Unfolding and finite prefix for nets with read arcs

Abstract

Petri nets with read arcs are investigated w.r.t their unfolding, where read arcs model reading without consuming, which is often more adequate than the destructive-read-and-rewrite modelled with loops in ordinary nets. The paper redefines the concepts of a branching process and unfolding for nets with read arcs and proves that the set of reachable markings of a net is completely represented by its unfolding. The specific feature of branching processes of nets with read arcs is that the notion of a co-set is no longer based only on the binary concurrency relation between the elements of the unfolding, contrary to ordinary nets. It is shown that the existing conditions for finite prefix construction (McMillan's one and its improvement by Esparza et al.) can only be applied for a subclass of nets with read arcs, the so-called read-persistent nets. Though being restrictive, this subclass is sufficiently practical due to its conformance to the notion of hazard-freedom in logic circuits. The latter appear to be one of the most promising applications for nets with read arcs.