Finite-state Strategies in Delay Games

TL;DR

This paper introduces a comprehensive framework for computing finite-state strategies in delay games, providing general conditions, complexity bounds, and unifying previous results in the field.

Contribution

It presents a universal framework for finite-state strategies in delay games applicable to automata with specific acceptance properties, extending and unifying prior work.

Findings

Finite-state strategies exist for all winning conditions recognized by automata with certain acceptance properties.

The framework provides upper bounds on the complexity of winner determination.

It establishes bounds on the necessary lookahead to secure a win.

Abstract

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question and present a very general framework for computing such strategies: they exist for all winning conditions that are recognized by automata with acceptance conditions that satisfy 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.