On the homology of small categories and asynchronous transition systems

Abstract

This work is devoted to an interpretation and computation of the first homology groups of the small category given by a rewriting system. It is shown that the elements of the first homology group may be regarded as the equivalence classes of the flows in a graph of the rewriting system. This is applied to calculating the homology groups of asynchronous transition systems and Petri nets. Examples of calculations are given.