Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

TL;DR

This paper introduces a semi-structural method using minimax basis reachability graphs to efficiently verify nonblockingness in bounded Petri nets, avoiding full reachability graph construction.

Contribution

It presents a novel approach that simplifies nonblockingness verification by using minimax-BRGs and integer constraints, applicable even when deadlocks are present.

Findings

Nonblockingness can be verified via minimax-BRGs without full reachability graphs.

The method handles deadlock detection through maximal implicit firing sequences.

Approach is broadly applicable and computationally efficient.

Abstract

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.