History-Deterministic B\"uchi Automata are Succinct
Formal Languages and Automata Theory
2026-05-28 v1
Abstract
We describe a history-deterministic B\"uchi automaton that has strictly less states than every language-equivalent deterministic B\"uchi automaton. This solves a problem that had been open since the introduction of history-determinism and actively investigated for over a decade. Our example automaton has 65 states, and proving its succinctness requires the combination of theoretical insights together with the aid of computers.
Keywords
Cite
@article{arxiv.2603.05380,
title = {History-Deterministic B\"uchi Automata are Succinct},
author = {Antonio Casares and Keya Prakash and K. S. Thejaswini},
journal= {arXiv preprint arXiv:2603.05380},
year = {2026}
}
Comments
40 pages