Irreducible Decompositions of Transformation Graphs by Assignment Techniques

Autonomous sequential networks are represent­ ed 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 sim­ pler graphs. An algorithm for obtaining the vari­ ous decompositions of a given transformation graph into irreducible factors is presented. The par­ ticular decompositions into a minimum number of factors and into factors of smallest size are di­ rectly reached by the method.