Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Kleene Theorem for Higher-Dimensional Automata   We prove a Kleene theorem for higher-dimensional automata. It states that the
languages they recognise are precisely the rational subsumption-closed sets of
labelled interval orders. Higher-dimensional automata are general models of
concurrency that subsume, for instance, Petri nets, event structures and
asynchronous transition systems. We formalise them as presheaves over labelled
precube categories. Interval orders are used as non-interleaving semantics of
concurrent or distributed systems where events have duration. For the proof, we
introduce higher-dimensional automata with interfaces and several tools
inspired by model categories, such as cylinders, necessary for handling cycles,
and (co)fibrations.

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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin