Topologie/Informatique théorique
Automate parallèle à homotopie près (I)
[Concurrent process up to homotopy (I)]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 593-596.

Globular CW-complexes and flows are both geometric models of concurrent processes which allow to model in a precise way the notion of dihomotopy. Dihomotopy is an equivalence relation which preserves computer-scientific properties like the presence or not of deadlock. One constructs an embedding from globular CW-complexes to flows and one proves that two globular CW-complexes are dihomotopic if and only if the corresponding flows are dihomotopic.

Les CW-complexes globulaires et les flots sont deux modélisations géométriques des automates parallèles qui permettent de formaliser la notion de dihomotopie. La dihomotopie est une relation d'équivalence sur les automates parallèles qui préserve des propriétés informatiques comme la présence ou non de deadlock. On construit un plongement des CW-complexes globulaires dans les flots et on démontre que deux CW-complexes globulaires sont dihomotopes si et seulement si les flots associés sont dihomotopes.

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Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00118-3
Gaucher, Philippe 1

1 Institut de recherche mathématique avancée, ULP et CNRS, 7, rue René Descartes, 67084 Strasbourg cedex, France
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Gaucher, Philippe. Automate parallèle à homotopie près (I). Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 593-596. doi : 10.1016/S1631-073X(03)00118-3. http://www.numdam.org/articles/10.1016/S1631-073X(03)00118-3/

[1] Bousfield, A.K.; Kan, D.M. Homotopy Limits, Completions and Localizations, Lecture Notes in Math., 304, Springer-Verlag, Berlin, 1972

[2] Gaucher, P. Homotopy invariants of higher dimensional categories and concurrency in computer science, Math. Structures Comput. Sci., Volume 10 (2000) no. 4, pp. 481-524

[3] Gaucher, P. A convenient category for the homotopy theory of concurrency (2002) | arXiv

[4] Gaucher, P.; Goubault, E. Topological deformation of higher dimensional automata (2001 à paraître dans Homology, Homotopy and Applications) | arXiv

[5] Goerss, P.G.; Jardine, J.F. Simplicial Homotopy Theory, Birkhäuser, Basel, 1999

[6] L.G. Lewis, The stable category and generalized Thom spectra, Ph.D. thesis, University of Chicago, 1978

[7] Pratt, V. Modeling concurrency with geometry, Proc. of the 18th ACM Symposium on Principles of Programming Languages, ACM Press, 1991

[8] Steenrod, N.E. A convenient category of topological spaces, Michigan Math. J., Volume 14 (1967), pp. 133-152

[9] Whitehead, G.W. Elements of Homotopy Theory, Springer-Verlag, New York, 1978

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