AbstractThe free‐choice net is a subclass of the Petri net. It is a class which can explicitly represent both the essential concurrency and the nondeterministic aspects of the concurrent system. the class can be considered as an extension of the state machine where concurrency is included. It can also be considered as an extension of the marked graph where the nondeterministic aspect is included. There have been a number of studies on the free choice net with the dynamic constraint that it should be live and safe (LSFC). This LSFC net has a structural feature: it can be decomposed into a set of strongly connected state machines (called S components). If the minimal set of S components (S decomposition set) covering the given LSFC net can be efficiently determined, it will be possible to derive powerful methods in the analysis and performance evaluation of the parallel system. This paper discusses the polynomial‐order algorithm that determines the S‐decomposition set for the LSFC net.