Skip to main content
SpringerLink
Log in

On Parity Game Preorders and the Logic of Matching Plays

  • Conference paper
  • First Online:
SOFSEM 2016: Theory and Practice of Computer Science (SOFSEM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9587))

Abstract

Parity games can be used to solve satisfiability, verification and controller synthesis problems. As part of an effort to better understand their nature, or the nature of the problems they solve, preorders on parity games have been studied. Defining these relations, and in particular proving their transitivity, has proven quite difficult on occasion. We propose a uniform way of lifting certain preorders on Kripke structures to parity games and study the resulting preorders. We explore their relation with parity game preorders from the literature and we study new relations. Finally, we investigate whether these preorders can also be obtained via modal characterisations of the preorders.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)

    Article  MathSciNet  Google Scholar 

  2. Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. TCS 303(1), 7–34 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cranen, S., Keiren, J.J.A., Willemse, T.A.C.: Stuttering mostly speeds up solving parity games. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 207–221. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Cranen, S., Keiren, J.J.A., Willemse, T.A.C.: A cure for stuttering parity games. In: Roychoudhury, A., D’Souza, M. (eds.) ICTAC 2012. LNCS, vol. 7521, pp. 198–212. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Dawar, A., Grädel, E.: The descriptive complexity of parity games. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 354–368. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Emerson, E.A., Jutla, C.S.: Tree automata, Mu-Calculus and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society (1991)

    Google Scholar 

  7. Friedmann, O., Lange, M.: The modal \(\mu \)-calculus caught off guard. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 149–163. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Fritz, C., Wilke, T.: Simulation relations for alternating parity automata and parity games. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 59–70. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Gazda, M.W., Willemse, T.A.C.: Consistent consequence for boolean equation systems. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 277–288. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Gazda, M.W.: Parity Games, Fixpoint Logic and Relations of Consequence. Eindhoven University of Technology, Forthcoming (2016)

    Google Scholar 

  11. Keiren, J.J.A.: Advanced Reduction Techniques for Model Checking. Eindhoven University of Technology (2013)

    Google Scholar 

  12. Kissig, C., Venema, Y.: Complementation of coalgebra automata. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 81–96. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Namjoshi, K.S.: Abstraction for branching time properties. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 288–300. Springer, Heidelberg (2003)

    Google Scholar 

  14. Ranzato, F., Tapparo, F.: Computing stuttering simulations. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 542–556. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. TCS 200(1–2), 135–183 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    M. W. Gazda & T. A. C. Willemse

Authors
  1. M. W. Gazda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. A. C. Willemse
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. C. Willemse .

Editor information

Editors and Affiliations

  1. University of Latvia, Riga, Latvia

    Rūsiņš Mārtiņš Freivalds

  2. University of Paderborn, Paderborn, Germany

    Gregor Engels

  3. University of Genoa, Genoa, Italy

    Barbara Catania

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gazda, M.W., Willemse, T.A.C. (2016). On Parity Game Preorders and the Logic of Matching Plays. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-49192-8_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49191-1

  • Online ISBN: 978-3-662-49192-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation