Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T06:17:51.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive algorithm for parity games requires exponential time

Published online by Cambridge University Press:  14 November 2011

Oliver Friedmann
Oliver Friedmann*
Affiliation:
Institut für Informatik, LMU München 80538 Munich, Germany. [email protected]
Get access

Abstract

This paper presents a new lower bound for the recursive algorithm for solving parity games which is induced by the constructive proof of memoryless determinacy by Zielonka. We outline a family of games of linear size on which the algorithm requires exponential time.

Keywords

Parity gamesrecursive algorithmlower boundμcalculusmodel checking
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 45 , Issue 4 , November 2011 , pp. 449 - 457
Copyright
© EDP Sciences 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

E.A. Emerson and C.S. Jutla, Tree automata, μ-calculus and determinacy, in Proc. 32nd Symp. on Foundations of Computer Science. San Juan, Puerto Rico, IEEE (1991) 368–377.
Emerson, E.A., Jutla, C.S. and Sistla, A.P., On model-checking for fragments of μ-calculus, in Proc. 5th Conf. on Computer Aided Verification, CAV’93. Lect. Notes Comput. Sci. 697 (1993) 385–396. Google Scholar
O. Friedmann, An exponential lower bound for the parity game strategy improvement algorithm as we know it, in Proc. of LICS (2009) 145–156.
O. Friedmann and M. Lange, Solving parity games in practice, in Proc. of ATVA (2009) 182–196.
E. Grädel, W. Thomas and Th. Wilke Eds., Automata, Logics, and Infinite Games. Lect. Notes Comput. Sci. 2500 (2002).
Jurdzinski, M., Deciding the winner in parity games is in up ∩ co − up. Inf. Process. Lett. 68 (1998) 119–124. Google Scholar
Jurdziński, M., Small progress measures for solving parity games, in Proc. 17th Ann. Symp. on Theoretical Aspects of Computer Science, STACS’00, edited by H. Reichel and S. Tison. Lect. Notes Comput. Sci. 1770 (2000) 290–301. Google Scholar
M. Jurdziński, M. Paterson and U. Zwick, A deterministic subexponential algorithm for solving parity games, in Proc. 17th Ann. ACM-SIAM Symp. on Discrete Algorithm, SODA’06. ACM (2006) 117–123.
S. Schewe, Solving parity games in big steps, in Proc. FST TCS. Springer-Verlag (2007).
S. Schewe, An optimal strategy improvement algorithm for solving parity and payoff games, in 17th Annual Conference on Computer Science Logic (CSL) (2008).
Stevens, P. and Stirling, C., Practical model-checking using games, in Proc. 4th Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, TACAS’98, edited by B. Steffen. Lect. Notes Comput. Sci. 1384 (1998) 85–101. Google Scholar
Stirling, C., Local model checking games, in Proc. 6th Conf. on Concurrency Theory, CONCUR’95. Lect. Notes Comput. Sci. 962 (1995) 1–11. Google Scholar
Vöge, J. and Jurdziński, M., A discrete strategy improvement algorithm for solving parity games, in Proc. 12th Int. Conf. on Computer Aided Verification, CAV’00. Lect. Notes Comput. Sci. 1855 (2000) 202–215. Google Scholar
Zielonka, W., Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoret. Comput. Sci. 200 (1998) 135–183. Google Scholar