Abstract
Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in publicly available benchmark suites. In this paper, we combine those partial solvers with the classical algorithm for parity games due to Zielonka. We also extend partial solvers to generalized parity games that are games with conjunction of parity objectives. We have implemented those algorithms and evaluated them on a large set of benchmarks proposed in the last LTL synthesis competition.
Work partially supported by the PDR project Subgame perfection in graph games (F.R.S.-FNRS), the ARC project Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond (Fédération Wallonie-Bruxelles), the EOS project Verifying Learning Artificial Intelligence Systems (F.R.S.-FNRS & FWO), the COST Action 16228 GAMENET (European Cooperation in Science and Technology). The full version of this article is available at https://arxiv.org/abs/1907.06913.
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Notes
- 1.
This condition guarantees that there is no deadlock.
- 2.
- 3.
This result is obtained with a classical reduction to games with Büchi objectives [2].
- 4.
This algorithm is referred to as “the classical algorithm” in [6].
- 5.
The variant with safety objectives.
- 6.
The tool we implemented to realize this translation can be fetched from https://github.com/gaperez64/tlsf2gpg.
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Bruyère, V., Pérez, G.A., Raskin, JF., Tamines, C. (2019). Partial Solvers for Generalized Parity Games. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_6
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