The cubical homology of trace monoids

This article contains an overview of the results of the author's study in the field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid actions is described. Algorithms for computing the homology groups of asynchronous systems, Petri nets, and Mazurkiewicz trace languages are shown.
The main results of the paper were reported at the International conference «Toric Topology and Automorphic Functions» (September, 5–10th, 2011, Khabarovsk, Russia).