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.
Mots clés : parity games, recursive algorithm, lower bound, μcalculus, model checking
@article{ITA_2011__45_4_449_0,
author = {Friedmann, Oliver},
title = {Recursive algorithm for parity games requires exponential time},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {449--457},
publisher = {EDP-Sciences},
volume = {45},
number = {4},
year = {2011},
doi = {10.1051/ita/2011124},
mrnumber = {2876116},
zbl = {1232.91064},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2011124/}
}
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 SP - 449 EP - 457 VL - 45 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2011124/ DO - 10.1051/ita/2011124 LA - en ID - ITA_2011__45_4_449_0 ER -
%0 Journal Article %A Friedmann, Oliver %T Recursive algorithm for parity games requires exponential time %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2011 %P 449-457 %V 45 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2011124/ %R 10.1051/ita/2011124 %G en %F ITA_2011__45_4_449_0
Friedmann, Oliver. Recursive algorithm for parity games requires exponential time. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 4, pp. 449-457. doi : 10.1051/ita/2011124. http://archive.numdam.org/articles/10.1051/ita/2011124/
[1] and , Tree automata, μ-calculus and determinacy, in Proc. 32nd Symp. on Foundations of Computer Science. San Juan, Puerto Rico, IEEE (1991) 368-377.
[2] , and , 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. | MR
[3] , An exponential lower bound for the parity game strategy improvement algorithm as we know it, in Proc. of LICS (2009) 145-156. | MR
[4] and , Solving parity games in practice, in Proc. of ATVA (2009) 182-196. | Zbl
[5] , and Eds., Automata, Logics, and Infinite Games. Lect. Notes Comput. Sci. 2500 (2002). | Zbl
[6] , Deciding the winner in parity games is in up ∩ co − up. Inf. Process. Lett. 68 (1998) 119-124. | MR
[7] , 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. | MR | Zbl
[8] , and , A deterministic subexponential algorithm for solving parity games, in Proc. 17th Ann. ACM-SIAM Symp. on Discrete Algorithm, SODA'06. ACM (2006) 117-123. | MR | Zbl
[9] , Solving parity games in big steps, in Proc. FST TCS. Springer-Verlag (2007). | MR | Zbl
[10] , An optimal strategy improvement algorithm for solving parity and payoff games, in 17th Annual Conference on Computer Science Logic (CSL) (2008). | MR | Zbl
[11] and , 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] , Local model checking games, in Proc. 6th Conf. on Concurrency Theory, CONCUR'95. Lect. Notes Comput. Sci. 962 (1995) 1-11.
[13] and , 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. | Zbl
[14] , Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoret. Comput. Sci. 200 (1998) 135-183. | MR | Zbl
Cité par Sources :
