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A Brief Excursion to Parity Games

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Developments in Language Theory (DLT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11088))

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Abstract

The author in collaboration with Calude, Jain, Li and Stephan provided an algorithm that solves the parity games problem in quasi-polynomial time. In terms of running time, this is currently the most efficient algorithm that solves the parity games problem. The goal of this lecture is to give a brief background to the problem and present the algorithm in a somewhat informal way with a bit more emphasis on ideas rather than formal details.

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References

  1. Björklund, H., Sandberg, S., Vorobyov, S.: Memoryless determinacy of parity and mean payoff games: a simple proof. Theor. Comput. Sci. 310(1–3), 365–378 (2004)

    Article  MathSciNet  Google Scholar 

  2. Bodlaender, H.L., Dinneen, M.J., Khoussainov, B.: On game-theoretic models of networks. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 550–561. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45678-3_47

    Chapter  Google Scholar 

  3. Bodlaender, H.L., Dinneen, M.J., Khoussainov, B.: Relaxed update and partition network games. Fundamenta Informaticae 49(4), 301–312 (2002)

    MathSciNet  MATH  Google Scholar 

  4. Bernet, J., Janin, D., Walukiewich, I.: Permissive strategies from parity games to safety games. ITA 36(3), 261–275 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Bradfield, J., Walukiewicz, I.: The mu-calculus and model checking. Handbook of Model Checking, pp. 871–919. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_26

    Chapter  MATH  Google Scholar 

  6. Richard Büchi, J.: On a decision method in the restricted second order arithmetic. In: Proceedings of the International Congress on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1960)

    Google Scholar 

  7. Richard Büchi, J.: Decision methods in the theory of ordinals. Bull. Am. Math. Soc. 71, 767–770 (1965)

    Article  MathSciNet  Google Scholar 

  8. Calude, C.S., Jain, S., Khoussainov, B., Li, W., Stephan, F.: Deciding parity games in quasipolynomial time. Proc. STOC 2017, 252–263 (2017)

    MathSciNet  MATH  Google Scholar 

  9. Di Stasio, A., Murano, A., Perelli, G., Vardi, M.Y.: Solving parity games using an automata-based algorithm. In: Han, Y.-S., Salomaa, K. (eds.) CIAA 2016. LNCS, vol. 9705, pp. 64–76. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40946-7_6

    Chapter  MATH  Google Scholar 

  10. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity Theory. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4471-5559-1

    Book  MATH  Google Scholar 

  11. Friedmann, O.: An exponential lower bound for the parity game strategy improvement algorithm as we know it. In: Logic in Computer Science, LICS vol. 2009, pp. 145–156 (2009)

    Google Scholar 

  12. Emerson, E.A., Jutla, C.S.: Tree automata, \(\mu \)-calculus and determinacy. In: Annals of IEEE Symposium on Foundations of Computer Science, pp. 368–377 (1991)

    Google Scholar 

  13. Emerson, E.A., Jutla, C.S., Sistla, A.P.: On model checking for the \(\mu \)-calculus and its fragments. Theor. Comput. Sci. 258(1–2), 491–522 (2001)

    Article  MathSciNet  Google Scholar 

  14. Gandhi, A., Khoussainov, B., Liu, J.: Efficient algorithms for games played on trees with back-edges. Fundamenta Informaticae 111(4), 391–412 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Gurevich, Y., Harrington, L.: Trees, automata and games. In: Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, STOC 1982, 5–7 May 1982, San Francisco, California, USA, pp. 60–65 (1982)

    Google Scholar 

  16. Ishihara, H., Khoussainov, B.: Complexity of some infinite games played on finite graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds.) WG 2002. LNCS, vol. 2573, pp. 270–281. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36379-3_24

    Chapter  Google Scholar 

  17. Jurdzinski, M.: Deciding the winner in parity games is in UP \(\cap \) co -UP. Inf. Process. Lett. 68(3), 119–124 (1998)

    Article  MathSciNet  Google Scholar 

  18. 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). https://doi.org/10.1007/3-540-46541-3_24

    Chapter  Google Scholar 

  19. Jurdziński, M., Paterson, M., Zwick, U.: A deterministic subexponential algorithm for solving parity games. SIAM J. Comput. 38(4), 1519–1532 (2008)

    Article  MathSciNet  Google Scholar 

  20. Kozen, D.: Results on the propositional \(\mu \)-calculus. Theor. Comput. Sci. 27(3), 333–354 (1983)

    Article  MathSciNet  Google Scholar 

  21. Kupferman, O., Vardi, M.Y.: Weal alternating automata and tree automata emtiness. In: STOC, pp. 224–233 (1998)

    Google Scholar 

  22. Martin, D.A.: Borel determinacy. Ann. Math. Second Ser. 102(2), 363–371 (1975)

    Article  MathSciNet  Google Scholar 

  23. McNaughton, R.: Infinite games played on finite graphs. Ann. Pure Appl. Logic 65(2), 149–184 (1993)

    Article  MathSciNet  Google Scholar 

  24. Obdrzalek, J.: Algorithmic analysis of parity games. Ph.D. thesis, University of Edinburgh (2006)

    Google Scholar 

  25. Petersson, V., Vorobyov, S.G.: A randomized subexponential algorithm for parity games. Nordic J. Comput. 8, 324–345 (2001)

    MathSciNet  MATH  Google Scholar 

  26. Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Am. Math. Soc. 141, 1–35 (1969)

    MathSciNet  MATH  Google Scholar 

  27. Schewe, S.: Solving parity games in big steps. J. Comput. Syst. Sci. 84, 243–262 (2017)

    Article  MathSciNet  Google Scholar 

  28. Stirling, C.: Bisimulation, modal logic and model checking games. Logic J. IGPL 7(1), 103–124 (1999)

    Article  MathSciNet  Google Scholar 

  29. Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59042-0_57

    Chapter  Google Scholar 

  30. Wilkie, T.: Alternating tree automata, parity games and modal \(\mu \)-calculus. Bull. Belg. Math. Soc. 8(2), 359–391 (2001)

    MathSciNet  MATH  Google Scholar 

  31. Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci. 200, 135–183 (1998)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

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  1. Bakhadyr Khoussainov
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Correspondence to Bakhadyr Khoussainov .

Editor information

Editors and Affiliations

  1. National Archives of Japan, Tokyo, Japan

    Mizuho Hoshi

  2. The University of Electro-Communications, Tokyo, Japan

    Shinnosuke Seki

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Khoussainov, B. (2018). A Brief Excursion to Parity Games. In: Hoshi, M., Seki, S. (eds) Developments in Language Theory. DLT 2018. Lecture Notes in Computer Science(), vol 11088. Springer, Cham. https://doi.org/10.1007/978-3-319-98654-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-98654-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-98653-1

  • Online ISBN: 978-3-319-98654-8

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