Probabilistic unfoldings and partial order fairness in Petri nets

Abstract

The article investigates fairness and conspiracy in a probabilistic framework, based on unfoldings of Petri nets. Here, the unfolding semantics uses a new, cluster-based view of local choice. The algorithmic construction of the unfolding proceeds on two levels, choice of steps inside conflict clusters, where the choice may be fair or unfair, and the policy controlling the order in which clusters may act; this policy may or may not conspire, e.g., against a transition. In the context of an example where conspiracy can hide in the partial order behavior of a life and 1-safe Petri net, we show that, under non-degenerate i.i.d. randomization on both levels, both conspiracy and unfair behavior have probability 0. The probabilistic model, using special Gibbs potentials, is presented here in the context of 1-safe nets, but extends to any Petri net.