Computing the Reveals Relation in Occurrence Nets

TL;DR

This paper introduces an efficient method to compute the reveals relation in Petri net unfoldings, improving bounds and providing algorithms with practical implementation for analyzing causal relations in systems.

Contribution

It significantly improves the bounds for deciding the reveals relation and presents an efficient algorithm with implementation for its computation in Petri net unfoldings.

Findings

Improved bounds on prefix size for reveals relation decision

Development of an efficient algorithm for computing the reveals relation

Implementation and experimental validation of the algorithm

Abstract

Petri net unfoldings are a useful tool to tackle state-space explosion in verification and related tasks. Moreover, their structure allows to access directly the relations of causal precedence, concurrency, and conflict between events. Here, we explore the data structure further, to determine the following relation: event a is said to reveal event b iff the occurrence of a implies that b inevitably occurs, too, be it before, after, or concurrently with a. Knowledge of reveals facilitates in particular the analysis of partially observable systems, in the context of diagnosis, testing or verification; it can also be used to generate more concise representations of behaviours via abstractions. The reveals relation was previously introduced in the context of fault diagnosis, where it was shown that the reveals relation was decidable: for a given pair a,b in the unfolding U of a safe Petri net N, a finite prefix P of U is sufficient to decide whether or not a reveals b. In this paper, we first considerably improve the bound on |P|. We then show that there exists an efficient algorithm for computing the relation on a given prefix. We have implemented the algorithm and report on experiments.