Languages of higher-dimensional automata

We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. HDAs are then finite, labeled, event-consistent...

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Bibliographic Details
Published inMathematical structures in computer science Vol. 31; no. 5; pp. 575 - 613
Main Authors Fahrenberg, Uli, Johansen, Christian, Struth, Georg, Ziemiański, Krzysztof
Format Journal Article
LanguageEnglish
Published Cambridge University Press (CUP) 01.05.2021
Subjects
Computer Science
Formal Languages and Automata Theory
concurrency theory
pomset
Higher-dimensional automaton
directed topology
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ISSN0960-1295
1469-8072
1469-8072
DOI10.1017/S0960129521000293

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Summary:We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. 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.
ISSN:0960-1295
1469-8072
1469-8072
DOI:10.1017/S0960129521000293