A CSP-Based Approach for Solving Parity Game

No matter from the theoretical or practical perspective, solving parity game plays a very important role. On one side, this problem possesses some amazing properties of computational complexity, and people are still searching for a polynomial time algorithm. On the other side, solving it and modal mu-calculus are almost the same in nature, so any efficient algorithm concerning this topic can be applied to model checking problem of modal mu-calculus. Considering the importance of modal mu-calculus in the automatic verification field, a series of model checkers will benefit from it. The main purpose of our study is to use constraints satisfaction problem (CSP), a deeply-studied and widely-accepted method, to settle parity game. The significance lies in that we can design efficient model checker through introducing various CSP algorithms, hence open a door to explore this problem of practical importance from a different viewpoint. In the paper, we propose a CSP-based algorithm and the related experimental results are presented.

[1]  E. Allen Emerson,et al.  Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[2]  Xiaotie Deng,et al.  Settling the Complexity of Two-Player Nash Equilibrium , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[3]  Gerald Jay Sussman,et al.  Propagation of constraints applied to circuit synthesis , 1980 .

[4]  Christos H. Papadimitriou,et al.  On Total Functions, Existence Theorems and Computational Complexity , 1991, Theor. Comput. Sci..

[5]  Xi Chen,et al.  3-NASH is PPAD-Complete , 2005, Electron. Colloquium Comput. Complex..

[6]  Marcin Jurdzinski,et al.  A Discrete Strategy Improvement Algorithm for Solving Parity Games , 2000, CAV.

[7]  Bernd Gärtner,et al.  Simple Stochastic Games and P-Matrix Generalized Linear Complementarity Problems , 2005, FCT.

[8]  Marcin Jurdzinski,et al.  Small Progress Measures for Solving Parity Games , 2000, STACS.

[9]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[10]  Robin Milner.  An Action Structure for Synchronous pi-Calculus , 1993, FCT.

[11]  Christos H. Papadimitriou,et al.  On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence , 1994, J. Comput. Syst. Sci..

[12]  A. Prasad Sistla,et al.  On Model-Checking for Fragments of µ-Calculus , 1993, CAV.

[13]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[14]  A. Puri.  Theory of hybrid systems and discrete event systems , 1996 .

[15]  M. Paterson,et al.  A deterministic subexponential algorithm for solving parity games , 2006, SODA 2006.

[16]  Vasant Dhar,et al.  Integer programming vs. expert systems: an experimental comparison , 1990, CACM.

[17]  David S. Johnson.  The NP-completeness column: Finding needles in haystacks , 2007, TALG.

[18]  Marcin Jurdziński,et al.  Deciding the Winner in Parity Games is in UP \cap co-Up , 1998, Inf. Process. Lett..

[19]  Henrik Björklund,et al.  A Discrete Subexponential Algorithm for Parity Games , 2003, STACS.

[20]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[21]  Christos H. Papadimitriou,et al.  Three-Player Games Are Hard , 2005, Electron. Colloquium Comput. Complex..

[22]  R. Karp,et al.  On Nonterminating Stochastic Games , 1966 .

[23]  Mihalis Yannakakis,et al.  How easy is local search? , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[24]  Anne Condon,et al.  The Complexity of Stochastic Games , 1992, Inf. Comput..

[25]  Azriel Rosenfeld,et al.  Cooperating Processes for Low-Level Vision: A Survey , 1981, Artif. Intell..

[26]  Nils Klarlund,et al.  Rabin measures and their applications to fairness and automata theory , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.