Infinite-state games with finitary conditions

Krishnendu Chatterjee (1) , Nathanaël Fijalkow (2, 3)

1 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We study two-player zero-sum games over infinite-state graphs equipped with finitary conditions. Such conditions refine the classical omega-regular conditions: instead of requiring that good events occur infinitely often, they ensure the existence of a bound B such that in the limit good events occur within B steps. Our first contribution is to give (non-effective) characterizations of the winning regions for finitary games over countably infinite-state graphs. From these results we obtain the strategy complexity, i.e the memory required for winning strategies: we prove that memoryless strategies are sufficient for finitary Büchi, and finite memory suffices for finitary parity. We then study pushdown games with finitary conditions, with two contributions. First we prove a collapse result for pushdown games with finitary conditions, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.

Mots clés: Two-player games; Infinite-state systems; Pushdown games; Bounds in omega-regularity; Verification and synthesis

Domaines: Informatique et théorie des jeux [cs.GT]

Krishnendu Chatterjee, Nathanaël Fijalkow. Infinite-state games with finitary conditions. 2013. ⟨hal-00773190v1⟩