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DOI: 10.4230/LIPIcs.CSL.2026.43

Kamp Theorem for Pomset Languages of Higher Dimensional Automata

Authors: Emily Clement, Enzo Erlich, and Jérémy Ledent

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp’s theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets (LTL_Poms), and show that it is equivalent to FO.

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Emily Clement, Enzo Erlich, and Jérémy Ledent. Kamp Theorem for Pomset Languages of Higher Dimensional Automata. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 43:1-43:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clement_et_al:LIPIcs.CSL.2026.43,
  author =	{Clement, Emily and Erlich, Enzo and Ledent, J\'{e}r\'{e}my},
  title =	{{Kamp Theorem for Pomset Languages of Higher Dimensional Automata}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{43:1--43:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.43},
  URN =		{urn:nbn:de:0030-drops-254685},
  doi =		{10.4230/LIPIcs.CSL.2026.43},
  annote =	{Keywords: Higher dimensional automata, temporal logic, Kamp’s theorem}
}

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Kamp Theorem for Pomset Languages of Higher Dimensional Automata

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