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.
Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp.439-471