On the Minimisation of Deterministic and History-Deterministic Generalised (co)B\"uchi Automata
Formal Languages and Automata Theory
2026-05-28 v2
Abstract
We present a polynomial-time algorithm minimising the number of states of history-deterministic generalised coB\"uchi automata, building on the work of Abu Radi and Kupferman on coB\"uchi automata. On the other hand, we establish that the minimisation problem for both deterministic and history-deterministic generalised B\"uchi automata is NP-complete, as well as the problem of minimising at the same time the number of states and colours of history-deterministic generalised coB\"uchi automata.
Keywords
Cite
@article{arxiv.2407.18090,
title = {On the Minimisation of Deterministic and History-Deterministic Generalised (co)B\"uchi Automata},
author = {Antonio Casares and Olivier Idir and Denis Kuperberg and Corto Mascle and Keya Prakash},
journal= {arXiv preprint arXiv:2407.18090},
year = {2026}
}