On interleaving in {P,A}-Time Petri nets with strong semantics

TL;DR

This paper proves that for {P,A}-Time Petri nets with strong semantics, the union of state classes from different interleavings is convex and can be computed directly, enhancing reachability analysis efficiency.

Contribution

It demonstrates convexity of the union of state classes in {P,A}-TPN's CSCG and introduces a method to compute it without intermediate classes, improving reachability analysis.

Findings

Union of state classes is convex in {P,A}-TPN.

Can compute the convex union directly, avoiding intermediate classes.

Enhances the efficiency of reachability analysis.

Abstract

This paper deals with the reachability analysis of {P,A}-Time Petri nets ({P,A}-TPN in short) in the context of strong semantics. It investigates the convexity of the union of state classes reached by different interleavings of the same set of transitions. In BB08, the authors have considered the T-TPN model and its Contracted State Class Graph (CSCG) and shown that this union is not necessarily convex. They have however established some sufficient conditions which ensure convexity. This paper shows that for the CSCG of {P,A}-TPN, this union is convex and can be computed without computing intermediate state classes. These results allow to improve the forward reachability analysis by agglomerating, in the same state class, all state classes reached by different interleavings of the same set of transitions (abstraction by convex-union).