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 behaviors 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| and show that the new bounds are optimal for the method presented. 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.
Highlights
Petri nets and their partial-order unfoldings [13, 4, 12] have long been used in model checking
In [1], we focus on reduced nets, i.e. where the contraction of facets has been carried out, and every event is a facet; in this framework, behavioural properties can be specified in a dedicated logic ERL, for which the synthesis problem is solved in [1]; the occurrence nets obtained in a canonical way from a logical formula belong to a distinguished subclass of reduced occurrence nets, the tight nets
We presented theoretical and algorithmic contributions towards the computation of the reveals relation
Summary
Petri nets (see e.g. [15, 14]) and their partial-order unfoldings [13, 4, 12] have long been used in model checking. We will focus on the problem of determining the following relation: an event a is said to reveal another event b iff, whenever a occurs, the occurrence of b is inevitable This does not imply that a and b are causally related (though they may be); b may have occurred before a, lie in the future of a, or even be concurrent to a. We have implemented the algorithm and report on experiments, notably on the following questions: how big is the prefix necessary to determine the reveals relation, and how much time does it take to compute said relation on a given prefix? We proceed as follows: Section 2 introduces Petri nets, their unfoldings, the reveals relation, and some of its salient properties.
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