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Mathematics > Algebraic Topology

arXiv:math/0701552 (math)
[Submitted on 19 Jan 2007 (v1), last revised 15 May 2008 (this version, v4)]

Title:Towards a homotopy theory of process algebra

Authors:Philippe Gaucher
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Abstract: This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimensional automata (HDA): one non-degenerate full $n$-dimensional cube (no more no less) in the underlying space of the time flow corresponding to the concurrent execution of $n$ actions. This result will enable us in future papers to develop a homotopical approach of process algebras. Indeed, several homological constructions related to the causal structure of time flow are possible only in the framework of flows.
Comments: 33 pages ; LaTeX2e ; 1 eps figure ; package semantics included ; v2 HDA paradigm clearly stated and simplification in a homotopical argument ; v3 "bug" fixed in notion of non-twisted shell + several redactional improvements ; v4 minor correction : the set of labels must not be ordered ; published at this http URL
Subjects: Algebraic Topology (math.AT); Category Theory (math.CT)
MSC classes: 55P99, 68Q85
Cite as: arXiv:math/0701552 [math.AT]
  (or arXiv:math/0701552v4 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.math/0701552
Journal reference: Homology Homotopy and Applications, vol. 10 (1):p.353-388, 2008
Related DOI: https://doi.org/10.4310/HHA.2008.v10.n1.a16

Submission history

From: Philippe Gaucher [view email]
[v1] Fri, 19 Jan 2007 18:49:28 UTC (31 KB)
[v2] Tue, 20 Feb 2007 18:56:51 UTC (33 KB)
[v3] Wed, 9 Apr 2008 14:30:46 UTC (36 KB)
[v4] Thu, 15 May 2008 09:35:15 UTC (37 KB)
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