In this paper, we give a self contained presentation of a recent breakthrough in the theory of infinite duration games: the existence of a quasipolynomial time algorithm for solving parity games. We introduce for this purpose two new notions: good for small games automata and universal graphs. The first object, good for small games automata, induces a generic algorithm for solving games by reduction to safety games. We show that it is in a strong sense equivalent to the second object, universal graphs, which is a combinatorial notion easier to reason with. Our equivalence result is very generic in that it holds for all existential memoryless winning conditions, not only for parity conditions.
CITATION STYLE
Colcombet, T., & Fijalkow, N. (2019). Universal Graphs and Good for Games Automata: New Tools for Infinite Duration Games. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11425 LNCS, pp. 1–26). Springer Verlag. https://doi.org/10.1007/978-3-030-17127-8_1
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