Abstract
We consider parity games, a special form of two-player infinite-duration games on numerically labeled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often during a play be of some specific parity. The problem of identifying the corresponding winning regions has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class $${\textsc {UPTime}} \cap {\textsc {CoUPTime}}$$ , and still open is the question whether it can be solved in polynomial time. Parity games also have great practical interest, as they arise in many fields of theoretical computer science, most notably logic, automata theory, and formal verification. In this paper, we propose a new algorithm for the solution of this decision problem, based on the idea of promoting vertexes to higher priorities during the search for winning regions. The proposed approach has nice computational properties, exhibiting the best space complexity among the currently known solutions. Experimental results on both random games and benchmark families show that the technique is also very effective in practice.
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