Algorithms for Parity Games
It is the aim of this chapter to review some of the algorithmic approaches to the problem of computing winning strategies (resp. of deciding if a player has a winning strategy from a given vertex) in parity games with finite arenas and other two-player games. Parity games are equivalent via linear time reductions to the problem of modal μ-calculus model checking (see Chapters 10 and 9), and this model checking problem plays a major role in computer-aided verification. Furthermore we will see that the problem is not too hard in a complexity-theoretic sense, while no efficient algorithm for it is known so far. Also parity games are the simplest of a whole chain of two-player games for which no efficient solutions are known, further underlining the importance of looking for an efficient algorithm solving this particular problem.
KeywordsModel Check Winning Strategy Simple Cycle Game Graph Model Check Problem
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