Determinate STG decomposition of marked graphs

Abstract

STGs give a formalism for the description of asynchronous circuits based on Petri nets. To overcome the state explosion problem one may encounter during circuit synthesis, a nondeterministic algorithm for decomposing STGs was suggested by Chu and improved by one of the present authors. To find the best possible result the algorithm might produce, it would be important to know to what extent nondeterminism influences the result, i.e. to what extent the algorithm is determinate. The result of the algorithm clearly depends on the partition of output signals that has to be chosen initially. In general, it also depends on the order of computation steps. We prove that for live marked graphs — a subclass of Petri nets of definite practical importance in the area of circuit design — the decomposition result depends only on the signal partition. In the proof, we also characterise redundant places in these marked graphs as shortcut places; this easy-to-apply graph-theoretic characterisation is of independent interest.