An Incremental and Modular Technique for Checking LTL∖X Properties of Petri Nets

Abstract

Abstract. Model-checking is a powerful and widespread technique for the verification of finite state concurrent systems. However, the main hindrance for wider application of this technique is the well-known state explosion problem. Modular verification is a promising natural approach to tackle this problem. It is based on the "divide and conquer" principle and aims at deducing the properties of the system from those of its components analysed in isolation. Unfortunately, several issues make the use of modular verification techniques difficult in practice. First, deciding how to partition the system into components is not trivial and can have a significant impact on the resources needed for verification. Second, when model-checking a component in isolation, how should the environment of this component be described? In this paper, we address these problems in the framework of model-checking LTL\X action-based properties on Petri nets. We propose an incremental and modular verification approach where the system model is partitioned according to the actions occurring in the property to be verified and where the environment of a component is taken into account using the linear place invariants of the system.

A Counterexample-Based Incremental and Modular Verification Approach

“…In [16], we proposed an incremental and compositional verification approach where the system model is partitioned according to the actions occurring in the property to be verified and where the environment of a component is taken into account using the linear place invariants of the system. The first component contains only the actions occurring in the formula, and each newly added component is obtained based on the neighbourhood of those already analysed.…”

“…Since, it has been empirically shown that breaking up a system is a difficult task (see for instance [5]), we assume here that the system is already given as a set of components sharing global actions. In order to use an approach derived from [16], either all actions of the formula belong to a single component, or we compose all those containing such actions, to start with. Note that [16] considered Petri nets models, whereas the technique is here generalised to Labelled Transitions Systems (LTSs).…”

“…In order to use an approach derived from [16], either all actions of the formula belong to a single component, or we compose all those containing such actions, to start with. Note that [16] considered Petri nets models, whereas the technique is here generalised to Labelled Transitions Systems (LTSs). In general, the LTS and a counterexample can be derived on-the-fly as long as an initial state and a transition relation are provided.…”

“…Even though the combination of both techniques from [15] and [16] is quite easy, it also leads to improvements. The definition of aggregates contains a more elaborate structure for detecting internal deadlocks, making things way easier at the composition stage.…”

A Parallel Construction of the Symbolic Observation Graph: the Basis for Efficient Model Checking of Concurrent Systems

“…Partial order approaches (e.g., [14,30]) exploit the fact that interleaving concurrent actions are equivalent, and only a representative interleaving needs to be explored, leading to a significant reduction of the constructed state space. Modularity is also used by limiting the exploration of state space to the parts that concern the property to check [21,26,29]. Symbolic techniques [4,13,15], on the other hand, represent the state space in a compressed manner.…”