We suggest a new randomized algorithm for solving parity games with worst case time complexity roughly

We present several new algorithms as well as new lower and upper bounds for optimizing functions underlying infinite games pertinent to computer-aided verification.

Abstract. This paper presents a reduction from the problem of solving parity games to the satisfiability problem for formulas of propositional logic in conjunctive normal form. It uses Jurdziński’s characterisation of winning strategies via progress measures. The reduction is motivated by the apparent success that using SAT solvers has had in symbolic verification. The paper reports on a prototype implementation of the reduction and presents some runtime results. 1

Parity Games form an intriguing family of infinite duration games whose solution is equivalent to the solution of important problems in automatic verification and automata theory. They also form a very natural subclass of Deterministic Mean Payoff Games, which in turn is a very natural subclass of turn-based Stochastic Mean Payoff Games. It is a major open problem whether these game families can be solved in polynomial time. The currently fastest algorithms for the solution of all these games are adaptations of the randomized generalizationof linear programming. We refer to the algorithm ofMatouˇsek, Sharir and Welzl as the Random Facet algorithm. The expected running time of these algorithmsis subexponential in the size of the game, i.e., 2

Parity games are discrete infinite games of two players with complete information. There are two main motivations to study parity games. Firstly the problem of deciding a winner in a parity game is polynomially equivalent to the modal µ-calculus model checking, and therefore is very important in the field of computer aided verification. Secondly it is the intriguing status of parity games from the point of view of complexity theory. Solving parity games is one of the few natural problems in the class NP∩co-NP (even in UP∩co-UP), and there is no known polynomial time algorithm, despite the substantial amount of effort to find one. In this thesis we add to the body of work on parity games. We start by presenting parity games and explaining the concepts behind them, giving a survey of known algorithms, and show their relationship to other problems. In the second part of the thesis we want to answer the following question: Are there classes of graphs on which we can solve parity games in polyno-

Abstract not found

Abstract not found