Infinite-state games with finitary conditions

TL;DR

This paper investigates infinite-state games with boundedness conditions, establishing strategy complexities, decidability results, and computational complexity for various classes of these games.

Contribution

It proves memoryless strategies suffice for finitary Büchi games, finite-memory for finitary parity games, and establishes decidability and complexity results for pushdown boundedness games.

Findings

Memoryless strategies suffice for finitary Büchi games.

Finite-memory strategies suffice for finitary parity games.

Decidability and EXPTIME-completeness results for pushdown boundedness games.

Abstract

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 B\"uchi 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.