Advertisement

Solving Parity Games on the GPU

  • Philipp Hoffmann
  • Michael Luttenberger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8172)

Abstract

We present our GPU-based implementations of three well-known algorithms for solving parity games. Our implementations are in general faster by a factor of at least two than the corresponding implementations found in the widely known PGSolver collection of solvers. For benchmarking we use several of PGSolver’s benchmarks as well as arenas obtained by means of the reduction of the language inclusion problem of nondeterministic Büchi automata to parity games with only three colors [3]. The benchmark suite of http://languageinclusion.org/CONCUR2011 was used in the latter case.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barnat, J., Bauch, P., Brim, L., Ceska, M.: Designing fast ltl model checking algorithms for many-core gpus. J. Parallel Distrib. Comput. 72(9), 1083–1097 (2012)CrossRefGoogle Scholar
  2. 2.
    Björklund, H., Sandberg, S., Vorobyov, S.: A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 673–685. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for büchi automata. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 694–707. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Friedmann, O., Lange, M.: The PGSolver collection of parity game solvers. University of Munich (2009), http://www2.tcs.ifi.lmu.de/pgsolver/
  5. 5.
    Jurdziński, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Luttenberger, M.: Strategy iteration using non-deterministic strategies for solving parity games. Tech. rep., Technische Universität München, Institut für Informatik (April 2008)Google Scholar
  7. 7.
    Schewe, S.: An optimal strategy improvement algorithm for solving parity and payoff games. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 369–384. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Vöge, J., Jurdziński, M.: A discrete strategy improvement algorithm for solving parity games (Extended abstract). In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci. 200(1-2), 135–183 (1998)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Philipp Hoffmann
    • 1
  • Michael Luttenberger
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGermany

Personalised recommendations