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Topologie Algébrique Dirigée et Concurrence

Abstract : In order to analyze concurrency by means of algebraic topology, we study the properties of the category of partially ordered spaces. The "fundamental category" functor sends any such space to a small loop-free category whose size of the set of objects is way too large in respect with the information it contains. Thus we are led to define the notion of category of components of a small loop-free category and prove a theorem which establishes the interest of this definition as well as a "van Kampen like" theorem which leads to effective calculations. Then we are able to modelize programs written in PV langage (the original Dijkstra's one) : several examples are detailed.
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Contributor : Emmanuel Haucourt <>
Submitted on : Monday, September 17, 2007 - 11:58:29 AM
Last modification on : Saturday, March 28, 2020 - 2:11:31 AM
Long-term archiving on: : Friday, April 9, 2010 - 2:16:56 AM


  • HAL Id : tel-00172472, version 1



Emmanuel Haucourt. Topologie Algébrique Dirigée et Concurrence. Autre [cs.OH]. Université Paris-Diderot - Paris VII, 2005. Français. ⟨tel-00172472⟩



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