Finite-state Strategies in Delay Games (full version)

TL;DR

This paper introduces a general framework for analyzing finite-state strategies in delay games, providing conditions for their existence, complexity bounds, and a unified approach that encompasses previous results.

Contribution

It presents a broad, automaton-based framework that characterizes when finite-state strategies exist in delay games and offers complexity and lookahead bounds.

Findings

Finite-state strategies exist for all winning conditions with automaton-recognized winning sets.

The framework provides upper bounds on the complexity of determining winners.

It generalizes and unifies previous results in delay game analysis.

Abstract

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning condition is recognized by an automaton with an acceptance condition that satisfies a certain aggregation property. Our framework also yields upper bounds on the complexity of determining the winner of such delay games and upper bounds on the necessary lookahead to win the game. In particular, we cover all previous results of that kind as special cases of our uniform approach.