Languages of Higher-Dimensional Automata
Abstract
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.
Cite
@article{arxiv.2103.07557,
title = {Languages of Higher-Dimensional Automata},
author = {Uli Fahrenberg and Christian Johansen and Georg Struth and Krzysztof Ziemiański},
journal= {arXiv preprint arXiv:2103.07557},
year = {2021}
}