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Documents authored by Struth, Georg

Document
DOI: 10.4230/LIPIcs.CONCUR.2022.29
A Kleene Theorem for Higher-Dimensional Automata

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

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

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.
Cite as

Uli Fahrenberg, Christian Johansen, Georg Struth, and Krzysztof Ziemiański. A Kleene Theorem for Higher-Dimensional Automata. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@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/entities/document/10.4230/LIPIcs.CONCUR.2022.29},
  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}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2017.28
On Decidability of Concurrent Kleene Algebra

Authors: Paul Brunet, Damien Pous, and Georg Struth

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract
Concurrent Kleene algebras support equational reasoning about computing systems with concurrent behaviours. Their natural semantics is given by series(-parallel) rational pomset languages, a standard true concurrency semantics, which is often associated with processes of Petri nets. We use constructions on Petri nets to provide two decision procedures for such pomset languages motivated by the equational and the refinement theory of concurrent Kleene algebra. The contribution to the first problem lies in a much simpler algorithm and an EXPSPACE complexity bound. Decidability of the second, more interesting problem is new and, in fact, EXPSPACE-complete.
Cite as

Paul Brunet, Damien Pous, and Georg Struth. On Decidability of Concurrent Kleene Algebra. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brunet_et_al:LIPIcs.CONCUR.2017.28,
  author =	{Brunet, Paul and Pous, Damien and Struth, Georg},
  title =	{{On Decidability of Concurrent Kleene Algebra}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.28},
  URN =		{urn:nbn:de:0030-drops-77881},
  doi =		{10.4230/LIPIcs.CONCUR.2017.28},
  annote =	{Keywords: Concurrent Kleene algebra, series-parallel pomsets, Petri nets}
}
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