Can parity games be solved in polynomial time

The fundamental open question is the membership of parity games in P. We will research in both directions, trying to improve the known upper and lower bounds and studying the relation between different types of parity and payoff games.

Upper bounds Assuming that solving parity games is tractable, the gold-brim solution would be to find a polynomial time algorithm for solving parity games. A second best upper bound would be to establish an FPTAS algorithm, where the number of priorities is the parameter. Another branch of research under this item is to estimate the complexity of known algorithms with unknown complexity.

Lower bounds Assuming that parity games are not tractable, finding a super-polynomial lower bound would be the gold-brim solution. However, there are no non-trivial polynomial bounds available, and proofs of lower bounds based, e. Connecting 2 player parity with mean, discounted, and simple stochastic games. There is a simple polynomial time reduction from parity through mean payoff and discounted payoff to simple stochastic games. The latter are polynomial time equivalent to the 2.

We will research reductions in the other directions. To describe classes of parity and payoff games that can be solved efficiently.

Many different cases where parity games can be solved in polynomial time are known. Active 4 years, 9 months ago. Viewed times. Improve this question. Andy Andy 1 1 gold badge 2 2 silver badges 5 5 bronze badges.

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View 1 excerpt, references background. Solving Parity Games in Big Steps. Strategy Derivation for Small Progress Measures. Computer Science, Mathematics. Synthesis of Reactive 1 designs. We address the problem of automatically synthesizing digital designs from linear-time specifications.