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2003 State spaces and dipaths up to dihomotopy
Martin Raussen
Homology Homotopy Appl. 5(2): 257-280 (2003).


Geometric models have been used by several authors to describe the behaviour of concurrent sytems in computer science. A concurrent computation corresponds to an oriented path (dipath) in a (locally) partially ordered state space, and dihomotopic dipaths correspond to equivalent computations. This paper studies several invariants of the state space in the spirit of those of algebraic topology, but taking partial orders into account as an important part of the structure. We use several categories of fractions of the fundamental category of the state space and define and investigate the related quotient categories of "components". For concurrency applications, the resulting categories can be interpreted as a dramatic reduction of the size of the state space to be considered.


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Martin Raussen. "State spaces and dipaths up to dihomotopy." Homology Homotopy Appl. 5 (2) 257 - 280, 2003.


Published: 2003
First available in Project Euclid: 28 June 2004

zbMATH: 1034.68020
MathSciNet: MR1994946

Rights: Copyright © 2003 International Press of Boston

Vol.5 • No. 2 • 2003
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