An Application of Algebraic Topology to Computer Sciences

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Rasouli Pichahi, Majid | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44643 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fanai, HamidReza
Abstract:
In this thesis we study one of the applications of algebraic topology to computer science and define some tools to analyze concurrent programs. For this purpose a geometric space is corresponded to every concurrent program and a partial order is considered on this space, so every path on it corresponds to an execution of the program. Some of these paths which are dihomotop (homotop in partial ordered spaces) with each other induce the same execution of the program. By defining “Fundamental Category” in which objects are points of the space and morphisms are dihomotopy classes, the space that should be analyzed shrinks to a smaller one. By defining component category in the next step, without losing necessary information, we’ll even have a smaller category and less computation to do
Keywords:
Directed Algebraic Topology ; Directed Homotopy ; Concurrency ; Fundamental Category ; Component Category ; Van Kampen Theorem

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