spot 2.9.4 (2020-09-07)
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New in spot 2.9.4 (2020-09-07)
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Bugs fixed:
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Bugs fixed:
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@ -216,11 +216,10 @@ namespace
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static spot::twa_graph_ptr
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static spot::twa_graph_ptr
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strat_to_aut(const spot::const_twa_graph_ptr& pg,
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strat_to_aut(const spot::const_twa_graph_ptr& pg,
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const spot::strategy_t& strat,
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const spot::strategy_t& strat,
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const spot::twa_graph_ptr& dpa,
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bdd all_outputs)
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bdd all_outputs)
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{
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{
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auto aut = spot::make_twa_graph(dpa->get_dict());
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auto aut = spot::make_twa_graph(pg->get_dict());
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aut->copy_ap_of(dpa);
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aut->copy_ap_of(pg);
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unsigned pg_init = pg->get_init_state_number();
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unsigned pg_init = pg->get_init_state_number();
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std::vector<unsigned> todo{pg_init};
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std::vector<unsigned> todo{pg_init};
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std::vector<int> pg2aut(pg->num_states(), -1);
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std::vector<int> pg2aut(pg->num_states(), -1);
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@ -230,10 +229,10 @@ namespace
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{
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{
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unsigned s = todo.back();
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unsigned s = todo.back();
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todo.pop_back();
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todo.pop_back();
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for (auto& e1: dpa->out(s))
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for (auto& e1: pg->out(s))
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{
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{
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unsigned i = 0;
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unsigned i = 0;
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for (auto& e2: dpa->out(e1.dst))
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for (auto& e2: pg->out(e1.dst))
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{
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{
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bool self_loop = false;
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bool self_loop = false;
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if (e1.dst == s || e2.dst == e1.dst)
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if (e1.dst == s || e2.dst == e1.dst)
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@ -520,18 +519,16 @@ namespace
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return 0;
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return 0;
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}
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}
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spot::strategy_t strategy[2];
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spot::region_t winning_region[2];
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if (want_time)
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if (want_time)
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sw.start();
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sw.start();
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parity_game_solve(dpa, winning_region, strategy);
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auto solution = parity_game_solve(dpa);
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if (want_time)
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if (want_time)
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solve_time = sw.stop();
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solve_time = sw.stop();
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if (verbose)
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if (verbose)
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std::cerr << "parity game solved in " << solve_time << " seconds\n";
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std::cerr << "parity game solved in " << solve_time << " seconds\n";
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nb_states_parity_game = dpa->num_states();
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nb_states_parity_game = dpa->num_states();
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timer.stop();
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timer.stop();
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if (winning_region[1].count(dpa->get_init_state_number()))
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if (solution.player_winning_at(1, dpa->get_init_state_number()))
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{
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{
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std::cout << "REALIZABLE\n";
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std::cout << "REALIZABLE\n";
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if (!opt_real)
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if (!opt_real)
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@ -539,7 +536,7 @@ namespace
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if (want_time)
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if (want_time)
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sw.start();
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sw.start();
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auto strat_aut =
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auto strat_aut =
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strat_to_aut(dpa, strategy[1], dpa, all_outputs);
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strat_to_aut(dpa, solution.winning_strategy[1], all_outputs);
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if (want_time)
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if (want_time)
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strat2aut_time = sw.stop();
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strat2aut_time = sw.stop();
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@ -72,6 +72,7 @@ real notebooks instead.
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automata
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automata
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- [[https://spot.lrde.epita.fr/ipynb/parity.html][=parity.ipynb=]] documents algorithms for manipulating parity automata
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- [[https://spot.lrde.epita.fr/ipynb/parity.html][=parity.ipynb=]] documents algorithms for manipulating parity automata
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in Python
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in Python
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- [[https://spot.lrde.epita.fr/ipynb/paritygame.html][=paritygame.ipynb=]] illustrates support for parity games
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- [[https://spot.lrde.epita.fr/ipynb/product.html][=product.ipynb=]] shows how to re-implement the product of two automata
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- [[https://spot.lrde.epita.fr/ipynb/product.html][=product.ipynb=]] shows how to re-implement the product of two automata
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in Python
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in Python
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- [[https://spot.lrde.epita.fr/ipynb/randltl.html][=randltl.ipynb=]] demonstrates a Python-version of [[file:randltl.org][=randltl=]]
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- [[https://spot.lrde.epita.fr/ipynb/randltl.html][=randltl.ipynb=]] demonstrates a Python-version of [[file:randltl.org][=randltl=]]
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@ -1,5 +1,5 @@
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// -*- coding: utf-8 -*-
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// -*- coding: utf-8 -*-
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// Copyright (C) 2009-2019 Laboratoire de Recherche et Développement
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// Copyright (C) 2009-2020 Laboratoire de Recherche et Développement
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// de l'Epita (LRDE).
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// de l'Epita (LRDE).
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// Copyright (C) 2003-2006 Laboratoire d'Informatique de Paris 6
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// Copyright (C) 2003-2006 Laboratoire d'Informatique de Paris 6
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// (LIP6), département Systèmes Répartis Coopératifs (SRC), Université
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// (LIP6), département Systèmes Répartis Coopératifs (SRC), Université
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@ -164,6 +164,8 @@
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#include <spot/parseaut/public.hh>
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#include <spot/parseaut/public.hh>
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#include <spot/misc/game.hh>
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#include <spot/kripke/fairkripke.hh>
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#include <spot/kripke/fairkripke.hh>
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#include <spot/kripke/kripke.hh>
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#include <spot/kripke/kripke.hh>
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#include <spot/kripke/kripkegraph.hh>
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#include <spot/kripke/kripkegraph.hh>
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@ -690,6 +692,8 @@ def state_is_accepting(self, src) -> "bool":
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%include <spot/twaalgos/complement.hh>
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%include <spot/twaalgos/complement.hh>
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%include <spot/misc/game.hh>
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%include <spot/kripke/fairkripke.hh>
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%include <spot/kripke/fairkripke.hh>
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%include <spot/kripke/kripke.hh>
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%include <spot/kripke/kripke.hh>
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%include <spot/kripke/kripkegraph.hh>
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%include <spot/kripke/kripkegraph.hh>
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@ -230,9 +230,11 @@ namespace spot
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}
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}
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}
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}
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void parity_game_solve(const const_twa_graph_ptr& arena,
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solved_game parity_game_solve(const const_twa_graph_ptr& arena)
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region_t (&w)[2], strategy_t (&s)[2])
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{
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{
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solved_game result;
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result.arena = arena;
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const std::vector<bool>* owner =
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const std::vector<bool>* owner =
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ensure_parity_game(arena, "parity_game_solve");
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ensure_parity_game(arena, "parity_game_solve");
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@ -245,7 +247,10 @@ namespace spot
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for (const auto& e: arena->edges())
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for (const auto& e: arena->edges())
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m |= e.acc;
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m |= e.acc;
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solve_rec(arena, owner, states_, m.max_set(), w, s);
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solve_rec(arena, owner, states_, m.max_set(),
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result.winning_region, result.winning_strategy);
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return result;
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}
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}
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void propagate_players(spot::twa_graph_ptr& arena,
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void propagate_players(spot::twa_graph_ptr& arena,
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@ -304,4 +309,44 @@ namespace spot
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arena->set_named_prop("state-player", owner);
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arena->set_named_prop("state-player", owner);
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}
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}
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twa_graph_ptr
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highlight_strategy(twa_graph_ptr& aut, const strategy_t& s,
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unsigned color)
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{
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unsigned ns = aut->num_states();
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auto* highlight = aut->get_or_set_named_prop<std::map<unsigned, unsigned>>
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("highlight-edges");
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for (auto [src, n]: s)
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{
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if (src >= ns)
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throw std::runtime_error
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("highlight_strategy(): strategy refers to unexisting states");
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unsigned int i = 0;
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for (auto& t: aut->out(src))
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if (i++ == n)
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{
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(*highlight)[aut->edge_number(t)] = color;
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break;
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}
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}
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return aut;
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}
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twa_graph_ptr
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solved_game::highlight_strategy(unsigned player, unsigned color)
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{
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auto aut = std::const_pointer_cast<twa_graph>(arena);
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auto* highlight = aut->get_or_set_named_prop<std::map<unsigned, unsigned>>
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("highlight-states");
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unsigned ns = aut->num_states();
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for (unsigned i = 0; i < ns; ++i)
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if (player_winning_at(player, i))
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(*highlight)[i] = color;
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return spot::highlight_strategy(aut, winning_strategy[!!player], color);
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}
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}
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}
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@ -50,6 +50,24 @@ namespace spot
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typedef std::unordered_set<unsigned> region_t;
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typedef std::unordered_set<unsigned> region_t;
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typedef std::unordered_map<unsigned, unsigned> strategy_t;
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typedef std::unordered_map<unsigned, unsigned> strategy_t;
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struct SPOT_API solved_game
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{
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const_twa_graph_ptr arena;
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region_t winning_region[2];
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strategy_t winning_strategy[2];
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/// \brief Highlight the edges of a strategy on the automaton.
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twa_graph_ptr highlight_strategy(unsigned player, unsigned color);
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bool player_winning_at(unsigned player, unsigned state)
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{
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auto& w = winning_region[player];
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return w.find(state) != w.end();
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}
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};
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/// \brief solve a parity-game
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/// \brief solve a parity-game
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///
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///
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/// The arena is a deterministic max odd parity automaton with a
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/// The arena is a deterministic max odd parity automaton with a
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/// game for player 1 using Zielonka's recursive algorithm.
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/// game for player 1 using Zielonka's recursive algorithm.
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/// \cite zielonka.98.tcs
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/// \cite zielonka.98.tcs
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SPOT_API
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SPOT_API
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void parity_game_solve(const const_twa_graph_ptr& arena,
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solved_game parity_game_solve(const const_twa_graph_ptr& arena);
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region_t (&w)[2], strategy_t (&s)[2]);
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/// \brief Print a max odd parity game using PG-solver syntax
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/// \brief Print a max odd parity game using PG-solver syntax
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SPOT_API
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SPOT_API
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void pg_print(std::ostream& os, const const_twa_graph_ptr& arena);
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void pg_print(std::ostream& os, const const_twa_graph_ptr& arena);
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/// \brief Highlight the edges of a strategy on an automaton.
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SPOT_API
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twa_graph_ptr highlight_strategy(twa_graph_ptr& arena,
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const strategy_t& s,
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unsigned color);
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}
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}
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@ -362,6 +362,7 @@ TESTS_ipython = \
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python/ltsmin-dve.ipynb \
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python/ltsmin-dve.ipynb \
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python/ltsmin-pml.ipynb \
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python/ltsmin-pml.ipynb \
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python/parity.ipynb \
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python/parity.ipynb \
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python/paritygame.ipynb \
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python/product.ipynb \
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python/product.ipynb \
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python/randaut.ipynb \
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python/randaut.ipynb \
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python/randltl.ipynb \
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python/randltl.ipynb \
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947
tests/python/paritygame.ipynb
Normal file
947
tests/python/paritygame.ipynb
Normal file
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@ -0,0 +1,947 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import spot\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 parity games\n",
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"\n",
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"The support for parity 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, a parity game is just a parity automaton with a property named `state-player` that stores the player owning each state. The players are named 0 and 1.\n",
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"\n",
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"Player 1 is winning if it has a strategy to satisfy the acceptance condition regardless of player 0's moves.\n",
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"Player 0 is winning if it has a strategy to not satisfy the acceptance codition regardless of player 1's moves."
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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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"## Input/Output\n",
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"\n",
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"An extension of the HOA format makes it possible to store the `state-player` property. This allows us to read the parity game constructed by `ltlsynt` using `spot.automaton()` like any other automaton."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": [
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"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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||||||
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" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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||||||
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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=\"567pt\" height=\"338pt\"\n",
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"<text text-anchor=\"start\" x=\"197.79\" y=\"-315.56\" font-family=\"Lato\" font-size=\"14.00\">Fin(</text>\n",
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"<text text-anchor=\"start\" x=\"220.79\" y=\"-315.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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||||||
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"<text text-anchor=\"start\" x=\"336.79\" y=\"-315.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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"<text text-anchor=\"start\" x=\"352.79\" y=\"-315.56\" font-family=\"Lato\" font-size=\"14.00\">))</text>\n",
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"<text text-anchor=\"start\" x=\"223.79\" y=\"-301.56\" font-family=\"Lato\" font-size=\"14.00\">[parity max odd 3]</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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"<title>0</title>\n",
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"</g>\n",
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|
"<!-- I->0 -->\n",
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"<title>I->0</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M1.15,-171.76C2.79,-171.76 17.15,-171.76 30.63,-171.76\"/>\n",
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|
"</g>\n",
|
||||||
|
"<!-- 1 -->\n",
|
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"<title>1</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"148.98,-163.76 126.02,-145.76 148.98,-127.76 171.94,-145.76 148.98,-163.76\"/>\n",
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"<text text-anchor=\"middle\" x=\"148.98\" y=\"-142.06\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
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"</g>\n",
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|
"<!-- 0->1 -->\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=\"94.5\" y=\"-165.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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"</g>\n",
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"<!-- 2 -->\n",
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"<text text-anchor=\"middle\" x=\"148.98\" y=\"-196.06\" font-family=\"Lato\" font-size=\"14.00\">2</text>\n",
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"</g>\n",
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|
"<!-- 0->2 -->\n",
|
||||||
|
"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M73.69,-176.89C88.1,-181.33 109.07,-187.78 125.05,-192.7\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"132.01,-194.84 124.39,-195.79 128.66,-193.81 125.32,-192.78 125.32,-192.78 125.32,-192.78 128.66,-193.81 126.24,-189.77 132.01,-194.84 132.01,-194.84\"/>\n",
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"</g>\n",
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||||||
|
"<!-- 3 -->\n",
|
||||||
|
"<g id=\"node5\" class=\"node\">\n",
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"<title>3</title>\n",
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"<text text-anchor=\"middle\" x=\"241.96\" y=\"-57.06\" font-family=\"Lato\" font-size=\"14.00\">3</text>\n",
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"</g>\n",
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|
"<!-- 1->3 -->\n",
|
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|
"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->3</title>\n",
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|
"<path fill=\"none\" stroke=\"black\" d=\"M160.06,-136.34C175.16,-122.24 203.86,-95.42 222.7,-77.82\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"228.21,-72.67 225.24,-79.75 225.65,-75.06 223.09,-77.45 223.09,-77.45 223.09,-77.45 225.65,-75.06 220.94,-75.15 228.21,-72.67 228.21,-72.67\"/>\n",
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"<text text-anchor=\"start\" x=\"191.96\" y=\"-126.56\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-111.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
||||||
|
"<!-- 4 -->\n",
|
||||||
|
"<g id=\"node6\" class=\"node\">\n",
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|
"<title>4</title>\n",
|
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"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"241.96\" cy=\"-182.76\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"241.96\" y=\"-179.06\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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|
"<!-- 1->4 -->\n",
|
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|
"<g id=\"edge5\" class=\"edge\">\n",
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"<title>1->4</title>\n",
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||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M170.91,-146.58C181.75,-147.62 194.98,-149.89 205.96,-154.76 212.12,-157.49 218.12,-161.58 223.37,-165.8\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"228.73,-170.36 221.36,-168.22 226.07,-168.09 223.4,-165.83 223.4,-165.83 223.4,-165.83 226.07,-168.09 225.44,-163.43 228.73,-170.36 228.73,-170.36\"/>\n",
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"<text text-anchor=\"start\" x=\"193.96\" y=\"-173.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-158.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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|
"</g>\n",
|
||||||
|
"<!-- 2->4 -->\n",
|
||||||
|
"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->4</title>\n",
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||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M167.95,-196.4C181.93,-193.79 201.45,-190.14 216.79,-187.27\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"223.94,-185.94 217.64,-190.32 220.5,-186.58 217.06,-187.22 217.06,-187.22 217.06,-187.22 220.5,-186.58 216.48,-184.13 223.94,-185.94 223.94,-185.94\"/>\n",
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"<text text-anchor=\"start\" x=\"193.96\" y=\"-210.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
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||||||
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-195.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 5 -->\n",
|
||||||
|
"<g id=\"node7\" class=\"node\">\n",
|
||||||
|
"<title>5</title>\n",
|
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|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"427.92\" cy=\"-140.76\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"427.92\" y=\"-137.06\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 2->5 -->\n",
|
||||||
|
"<g id=\"edge7\" class=\"edge\">\n",
|
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|
"<title>2->5</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M160.75,-208.85C168.39,-214.75 179.16,-222.01 189.96,-225.76 275.06,-255.28 319.26,-296.01 391.92,-242.76 413.34,-227.05 401.22,-210.86 409.92,-185.76 412.38,-178.66 415.21,-170.99 417.85,-164.03\"/>\n",
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||||||
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"<text text-anchor=\"start\" x=\"277.96\" y=\"-267.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 6 -->\n",
|
||||||
|
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"<text text-anchor=\"middle\" x=\"528.25\" y=\"-50.06\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 3->6 -->\n",
|
||||||
|
"<g id=\"edge8\" class=\"edge\">\n",
|
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|
"<title>3->6</title>\n",
|
||||||
|
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||||||
|
"<text text-anchor=\"start\" x=\"378.42\" y=\"-20.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-5.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 7 -->\n",
|
||||||
|
"<g id=\"node9\" class=\"node\">\n",
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|
"<title>7</title>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 3->7 -->\n",
|
||||||
|
"<g id=\"edge9\" class=\"edge\">\n",
|
||||||
|
"<title>3->7</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M258.39,-68.56C273.79,-76.35 297.5,-88.33 314.24,-96.8\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"320.51,-99.97 312.84,-99.62 317.38,-98.39 314.26,-96.81 314.26,-96.81 314.26,-96.81 317.38,-98.39 315.68,-94 320.51,-99.97 320.51,-99.97\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"282.46\" y=\"-104.56\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-89.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8 -->\n",
|
||||||
|
"<g id=\"node10\" class=\"node\">\n",
|
||||||
|
"<title>8</title>\n",
|
||||||
|
"<polygon fill=\"#ffffaa\" stroke=\"black\" points=\"334.94,-222.76 311.98,-204.76 334.94,-186.76 357.89,-204.76 334.94,-222.76\"/>\n",
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|
"<text text-anchor=\"middle\" x=\"334.94\" y=\"-201.06\" font-family=\"Lato\" font-size=\"14.00\">8</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 4->8 -->\n",
|
||||||
|
"<g id=\"edge10\" class=\"edge\">\n",
|
||||||
|
"<title>4->8</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M259.64,-186.79C273.79,-190.21 294.25,-195.16 310.12,-199\"/>\n",
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|
"<polygon fill=\"black\" stroke=\"black\" points=\"317.05,-200.67 309.5,-202.09 313.65,-199.85 310.24,-199.03 310.24,-199.03 310.24,-199.03 313.65,-199.85 310.98,-195.97 317.05,-200.67 317.05,-200.67\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"281.46\" y=\"-213.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-198.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 5->6 -->\n",
|
||||||
|
"<g id=\"edge12\" class=\"edge\">\n",
|
||||||
|
"<title>5->6</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M442.18,-129.03C460.14,-113.14 492.15,-84.82 511.36,-67.81\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"516.89,-62.92 513.73,-69.92 514.27,-65.24 511.65,-67.56 511.65,-67.56 511.65,-67.56 514.27,-65.24 509.56,-65.2 516.89,-62.92 516.89,-62.92\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"466.42\" y=\"-125.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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||||||
|
"<text text-anchor=\"start\" x=\"463.92\" y=\"-110.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 5->7 -->\n",
|
||||||
|
"<g id=\"edge11\" class=\"edge\">\n",
|
||||||
|
"<title>5->7</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M409.86,-142.24C399.69,-142.52 386.71,-141.81 375.92,-137.76 366.67,-134.29 357.82,-127.88 350.82,-121.79\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"345.4,-116.81 352.69,-119.22 347.98,-119.18 350.56,-121.55 350.56,-121.55 350.56,-121.55 347.98,-119.18 348.43,-123.87 345.4,-116.81 345.4,-116.81\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"380.42\" y=\"-159.56\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-144.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 6->3 -->\n",
|
||||||
|
"<g id=\"edge13\" class=\"edge\">\n",
|
||||||
|
"<title>6->3</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M505.57,-54.29C453.62,-55.57 322.27,-58.81 267.52,-60.15\"/>\n",
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|
"<polygon fill=\"black\" stroke=\"black\" points=\"260.31,-60.33 267.23,-57.01 263.81,-60.25 267.31,-60.16 267.31,-60.16 267.31,-60.16 263.81,-60.25 267.39,-63.31 260.31,-60.33 260.31,-60.33\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"379.42\" y=\"-75.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-60.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 7->5 -->\n",
|
||||||
|
"<g id=\"edge14\" class=\"edge\">\n",
|
||||||
|
"<title>7->5</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M352.29,-102.15C363.83,-99.77 379.4,-98.37 391.92,-103.76 400.16,-107.31 407.38,-113.87 413.08,-120.49\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"417.5,-126 410.66,-122.51 415.31,-123.27 413.12,-120.54 413.12,-120.54 413.12,-120.54 415.31,-123.27 415.57,-118.57 417.5,-126 417.5,-126\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"379.42\" y=\"-122.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-107.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8->4 -->\n",
|
||||||
|
"<g id=\"edge15\" class=\"edge\">\n",
|
||||||
|
"<title>8->4</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M327.6,-192.49C320.95,-181.1 309.32,-164.86 293.96,-157.76 282.73,-152.57 270.27,-158.46 260.47,-165.83\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"255.04,-170.26 258.47,-163.39 257.75,-168.04 260.47,-165.83 260.47,-165.83 260.47,-165.83 257.75,-168.04 262.46,-168.27 255.04,-170.26 255.04,-170.26\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"281.96\" y=\"-176.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-161.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 9 -->\n",
|
||||||
|
"<g id=\"node11\" class=\"node\">\n",
|
||||||
|
"<title>9</title>\n",
|
||||||
|
"<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"427.92\" cy=\"-212.76\" rx=\"18\" ry=\"18\"/>\n",
|
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|
"<text text-anchor=\"middle\" x=\"427.92\" y=\"-209.06\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8->9 -->\n",
|
||||||
|
"<g id=\"edge16\" class=\"edge\">\n",
|
||||||
|
"<title>8->9</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M356.13,-206.53C369.86,-207.74 388.1,-209.35 402.62,-210.62\"/>\n",
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|
||||||
|
"<text text-anchor=\"start\" x=\"377.92\" y=\"-227.56\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
|
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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",
|
||||||
|
"game"
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]
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},
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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",
|
||||||
|
"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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"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",
|
||||||
|
"States: 11\n",
|
||||||
|
"Start: 0\n",
|
||||||
|
"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",
|
||||||
|
"spot-state-player: 0 1 1 0 0 0 1 1 1 0 1\n",
|
||||||
|
"--BODY--\n",
|
||||||
|
"State: 0\n",
|
||||||
|
"[!1] 1 {1}\n",
|
||||||
|
"[1] 2 {1}\n",
|
||||||
|
"State: 1\n",
|
||||||
|
"[!0] 3 {1}\n",
|
||||||
|
"[0] 4 {1}\n",
|
||||||
|
"State: 2\n",
|
||||||
|
"[0] 4 {1}\n",
|
||||||
|
"[!0] 5 {1}\n",
|
||||||
|
"State: 3\n",
|
||||||
|
"[!1] 6 {1}\n",
|
||||||
|
"[1] 7 {2}\n",
|
||||||
|
"State: 4\n",
|
||||||
|
"[t] 8 {2}\n",
|
||||||
|
"State: 5\n",
|
||||||
|
"[1] 7 {2}\n",
|
||||||
|
"[!1] 6 {1}\n",
|
||||||
|
"State: 6\n",
|
||||||
|
"[t] 3 {1}\n",
|
||||||
|
"State: 7\n",
|
||||||
|
"[t] 5 {2}\n",
|
||||||
|
"State: 8\n",
|
||||||
|
"[0] 4 {2}\n",
|
||||||
|
"[!0] 9 {1}\n",
|
||||||
|
"State: 9\n",
|
||||||
|
"[t] 10 {1}\n",
|
||||||
|
"State: 10\n",
|
||||||
|
"[t] 9 {1}\n",
|
||||||
|
"--END--\n"
|
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|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"print(game.to_str('hoa'))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
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||||||
|
"cell_type": "markdown",
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"metadata": {},
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"source": [
|
||||||
|
"# Solving games"
|
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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 `parity_game_solve()` function returns a `solved_game` object."
|
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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": 4,
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|
"metadata": {},
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"outputs": [],
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||||||
|
"source": [
|
||||||
|
"sol = spot.parity_game_solve(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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||||||
|
"The solved game can be queried to know if a player is winning when the game starts in some given."
|
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|
]
|
||||||
|
},
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|
{
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"cell_type": "code",
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"execution_count": 5,
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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": [
|
||||||
|
"sol.player_winning_at(1, game.get_init_state_number())"
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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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||||||
|
"Calling the `highlight_strategy` method will decorate the original game with colors showing the winning region (states from which a player has a strategy to win), and strategy (which transition should be used for each winning state owned by that player) of a given player. Let's paint the strategy of player 1 in green (color 4) for this example:"
|
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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": 6,
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"metadata": {},
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"outputs": [
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"</g>\n",
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"<!-- 1 -->\n",
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"<!-- 0->1 -->\n",
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"<g id=\"edge2\" class=\"edge\">\n",
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"<title>0->1</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M69.9,-159.68C76.09,-154.68 83.92,-149.43 92,-146.76 101.41,-143.65 112.21,-142.86 121.8,-143.03\"/>\n",
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"<text text-anchor=\"start\" x=\"94.5\" y=\"-165.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-150.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
||||||
|
"<!-- 2 -->\n",
|
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"<g id=\"node4\" class=\"node\">\n",
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"<title>2</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"148.98,-217.76 126.02,-199.76 148.98,-181.76 171.94,-199.76 148.98,-217.76\"/>\n",
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"</g>\n",
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|
"<!-- 0->2 -->\n",
|
||||||
|
"<g id=\"edge3\" class=\"edge\">\n",
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"<title>0->2</title>\n",
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"<path fill=\"none\" stroke=\"black\" d=\"M73.69,-176.89C88.1,-181.33 109.07,-187.78 125.05,-192.7\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"132.01,-194.84 124.39,-195.79 128.66,-193.81 125.32,-192.78 125.32,-192.78 125.32,-192.78 128.66,-193.81 126.24,-189.77 132.01,-194.84 132.01,-194.84\"/>\n",
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"<text text-anchor=\"start\" x=\"96.5\" y=\"-205.56\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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"<text text-anchor=\"start\" x=\"92\" y=\"-190.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
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|
"<!-- 3 -->\n",
|
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"<g id=\"node5\" class=\"node\">\n",
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"<title>3</title>\n",
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"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"241.96\" cy=\"-60.76\" rx=\"18\" ry=\"18\"/>\n",
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"</g>\n",
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|
"<!-- 1->3 -->\n",
|
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|
"<g id=\"edge4\" class=\"edge\">\n",
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"<title>1->3</title>\n",
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||||||
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"<path fill=\"none\" stroke=\"black\" d=\"M160.06,-136.34C175.16,-122.24 203.86,-95.42 222.7,-77.82\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"228.21,-72.67 225.24,-79.75 225.65,-75.06 223.09,-77.45 223.09,-77.45 223.09,-77.45 225.65,-75.06 220.94,-75.15 228.21,-72.67 228.21,-72.67\"/>\n",
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||||||
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"<text text-anchor=\"start\" x=\"191.96\" y=\"-126.56\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-111.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
||||||
|
"<!-- 4 -->\n",
|
||||||
|
"<g id=\"node6\" class=\"node\">\n",
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|
"<title>4</title>\n",
|
||||||
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"241.96\" cy=\"-182.76\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"241.96\" y=\"-179.06\" font-family=\"Lato\" font-size=\"14.00\">4</text>\n",
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"</g>\n",
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|
"<!-- 1->4 -->\n",
|
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|
"<g id=\"edge5\" class=\"edge\">\n",
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|
"<title>1->4</title>\n",
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||||||
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M170.91,-146.58C181.75,-147.62 194.98,-149.89 205.96,-154.76 212.12,-157.49 218.12,-161.58 223.37,-165.8\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"228.73,-170.36 221.36,-168.22 225.74,-168.48 223.08,-166.21 223.4,-165.83 223.72,-165.44 226.39,-167.71 225.44,-163.43 228.73,-170.36 228.73,-170.36\"/>\n",
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"<text text-anchor=\"start\" x=\"193.96\" y=\"-173.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-158.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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"</g>\n",
|
||||||
|
"<!-- 2->4 -->\n",
|
||||||
|
"<g id=\"edge6\" class=\"edge\">\n",
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"<title>2->4</title>\n",
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||||||
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M167.95,-196.4C181.93,-193.79 201.45,-190.14 216.79,-187.27\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"223.94,-185.94 217.64,-190.32 220.6,-187.07 217.15,-187.72 217.06,-187.22 216.97,-186.73 220.41,-186.09 216.48,-184.13 223.94,-185.94 223.94,-185.94\"/>\n",
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"<text text-anchor=\"start\" x=\"193.96\" y=\"-210.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
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"<text text-anchor=\"start\" x=\"189.96\" y=\"-195.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 5 -->\n",
|
||||||
|
"<g id=\"node7\" class=\"node\">\n",
|
||||||
|
"<title>5</title>\n",
|
||||||
|
"<ellipse fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" cx=\"427.92\" cy=\"-140.76\" rx=\"18\" ry=\"18\"/>\n",
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"<text text-anchor=\"middle\" x=\"427.92\" y=\"-137.06\" font-family=\"Lato\" font-size=\"14.00\">5</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 2->5 -->\n",
|
||||||
|
"<g id=\"edge7\" class=\"edge\">\n",
|
||||||
|
"<title>2->5</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M160.75,-208.85C168.39,-214.75 179.16,-222.01 189.96,-225.76 275.06,-255.28 319.26,-296.01 391.92,-242.76 413.34,-227.05 401.22,-210.86 409.92,-185.76 412.38,-178.66 415.21,-170.99 417.85,-164.03\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"420.4,-157.35 420.84,-165.01 419.15,-160.62 417.9,-163.89 417.9,-163.89 417.9,-163.89 419.15,-160.62 414.96,-162.76 420.4,-157.35 420.4,-157.35\"/>\n",
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"<text text-anchor=\"start\" x=\"279.96\" y=\"-282.56\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
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||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-267.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 6 -->\n",
|
||||||
|
"<g id=\"node8\" class=\"node\">\n",
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"<title>6</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"528.25,-71.76 505.29,-53.76 528.25,-35.76 551.21,-53.76 528.25,-71.76\"/>\n",
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"<text text-anchor=\"middle\" x=\"528.25\" y=\"-50.06\" font-family=\"Lato\" font-size=\"14.00\">6</text>\n",
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"</g>\n",
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||||||
|
"<!-- 3->6 -->\n",
|
||||||
|
"<g id=\"edge8\" class=\"edge\">\n",
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|
"<title>3->6</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M257.63,-51.19C263.78,-47.39 271.08,-43.12 277.96,-39.76 319.9,-19.23 330.01,-10.35 375.92,-1.76 425.97,7.61 481.93,-23.1 509.68,-41.29\"/>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"515.79,-45.4 508.22,-44.11 512.88,-43.45 509.98,-41.5 509.98,-41.5 509.98,-41.5 512.88,-43.45 511.74,-38.88 515.79,-45.4 515.79,-45.4\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"378.42\" y=\"-20.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
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||||||
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"<text text-anchor=\"start\" x=\"375.92\" y=\"-5.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
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||||||
|
"</g>\n",
|
||||||
|
"<!-- 7 -->\n",
|
||||||
|
"<g id=\"node9\" class=\"node\">\n",
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|
"<title>7</title>\n",
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"<polygon fill=\"#ffffaa\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"334.94,-124.76 311.98,-106.76 334.94,-88.76 357.89,-106.76 334.94,-124.76\"/>\n",
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|
"</g>\n",
|
||||||
|
"<!-- 3->7 -->\n",
|
||||||
|
"<g id=\"edge9\" class=\"edge\">\n",
|
||||||
|
"<title>3->7</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M258.39,-68.56C273.79,-76.35 297.5,-88.33 314.24,-96.8\"/>\n",
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||||||
|
"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"320.51,-99.97 312.84,-99.62 317.16,-98.84 314.03,-97.26 314.26,-96.81 314.49,-96.36 317.61,-97.94 315.68,-94 320.51,-99.97 320.51,-99.97\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"282.46\" y=\"-104.56\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
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||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-89.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8 -->\n",
|
||||||
|
"<g id=\"node10\" class=\"node\">\n",
|
||||||
|
"<title>8</title>\n",
|
||||||
|
"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"334.94,-222.76 311.98,-204.76 334.94,-186.76 357.89,-204.76 334.94,-222.76\"/>\n",
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||||||
|
"<text text-anchor=\"middle\" x=\"334.94\" y=\"-201.06\" font-family=\"Lato\" font-size=\"14.00\">8</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 4->8 -->\n",
|
||||||
|
"<g id=\"edge10\" class=\"edge\">\n",
|
||||||
|
"<title>4->8</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M259.64,-186.79C273.79,-190.21 294.25,-195.16 310.12,-199\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"317.05,-200.67 309.5,-202.09 313.65,-199.85 310.24,-199.03 310.24,-199.03 310.24,-199.03 313.65,-199.85 310.98,-195.97 317.05,-200.67 317.05,-200.67\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"281.46\" y=\"-213.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-198.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 5->6 -->\n",
|
||||||
|
"<g id=\"edge12\" class=\"edge\">\n",
|
||||||
|
"<title>5->6</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M442.18,-129.03C460.14,-113.14 492.15,-84.82 511.36,-67.81\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"516.89,-62.92 513.73,-69.92 514.27,-65.24 511.65,-67.56 511.65,-67.56 511.65,-67.56 514.27,-65.24 509.56,-65.2 516.89,-62.92 516.89,-62.92\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"466.42\" y=\"-125.56\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"463.92\" y=\"-110.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 5->7 -->\n",
|
||||||
|
"<g id=\"edge11\" class=\"edge\">\n",
|
||||||
|
"<title>5->7</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"#e31a1c\" stroke-width=\"2\" d=\"M409.86,-142.24C399.69,-142.52 386.71,-141.81 375.92,-137.76 366.67,-134.29 357.82,-127.88 350.82,-121.79\"/>\n",
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||||||
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"<polygon fill=\"#e31a1c\" stroke=\"#e31a1c\" stroke-width=\"2\" points=\"345.4,-116.81 352.69,-119.22 348.32,-118.81 350.9,-121.18 350.56,-121.55 350.22,-121.91 347.64,-119.55 348.43,-123.87 345.4,-116.81 345.4,-116.81\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"380.42\" y=\"-159.56\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-144.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 6->3 -->\n",
|
||||||
|
"<g id=\"edge13\" class=\"edge\">\n",
|
||||||
|
"<title>6->3</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M505.57,-54.29C453.62,-55.57 322.27,-58.81 267.52,-60.15\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"260.31,-60.33 267.23,-57.01 263.81,-60.25 267.31,-60.16 267.31,-60.16 267.31,-60.16 263.81,-60.25 267.39,-63.31 260.31,-60.33 260.31,-60.33\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"379.42\" y=\"-75.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-60.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 7->5 -->\n",
|
||||||
|
"<g id=\"edge14\" class=\"edge\">\n",
|
||||||
|
"<title>7->5</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M352.29,-102.15C363.83,-99.77 379.4,-98.37 391.92,-103.76 400.16,-107.31 407.38,-113.87 413.08,-120.49\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"417.5,-126 410.66,-122.51 415.31,-123.27 413.12,-120.54 413.12,-120.54 413.12,-120.54 415.31,-123.27 415.57,-118.57 417.5,-126 417.5,-126\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"379.42\" y=\"-122.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-107.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8->4 -->\n",
|
||||||
|
"<g id=\"edge15\" class=\"edge\">\n",
|
||||||
|
"<title>8->4</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M327.6,-192.49C320.95,-181.1 309.32,-164.86 293.96,-157.76 282.73,-152.57 270.27,-158.46 260.47,-165.83\"/>\n",
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||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"255.04,-170.26 258.47,-163.39 257.75,-168.04 260.47,-165.83 260.47,-165.83 260.47,-165.83 257.75,-168.04 262.46,-168.27 255.04,-170.26 255.04,-170.26\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"281.96\" y=\"-176.56\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"277.96\" y=\"-161.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 9 -->\n",
|
||||||
|
"<g id=\"node11\" class=\"node\">\n",
|
||||||
|
"<title>9</title>\n",
|
||||||
|
"<ellipse fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" cx=\"427.92\" cy=\"-212.76\" rx=\"18\" ry=\"18\"/>\n",
|
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|
"<text text-anchor=\"middle\" x=\"427.92\" y=\"-209.06\" font-family=\"Lato\" font-size=\"14.00\">9</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 8->9 -->\n",
|
||||||
|
"<g id=\"edge16\" class=\"edge\">\n",
|
||||||
|
"<title>8->9</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M356.13,-206.53C369.86,-207.74 388.1,-209.35 402.62,-210.62\"/>\n",
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"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"409.84,-211.26 402.59,-213.78 406.31,-211.45 402.82,-211.14 402.86,-210.64 402.91,-210.15 406.39,-210.45 403.14,-207.51 409.84,-211.26 409.84,-211.26\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"377.92\" y=\"-227.56\" font-family=\"Lato\" font-size=\"14.00\">!b</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"375.92\" y=\"-212.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 10 -->\n",
|
||||||
|
"<g id=\"node12\" class=\"node\">\n",
|
||||||
|
"<title>10</title>\n",
|
||||||
|
"<polygon fill=\"#ffffaa\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"528.25,-229.76 498.08,-211.76 528.25,-193.76 558.41,-211.76 528.25,-229.76\"/>\n",
|
||||||
|
"<text text-anchor=\"middle\" x=\"528.25\" y=\"-208.06\" font-family=\"Lato\" font-size=\"14.00\">10</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 9->10 -->\n",
|
||||||
|
"<g id=\"edge17\" class=\"edge\">\n",
|
||||||
|
"<title>9->10</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"black\" d=\"M441.39,-200.41C447.61,-195.11 455.58,-189.52 463.92,-186.76 479.35,-181.65 496.47,-189.25 509.02,-197.37\"/>\n",
|
||||||
|
"<polygon fill=\"black\" stroke=\"black\" points=\"514.78,-201.34 507.23,-199.96 511.9,-199.36 509.02,-197.37 509.02,-197.37 509.02,-197.37 511.9,-199.36 510.81,-194.78 514.78,-201.34 514.78,-201.34\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"467.42\" y=\"-205.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"463.92\" y=\"-190.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"<!-- 10->9 -->\n",
|
||||||
|
"<g id=\"edge18\" class=\"edge\">\n",
|
||||||
|
"<title>10->9</title>\n",
|
||||||
|
"<path fill=\"none\" stroke=\"#33a02c\" stroke-width=\"2\" d=\"M503.51,-215.16C491.63,-216.48 477.02,-217.51 463.92,-216.76 460.44,-216.56 456.77,-216.25 453.17,-215.89\"/>\n",
|
||||||
|
"<polygon fill=\"#33a02c\" stroke=\"#33a02c\" stroke-width=\"2\" points=\"445.97,-215.1 453.27,-212.73 449.51,-214.99 452.98,-215.37 452.93,-215.87 452.88,-216.36 449.4,-215.98 452.59,-219 445.97,-215.1 445.97,-215.1\"/>\n",
|
||||||
|
"<text text-anchor=\"start\" x=\"467.42\" y=\"-235.56\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
|
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|
"<text text-anchor=\"start\" x=\"463.92\" y=\"-220.56\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"</g>\n",
|
||||||
|
"</svg>\n"
|
||||||
|
],
|
||||||
|
"text/plain": [
|
||||||
|
"<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fcb3c55a900> >"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 7,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"sol.highlight_strategy(0, 5)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": []
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"metadata": {
|
||||||
|
"kernelspec": {
|
||||||
|
"display_name": "Python 3",
|
||||||
|
"language": "python",
|
||||||
|
"name": "python3"
|
||||||
|
},
|
||||||
|
"language_info": {
|
||||||
|
"codemirror_mode": {
|
||||||
|
"name": "ipython",
|
||||||
|
"version": 3
|
||||||
|
},
|
||||||
|
"file_extension": ".py",
|
||||||
|
"mimetype": "text/x-python",
|
||||||
|
"name": "python",
|
||||||
|
"nbconvert_exporter": "python",
|
||||||
|
"pygments_lexer": "ipython3",
|
||||||
|
"version": "3.8.5"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 4
|
||||||
|
}
|
||||||
Loading…
Add table
Add a link
Reference in a new issue