License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2022.29
URN: urn:nbn:de:0030-drops-170925
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17092/
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Fahrenberg, Uli ; Johansen, Christian ; Struth, Georg ; Ziemiański, Krzysztof

A Kleene Theorem for Higher-Dimensional Automata

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Abstract

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 operations include a gluing composition, for which we equip pomsets with interfaces. For our proof, we introduce HDAs with interfaces as presheaves over labelled precube categories and use tools inspired by algebraic topology, such as cylinders and (co)fibrations. HDAs are a general model of non-interleaving concurrency, which subsumes many other models in this field. Interval orders are used as models for concurrent or distributed systems where events extend in time. Our tools and techniques may therefore yield templates for Kleene theorems in various models and applications.

BibTeX - Entry

@InProceedings{fahrenberg_et_al:LIPIcs.CONCUR.2022.29,
  author =	{Fahrenberg, Uli and Johansen, Christian and Struth, Georg and Ziemia\'{n}ski, Krzysztof},
  title =	{{A Kleene Theorem for Higher-Dimensional Automata}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17092},
  URN =		{urn:nbn:de:0030-drops-170925},
  doi =		{10.4230/LIPIcs.CONCUR.2022.29},
  annote =	{Keywords: higher-dimensional automata, interval posets, Kleene theorem, concurrency theory, labelled precube categories}
}

Keywords: higher-dimensional automata, interval posets, Kleene theorem, concurrency theory, labelled precube categories
Collection: 33rd International Conference on Concurrency Theory (CONCUR 2022)
Issue Date: 2022
Date of publication: 06.09.2022

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