2026-08-24T17:52:29Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27362 2026-08-24T14:08:31Z ddc:004 open_access

Algebraic Characterization of FO-Definable Languages of Higher-Dimensional Automata Erlich, Enzo Ledent, Jérémy Ziemiański, Krzysztof Higher-dimensional automata Pomset languages McNaughton-Papert theorem Counter-free HDA Aperiodic category Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially ordered. We prove a new algebraic characterization of HDA languages: a language of pomsets is regular if and only if it is the inverse image of a functor from the category of pomsets into a finite category. Furthermore, the language is definable in first-order logic exactly when it is recognized by an aperiodic category, generalizing the McNaughton-Papert theorem to HDA languages. We also investigate a notion of counter-free HDA, and show that if a language is accepted by a counter-free HDA, it must be definable in first-order logic. The converse, however, is still open. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Enzo Erlich and Jérémy Ledent and Krzysztof Ziemiański 2026 Is Part Of LIPIcs, Volume 391, 37th International Conference on Concurrency Theory (CONCUR 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2026.32 urn:nbn:de:0030-drops-273620 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2026.32 eng https://creativecommons.org/licenses/by/4.0/legalcode