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HDAs are then finite, labeled, event-consistent precubical sets with distinguished subsets of initial and accepting cells. Their languages are sets of interval orders closed under subsumption; as a major technical step, we expose a bijection between interval orders and a subclass of HDAs. We show that any finite subsumption-closed set of interval orders is the language of an HDA, that languages of HDAs are closed under binary unions and parallel composition, and that bisimilarity implies language equivalence.<\/jats:p>","DOI":"10.1017\/s0960129521000293","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T11:59:44Z","timestamp":1634644784000},"page":"575-613","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":17,"title":["Languages of higher-dimensional automata"],"prefix":"10.1017","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9094-7625","authenticated-orcid":false,"given":"Uli","family":"Fahrenberg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1525-0307","authenticated-orcid":false,"given":"Christian","family":"Johansen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9466-7815","authenticated-orcid":false,"given":"Georg","family":"Struth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7695-4028","authenticated-orcid":false,"given":"Krzysztof","family":"Ziemia\u0144ski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,10,18]]},"reference":[{"key":"S0960129521000293_ref3","unstructured":"Bezem, M. , Coquand, T. and Huber, S. 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