# Languages of Higher-Dimensional Automata

@article{Fahrenberg2021LanguagesOH, title={Languages of Higher-Dimensional Automata}, author={Ulrich Fahrenberg and Christian Johansen and Georg Struth and Krzysztof Ziemia'nski}, journal={Math. Struct. Comput. Sci.}, year={2021}, volume={31}, pages={575-613} }

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…

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## 6 Citations

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We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they recognise are precisely the rational subsumption-closed sets of interval pomsets. The rational…

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