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The Homology of Partial Monoid Actions and Petri Nets

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Abstract

The aim of this paper is to study the homology theory of partial monoid actions and apply it to computing the homology groups of mathematical models for concurrency. We study the Baues–Wirsching homology groups of a small category associated with a partial monoid action on a set. We prove that these groups can be reduced to the Leech homology groups of the monoid. For a trace monoid with a partial action on a set, we build a complex of free Abelian groups for computing the homology groups of this small category. It allows us to solve the problem posed by the author on the construction of an algorithm to computing the homology groups of elementary Petri nets. We describe the algorithm and give examples of computing the homology groups.

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Authors and Affiliations

  1. Komsomolsk-on-Amur State Technical University, prosp. Lenina, 27, Komsomolsk-on-Amur, 681013, Russian Federation

    Ahmet A. Husainov

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  1. Ahmet A. Husainov
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Correspondence to Ahmet A. Husainov.

Additional information

This work was performed as a part of the Strategic Development Program at the National Educational Institutions of the Higher Education, N 2011-PR-054. The paper was partially supported by the Scientific-Educational Center of Supercomputer Technology in the Far East Federal Region, under contract 2205/1-2011.

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Husainov, A.A. The Homology of Partial Monoid Actions and Petri Nets. Appl Categor Struct 21, 587–615 (2013). https://doi.org/10.1007/s10485-012-9280-9

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  • DOI: https://doi.org/10.1007/s10485-012-9280-9

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