Lookahead Games and Efficient Determinisation of History-Deterministic B\"uchi Automata

TL;DR

This paper introduces a polynomial-time determinisation method for history-deterministic B"uchi automata, utilizing a novel lookahead game concept that simplifies the characterization of history-determinism.

Contribution

It presents the first polynomial-time determinisation procedure for history-deterministic B"uchi automata and introduces the lookahead game as a key conceptual tool.

Findings

Polynomial-time determinisation procedure for history-deterministic B"uchi automata.

Equivalence of lookahead game and 1-token game.

Characterization of history-determinism via the 1-token game.

Abstract

Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic B\"uchi automata, which settles an open question of Kuperberg and Skrzypczak, 2015. A key conceptual contribution is the lookahead game, which is a variant of Bagnol and Kuperberg's token game, in which Adam is given a fixed lookahead. We prove that the lookahead game is equivalent to the 1-token game. This allows us to show that the 1-token game characterises history-determinism for semantically-deterministic B\"uchi automata, which paves the way to our polynomial-time determinisation procedure.