BibTeX
@MISC{Sokolowski98homotopyin,
author = {Stefan Sokolowski},
title = {Homotopy in Concurrent Processes},
year = {1998}
}
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Abstract
Homotopy in concurrent processes In theories of job scheduling and of distributed computing, there have been many attempts to introduce tools originating from algebraic and combinatorial topology, such as homotopy groups. Informally, the fundamental (or first homotopy) group gives an account of the nature of "holes" in a topological space. In the realm of processes, such holes may correspond to forbidden configurations; e.g. where more than one process is within the same critical region. However, many topological properties, technically necessary for the construction of the fundamental group, have no counterparts, or only artificial ones, in concurrent processes. The paths corresponding to process executions are not cyclic, because time only flows forwards, and they cannot be as naturally composed as looping paths in topological spaces. The fundamental "group" lacks therefore its group operations. This paper puts forward a simple remedy for the shortcomings: if you cannot find a usefu...
