Irreducible decompositions of transformation graphs by assignment techniques

Autonomous sequential networks are represented by transformation graphs, i.e., finite directed graphs, each vertex of which has out degree one. A network that can be realized by a set of simpler, parallel networks corresponds to a transformation graph representable as a cartesian product of simpler graphs. An algorithm for obtaining the various decompositions of a given transformation graph into irreducible factors is presented. The particular decompositions into a minimum number of factors and into factors of smallest size are directly reached by the method.