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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