On Persistent Reachability in Petri Nets

The notion of persistency, based on the rule “no action can disable another one” is one of the classical notions in concurrency theory. In this paper, we deal with arbitrary place/transition nets, but concentrate on their persistent computations. It leads to an interesting decision problem: Is a given marking reachable with a persistent run? In order to study the persistent-reachability problem we define a class of nets, called nonviolence nets. We show that inhibitor nets can be simulated by the nonviolence nets, and that reachability and coverability problems are undecidable in the class of the nonviolence nets. Then we prove more: nonviolence nets can be simulated by the inhibitor nets, thus they are computationally equivalent to Turing machines.