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arXiv · 2603.05380

History-Deterministic B\"uchi Automata are Succinct

Antonio Casares·Keya Prakash·K. S. Thejaswini
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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.

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Antonio Casares, Keya Prakash, K. S. Thejaswini. 2026-03-05. History-Deterministic B\"uchi Automata are Succinct. https://arxiv.org/abs/2603.05380

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