Variants of Higher-Dimensional Automata

Fuente: arXiv
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Main Authors: Bazille, Hugo, Dubut, Jérémy, Fahrenberg, Uli, Ziemiański, Krzysztof
Format: Preprint
Published: 2026
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author Bazille, Hugo
Dubut, Jérémy
Fahrenberg, Uli
Ziemiański, Krzysztof
author_facet Bazille, Hugo
Dubut, Jérémy
Fahrenberg, Uli
Ziemiański, Krzysztof
contents The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a formalism to use and reason about. In order to solve specific problems, weaker variants of HDAs have been introduced, such as HDAs with interfaces, partial HDAs, ST-automata or even relational HDAs. In this paper we collect definitions of these and a few other variants into a coherent whole and explore their properties and translations between them. We show that with regard to languages, the spectrum of variants collapses into two classes, languages closed under subsumption and those that are not. We also show that partial HDAs admit a Kleene theorem and that, contrary to HDAs, they are determinizable.
format Preprint
id arxiv_https___arxiv_org_abs_2601_17537
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Variants of Higher-Dimensional Automata
Bazille, Hugo
Dubut, Jérémy
Fahrenberg, Uli
Ziemiański, Krzysztof
Formal Languages and Automata Theory
Logic in Computer Science
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a formalism to use and reason about. In order to solve specific problems, weaker variants of HDAs have been introduced, such as HDAs with interfaces, partial HDAs, ST-automata or even relational HDAs. In this paper we collect definitions of these and a few other variants into a coherent whole and explore their properties and translations between them. We show that with regard to languages, the spectrum of variants collapses into two classes, languages closed under subsumption and those that are not. We also show that partial HDAs admit a Kleene theorem and that, contrary to HDAs, they are determinizable.
title Variants of Higher-Dimensional Automata
topic Formal Languages and Automata Theory
Logic in Computer Science
url https://arxiv.org/abs/2601.17537