# Recursive algorithm for parity games requires exponential time

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2011)

- Volume: 45, Issue: 4, page 449-457
- ISSN: 0988-3754

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topFriedmann, Oliver. "Recursive algorithm for parity games requires exponential time." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 45.4 (2011): 449-457. <http://eudml.org/doc/273062>.

@article{Friedmann2011,

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.},

author = {Friedmann, Oliver},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {parity games; recursive algorithm; lower bound; μcalculus; model checking; -calculus},

language = {eng},

number = {4},

pages = {449-457},

publisher = {EDP-Sciences},

title = {Recursive algorithm for parity games requires exponential time},

url = {http://eudml.org/doc/273062},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Friedmann, Oliver

TI - Recursive algorithm for parity games requires exponential time

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 4

SP - 449

EP - 457

AB - 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.

LA - eng

KW - parity games; recursive algorithm; lower bound; μcalculus; model checking; -calculus

UR - http://eudml.org/doc/273062

ER -

## References

top- [1] 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.
- [2] E.A. Emerson, C.S. Jutla and A.P. Sistla, 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. MR1254452
- [3] O. Friedmann, An exponential lower bound for the parity game strategy improvement algorithm as we know it, in Proc. of LICS (2009) 145–156. MR2932379
- [4] O. Friedmann and M. Lange, Solving parity games in practice, in Proc. of ATVA (2009) 182–196. Zbl1258.68077
- [5] E. Grädel, W. Thomas and Th. Wilke Eds., Automata, Logics, and Infinite Games. Lect. Notes Comput. Sci. 2500 (2002). Zbl1011.00037
- [6] M. Jurdzinski, Deciding the winner in parity games is in up ∩ co − up. Inf. Process. Lett. 68 (1998) 119–124. Zbl06590783MR1657581
- [7] M. Jurdziński, 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. Zbl0962.68111MR1781740
- [8] 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. Zbl1192.91013MR2368806
- [9] S. Schewe, Solving parity games in big steps, in Proc. FST TCS. Springer-Verlag (2007). Zbl1135.68480MR2480222
- [10] S. Schewe, An optimal strategy improvement algorithm for solving parity and payoff games, in 17th Annual Conference on Computer Science Logic (CSL) (2008). Zbl1156.68478MR2540256
- [11] P. Stevens and C. Stirling, 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.
- [12] C. Stirling, Local model checking games, in Proc. 6th Conf. on Concurrency Theory, CONCUR’95. Lect. Notes Comput. Sci. 962 (1995) 1–11.
- [13] J. Vöge and M. Jurdziński, 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. Zbl0974.68527
- [14] W. Zielonka, Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoret. Comput. Sci.200 (1998) 135–183. Zbl0915.68120MR1625527

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