On the homology of small categories and asynchronous transition systems
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.
scientific article; zbMATH DE number 2153120