New Algorithms for Combinations of Objectives using Separating Automata

TL;DR

This paper introduces new algorithms for solving games with combined objectives by leveraging separating automata, achieving optimal or improved complexity for disjunctions of parity and mean payoff objectives.

Contribution

It develops two novel algorithms for combined objectives, utilizing separating automata to improve efficiency and extend applicability in game-solving.

Findings

Algorithm for disjunctions of parity and mean payoff objectives matches best known complexity.

Algorithm for disjunctions of mean payoff objectives improves on previous state-of-the-art.

Constructs small separating automata using existing methods for parity and mean payoff objectives.

Abstract

The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games. In this paper we show that separating automata is a powerful tool for constructing algorithms solving games with combinations of objectives. We construct two new algorithms: the first for disjunctions of parity and mean payoff objectives, matching the best known complexity, and the second for disjunctions of mean payoff objectives, improving on the state of the art. In both cases the algorithms are obtained through the construction of small separating automata, using as black boxes the existing constructions for parity objectives and for mean payoff objectives.