Characterizing the Polynomial-Time Minimizable $\omega$-Automata

Bader Abu Radi; Rüdiger Ehlers

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arXiv · 2504.20553

Characterizing the Polynomial-Time Minimizable $\omega$-Automata

Bader Abu Radi·Rüdiger Ehlers

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Abstract

A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that deterministic co-B\"uchi automata with transition-based acceptance are NP-hard to minimize, as are history-deterministic B\"uchi automata with transition-based acceptance.

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Bader Abu Radi, Rüdiger Ehlers. 2025-04-29. Characterizing the Polynomial-Time Minimizable $\omega$-Automata. https://arxiv.org/abs/2504.20553

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