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 with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi games, and finite-memory suffices for finitary parity games. We then study pushdown boundedness games, with two contributions. First we prove a collapse result for pushdown omega B games, 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-00773190v2⟩