Concurrent Small Progress Measures

  • Michael Huth
  • Jim Huan-Pu Kuo
  • Nir Piterman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7261)


We report on multi-core implementations of parity game solvers based on Small Progress Measures. We revisit a known implementation of multi-core machines (PW solver), and change, in what we call the PW e solver, the way it computes progress measures. We then suggest an alternative implementation (CSPM), that reduces logical dependency on configuration state and makes performance less dependent on configuration details. In experimental evaluation, both PW e and CSPM out-perform PW. On most benchmarks, especially larger ones, CSPM performs better than PW e . The observed linear speed-up of parallelization shows great promise for parallel implementations of game solvers.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Etessami, K., Wilke, T., Schuller, R.A.: Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata. In: Yu, Y., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, p. 694. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Friedmann, O., Lange, M.: Solving Parity Games in Practice. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 182–196. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Friedmann, O., Lange, M.: The pgsolver Collection of Parity Game Solvers. Technical report, Institut für Informatik, LMU Munich (February 2010) Version 3Google Scholar
  4. 4.
    Friedmann, O., Latte, M., Lange, M.: A Decision Procedure for CTL* Based on Tableaux and Automata. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 331–345. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  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.
    Jurdziński, M.: Deciding the winner in parity games is in UP∩co-UP. Inf. Process. Lett. 68, 119–124 (1998)CrossRefGoogle Scholar
  7. 7.
    Kozen, D.: Results on the propositional μ-calculus. In: ICALP 1982, pp. 348–359 (1982)Google Scholar
  8. 8.
    Kress-Gazit, H., Fainekos, G.E., Pappas, G.J.: Where’s waldo? sensor-based temporal logic motion planning. In: ICRA, pp. 3116–3121 (2007)Google Scholar
  9. 9.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190 (1989)Google Scholar
  10. 10.
    Stirling, C.: Local Model Checking Games. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 1–11. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  11. 11.
    van de Pol, J., Weber, M.: A multi-core solver for parity games. In: PDMC. ENTCS, vol. 220(2), pp. 19–34 (2008)Google Scholar
  12. 12.
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200(1-2), 135–183 (1998)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Huth
    • 1
  • Jim Huan-Pu Kuo
    • 1
  • Nir Piterman
    • 2
  1. 1.Department of ComputingImperial College LondonLondonUnited Kingdom
  2. 2.Department of Computer ScienceUniversity of LeicesterLeicesterUnited Kingdom

Personalised recommendations