A Note on Persistent Petri Nets
Petri nets have traditionally been motivated by their ability to express concurrency. Subclasses of Petri nets with concurrency but without choices or conflicts have been studied extensively. One of the best known - and comparatively restricted - such class are the marked graphs . However, perhaps the largest class of (intuitively) choice-free nets are the persistent nets , a class of nets that is significantly larger than marked graphs.
Some early results about persistent nets are Keller’s theorem , which will be recalled in a later part of this paper, and the famous semilinearity result of Landweber and Robertson , which states that the set of reachable markings of a persistent net is semilinear. In this paper, we show that in bounded persistent nets, the smallest cycles of its reachability graph enjoy a uniqueness property.
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