Work

Languages of higher-dimensional automata

Year: 2021

Type: article

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.

Source: Mathematical Structures in Computer Science

DOI: 10.1017/s0960129521000293

Authors: Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof Ziemiański

Institutions: École Polytechnique, Norwegian University of Science and Technology, University of Sheffield, University of Warsaw

Language: English

Topic: Petri Nets in System Modeling

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3136052645

FWCI: 1.486

Cites: 49

Cited by: 18

Related to: 20