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Higher-Dimensional Automata: Extension to Infinite Tracks

Authors Luc Passemard , Amazigh Amrane , Uli Fahrenberg

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ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • Higher-dimensional automata
  • concurrency theory
  • omega pomsets
  • Büchi acceptance
  • Muller acceptance
  • interval pomsets
  • pomsets with interfaces

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Abstract

We introduce higher-dimensional automata for infinite interval ipomsets (ω-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by ω-HDAs under Büchi and Muller semantics. We show that Muller acceptance is more expressive than Büchi acceptance and, in contrast to the finite case, both semantics do not yield languages closed under subsumption. Then, we adapt the original rational operations to deal with ω-HDAs and show that while languages of ω-HDAs are ω-rational, not all ω-rational languages can be expressed by ω-HDAs.

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Luc Passemard, Amazigh Amrane, and Uli Fahrenberg. Higher-Dimensional Automata: Extension to Infinite Tracks. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSCD.2025.31

Author Details

Luc Passemard
  • IRIF & Université Paris Cité, Paris, France
Amazigh Amrane
  • EPITA Research Laboratory (LRE), Le Kremlin-Bicêtre, France
Uli Fahrenberg
  • EPITA Research Laboratory (LRE), Le Kremlin-Bicêtre, France

Funding

  • Passemard, Luc: This work was done while the first author was a Master’s intern at EPITA.

Acknowledgements

The authors are grateful to anonymous referees for their comments and corrections.

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