On the reversibility problem in a class of synthesized Petri nets

This paper enhances a Petri net synthesis theory with the capability to deal with reversibility, which is an important property related to the concept of error recovery in manufacturing. The theory has been proposed to synthesize a class of Petri nets for modeling shared-resource automated manufacturing systems. The class of nets has been shown to be conservative (boundedness) and possess structural liveness under two sufficient conditions which can be checked structurally by an algorithm without enumerating the states. In this paper it is further proven that under two sufficient conditions the class of nets possesses reversibility. It is shown that the first condition for reversibility is the same as that for liveness while the second condition for reversibility is contained in that for liveness. Thus the liveness-checking algorithm can be used to check reversibility with slight modification.