Simulations as Homotopies

Hess, Kathryn; Parent, Paul-Eugène; Tonks, Andrew; Worytkiewicz, Krzysztof

doi:10.1016/j.entcs.2004.08.016

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Cited by 2 publications

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“…The desire to establish this result motivated the research in this article, as it has an intriguing application in concurrency theory [14]. Finally, we give a proof of properness in Section 6.…”

Section: Introductionmentioning

confidence: 94%

A model structure à la Thomason on 2-Cat

Worytkiewicz

Hess

Parent

et al. 2007

Journal of Pure and Applied Algebra

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Section: Introductionmentioning

confidence: 94%

A model structure à la Thomason on 2-Cat

Worytkiewicz

Hess

Parent

et al. 2007

Journal of Pure and Applied Algebra

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“…Finally, our introduction of iHDA morphisms reminiscent of cofibrations and trivial fibrations hints at some notion of factorisation systems for HDAs. Weak factorisation systems and model categories have been considered in a bisimulation context for example in [24,21], and we wonder about the connections. of the quotient of Z under isomorphisms, so except for the labelling, this is again the same as our of Section 2.…”

Section: Discussionmentioning

confidence: 99%

A Kleene Theorem for Higher-Dimensional Automata

Fahrenberg¹,

Johansen²,

Struth³

et al. 2022

Preprint

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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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Simulations as Homotopies

Cited by 2 publications

References 15 publications

A model structure à la Thomason on 2-Cat

A model structure à la Thomason on 2-Cat

A Kleene Theorem for Higher-Dimensional Automata

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