Homology, Homotopy and Applications

Some geometric perspectives in concurrency theory

Eric Goubault

Full-text: Open access

Abstract

Concurrency, i.e., the domain in computer science which deals with parallel (asynchronous) computations, has very strong links with algebraic topology; this is what we are developing in this paper, giving a survey of "geometric" models for concurrency. We show that the properties we want to prove on concurrent systems are stable under some form of deformation, which is almost homotopy. In fact, as the "direction" of time matters, we have to allow deformation only as long as we do not reverse the direction of time. This calls for a new homotopy theory: "directed" or di-homotopy. We develop some of the geometric intuition behind this theory and give some hints about the algebraic objects one can associate with it (in particular homology groups). For some historic as well as for some deeper reasons, the theory is at a stage where there is a nice blend between cubical, $\omega$-categorical and topological techniques.

Article information

Source
Homology Homotopy Appl., Volume 5, Number 2 (2003), 95-136.

Dates
First available in Project Euclid: 28 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.hha/1088453323

Mathematical Reviews number (MathSciNet)
MR1994942

Zentralblatt MATH identifier
1034.68059

Citation

Goubault, Eric. Some geometric perspectives in concurrency theory. Homology Homotopy Appl. 5 (2003), no. 2, 95--136. https://projecteuclid.org/euclid.hha/1088453323


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