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Logic and Languages of Higher-Dimensional Automata

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Developments in Language Theory (DLT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14791))

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Abstract

In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (\({\textsf {iiPoms} }_{\le k}\)) closed under order extension. We prove that languages of HDAs are MSO-definable. For the converse, we show that the order extensions of MSO-definable sets of \({\textsf {iiPoms} }_{\le k}\) are languages of HDAs. Furthermore, both constructions are effective. As a consequence, unlike the case of all pomsets, the order extension of any MSO-definable set of \({\textsf {iiPoms} }_{\le k}\) is MSO-definable.

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Notes

  1. 1.

    A strict partial order is a relation which is irreflexive, asymmetric and transitive. We will omit the qualifier “strict”.

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Authors and Affiliations

  1. EPITA Research Laboratory (LRE), Paris, France

    Amazigh Amrane, Hugo Bazille & Uli Fahrenberg

  2. Université Paris Cité, CNRS, IRIF, Paris, France

    Marie Fortin

Authors
  1. Amazigh Amrane
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  2. Hugo Bazille
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  3. Uli Fahrenberg
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  4. Marie Fortin
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Corresponding author

Correspondence to Hugo Bazille .

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Editors and Affiliations

  1. Loughborough University, Loughborough, UK

    Joel D. Day

  2. University of Göttingen, Göttingen, Germany

    Florin Manea

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Amrane, A., Bazille, H., Fahrenberg, U., Fortin, M. (2024). Logic and Languages of Higher-Dimensional Automata. In: Day, J.D., Manea, F. (eds) Developments in Language Theory. DLT 2024. Lecture Notes in Computer Science, vol 14791. Springer, Cham. https://doi.org/10.1007/978-3-031-66159-4_5

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  • DOI: https://doi.org/10.1007/978-3-031-66159-4_5

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