Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata
This solves a long-standing open problem in automata theory, providing an efficient algorithm for determinising a class of automata that was previously not known to be polynomial-time determinisable.
The authors present a polynomial-time determinisation procedure for history-deterministic Büchi automata, solving an open problem from 2015. They introduce the lookahead game and prove it equivalent to the 1-token game, enabling the result.
Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic Büchi 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 Büchi automata, which paves the way to our polynomial-time determinisation procedure.