We present a polynomial-time algorithm minimising the number of states of history-deterministic generalised coBüchi automata, building on the work of Abu Radi and Kupferman on coBüchi automata. On the other hand, we establish that the minimisation problem for both deterministic and history-deterministic generalised Büchi 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 coBüchi automata.
@InProceedings{casares_et_al:LIPIcs.CSL.2025.22, author = {Casares, Antonio and Idir, Olivier and Kuperberg, Denis and Mascle, Corto and Prakash, Aditya}, title = {{On the Minimisation of Deterministic and History-Deterministic Generalised (Co)B\"{u}chi Automata}}, booktitle = {33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)}, pages = {22:1--22:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-362-1}, ISSN = {1868-8969}, year = {2025}, volume = {326}, editor = {Endrullis, J\"{o}rg and Schmitz, Sylvain}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.22}, URN = {urn:nbn:de:0030-drops-227798}, doi = {10.4230/LIPIcs.CSL.2025.22}, annote = {Keywords: Automata minimisation, omega-regular languages, good-for-games automata} }
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