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A Myhill-Nerode Theorem for Higher-Dimensional Automata

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13929))

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Abstract

We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular precisely if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible to distinguish between interleavings and concurrency. We also introduce deterministic HDAs and show that not all HDAs are determinizable, that is, there exist regular languages that cannot be recognised by a deterministic HDA. Using our theorem, we develop an internal characterisation of deterministic languages.

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Notes

  1. 1.

    Pronunciation: ell-oh-set.

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Acknowledgement

We are indebted to Amazigh Amrane, Hugo Bazille, Christian Johansen, and Georg Struth for numerous discussions regarding the subjects of this paper; any errors, however, are exclusively ours.

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Authors and Affiliations

  1. EPITA Research Laboratory (LRE), Le Kremlin-Bicêtre, France

    Uli Fahrenberg

  2. University of Warsaw, Warsaw, Poland

    Krzysztof Ziemiański

Authors
  1. Uli Fahrenberg
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  2. Krzysztof Ziemiański
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Correspondence to Uli Fahrenberg .

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Editors and Affiliations

  1. NOVA University Lisbon, Caparica, Portugal

    Luis Gomes

  2. University of Augsburg, Augsburg, Germany

    Robert Lorenz

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Fahrenberg, U., Ziemiański, K. (2023). A Myhill-Nerode Theorem for Higher-Dimensional Automata. In: Gomes, L., Lorenz, R. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. Lecture Notes in Computer Science, vol 13929. Springer, Cham. https://doi.org/10.1007/978-3-031-33620-1_9

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  • DOI: https://doi.org/10.1007/978-3-031-33620-1_9

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