Periodic structure and liveness of Petri net rings

For k/spl ges/2, let R/sup k/ be the ring consisting of k identical copies C/sub 0/, C/sub 1/, ..., C/sub k-1/ of a component C, where C is given as a Petri net. Assume that all components of R/sup k/ except possibly C/sub 0/ have an identical initial marking. We consider the problem of testing whether all rings R/sup k/, k/spl ges/2, are live, for the case when the rings are either state machines or marked graphs. We present various sufficient conditions under which all rings are live, and discuss the complexity issue of testing the liveness of marked graph rings. Such conditions can greatly simplify the analysis of large scale process rings given as a Petri net.