On the homology of small categories and asynchronous transition systems
type: Item
instance of: scholarly article
title: On the homology of small categories and asynchronous transition systems
zbMATH Open document ID: 1078.18005
author: Ahmet A. Khusainov
published in: Homology, Homotopy and Applications
publication date: 2005-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/51917
full work available at URL: volume6-1.htm
review text: The main subject of this paper is devoted to the calculation of homology groups of concurrent computing models. In a previous work, the author, together with \textit{V. V. Tkachenko} [KhGPU, 23--33 (2003); http://www.Knastu.ru], proved that the category of asyncronous transition systems admits a functor into the category of pointed sets over partially commutative monoids, permitting now to define homology groups for such systems. The interpretation and computation of the first homology group of the small category given by a rewriting system shows that its elements can be viewed as the equivalence classes of the flows in the graph of the rewriting system. Then, the homology groups of asyncronous transition systems and Petri nets are obtained.
reviewed by: Viorel Mihai Gontineac
Mathematics Subject Classification ID: 18B20
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 68M14
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 2153120
zbMATH Keywords: homology of categories
zbMATH Keywords: asynchronous system
zbMATH Keywords: Petri nets
MaRDI profile type: Publication
OpenAlex ID: W2103614868
DOI: 10.4310/HHA.2004.V6.N1.A22
description: scientific article; zbMATH DE number 2153120