Weak Muller Conditions Make Delay Games Hard

TL;DR

This paper proves that solving delay games with weak Muller automata as winning conditions is highly complex, requiring exponential lookahead, and highlights how automata succinctness impacts computational difficulty.

Contribution

It establishes the complexity bounds for delay games with weak Muller automata and demonstrates the influence of automata succinctness on problem difficulty.

Findings

Solving delay games with deterministic weak Muller automata is 2EXPTIME-complete.

Solving delay games with nondeterministic weak Muller automata is 3EXPTIME-complete.

Doubly and triply exponential lookahead is necessary and sufficient for winning such games.

Abstract

We show that solving delay games with winning conditions given by deterministic and nondeterministic weak Muller automata is 2EXPTIME-complete respectively 3EXPTIME-complete. Furthermore, doubly and triply exponential lookahead is necessary and sufficient to win such games. These results are the first that show that the succinctness of the automata types used to specify the winning conditions has an influence on the complexity of these problems.