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parity game: add Zielonka's recursive algorithm

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* spot/misc/game.cc, spot/misc/game.hh: Implement it.
* bin/ltlsynt.cc: Use it.
* doc/org/ltlsynt.org: Document it.
This commit is contained in:
Thibaud Michaud 2017-09-10 22:54:24 +02:00
parent 0821c97eb8
commit f414e9f5f2
4 changed files with 213 additions and 27 deletions
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78
spot/misc/game.hh
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@ -82,33 +82,74 @@ public:
return owner_[src];
}
unsigned max_parity() const
{
unsigned max_parity = 0;
for (auto& e: dpa_->edges())
max_parity = std::max(max_parity, e.acc.max_set());
SPOT_ASSERT(max_parity);
return max_parity - 1;
}
/// Print the parity game in PGSolver's format.
void print(std::ostream& os);
// Compute the winner of this game using Zielonka's recursive algorithm.
// False is Even and True is Odd.
/** \verbatim
@article{ zielonka.98.tcs
title = "Infinite games on finitely coloured graphs with applications to
automata on infinite trees",
journal = "Theoretical Computer Science",
volume = "200",
number = "1",
pages = "135 - 183",
year = "1998",
author = "Wieslaw Zielonka",
}
\endverbatim */
bool winner() const;
/// Whether player 1 has a winning strategy from the initial state.
/// Implements Calude et al.'s quasipolynomial time algorithm.
/** \verbatim
@inproceedings{calude.17.stoc,
author = {Calude, Cristian S. and Jain, Sanjay and Khoussainov,
Bakhadyr and Li, Wei and Stephan, Frank},
title = {Deciding Parity Games in Quasipolynomial Time},
booktitle = {Proceedings of the 49th Annual ACM SIGACT Symposium on
Theory of Computing},
series = {STOC 2017},
year = {2017},
isbn = {978-1-4503-4528-6},
location = {Montreal, Canada},
pages = {252--263},
numpages = {12},
url = {http://doi.acm.org/10.1145/3055399.3055409},
doi = {10.1145/3055399.3055409},
acmid = {3055409},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Muller Games, Parity Games, Quasipolynomial Time Algorithm},
author = {Calude, Cristian S. and Jain, Sanjay and Khoussainov,
Bakhadyr and Li, Wei and Stephan, Frank},
title = {Deciding Parity Games in Quasipolynomial Time},
booktitle = {Proceedings of the 49th Annual ACM SIGACT Symposium on
Theory of Computing},
series = {STOC 2017},
year = {2017},
isbn = {978-1-4503-4528-6},
location = {Montreal, Canada},
pages = {252--263},
numpages = {12},
url = {http://doi.acm.org/10.1145/3055399.3055409},
doi = {10.1145/3055399.3055409},
acmid = {3055409},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Muller Games, Parity Games, Quasipolynomial Time Algorithm},
}
\endverbatim */
bool solve_qp() const;
private:
typedef twa_graph::graph_t::edge_storage_t edge_t;
// Compute (in place) a set of states from which player can force a visit
// through set.
// if attr_max is true, states that can force a visit through an edge with
// max parity are also counted in.
void attractor(const std::unordered_set<unsigned>& subgame,
std::unordered_set<unsigned>& set, unsigned max_parity,
bool player, bool attr_max = false) const;
// Compute the winning region for player Odd.
std::unordered_set<unsigned>
winning_region(std::unordered_set<unsigned>& subgame,
unsigned max_parity) const;
};
@ -246,8 +287,7 @@ private:
public:
reachability_game(const parity_game& pg)
: twa(std::make_shared<bdd_dict>()),
pg_(pg)
: twa(std::make_shared<bdd_dict>()), pg_(pg)
{
init_state_ = std::shared_ptr<const reachability_state>(get_init_state());
}