Decomposition Theorems for Bounded Persistent Petri Nets
We show that the cycles of a finite, bounded, reversible, and persistent Petri net can be decomposed in the following sense. There exists in the reachability graph a finite set of transition-disjoint cycles such that any other cycle through a given marking is permutation equivalent to a sequential composition of cycles from this set.
We show that Parikh images of cycles of a finite, bounded, and persistent Petri net form an additive monoid with a finite set of transition-disjoint generators (for any two distinct generators Ψ(γ) and Ψ(γ′), Ψ(γ)(t) = 0 or Ψ(γ′)(t) = 0 for every transition t).
Persistent nets are a very general class of conflict-free nets. Boundedness means, as usual, that the reachability graph is finite. Reversibility means that the reachability graph is strongly connected.
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