Spotlight Abstraction with Shade Clustering -- Automatic Verification of Parameterised Systems

Abstract

Parameterised verification is concerned with checking global properties of systems composed of an arbitrary number of processes. An approach to this undecidable problem is combining symmetry arguments with spotlight abstraction. This allows to construct small models of systems on which the properties can be checked. Spotlight abstraction partitions the systems processes into a spotlight and a shade. Shade processes are summarised into a single approximative component and the loss of information is modelled by a third truth value unknown. Thus, a verification run may also return unknown, which does not allow to draw any conclusions whether the property holds or not.Here we introduce an extension of spotlight abstraction called shade clustering, which allows to divide the shade into multiple approximative components and thus to preserve more definite information under abstraction. Finding suitable clusters is not straightforward. Moreover, an inadequate clustering can lead to an unnecessary explosion of the abstract state space. Therefore, we present an automatic abstraction refinement framework for verifying parameterised systems. Based on abstract counterexamples, refinement is iteratively performed by either adding new predicates, shifting processes from the shade to the spotlight, or building appropriate shade clusters. Experimental results show that our shade clustering-based approach can significantly speed up parameterised verification.

Parameterisation of Three-Valued Abstractions

“…technique for concurrent software systems is three-valued spotlight abstraction [12,14,15]. In previous works [16,17],we have demonstrated that verifying concurrent systems via spotlight abstraction and three-valued model checking can significantly outperform approaches based on boolean predicate abstraction [2].…”

“…In preliminary experiments,we applied our procedure to multiple-resource allocation systems 3 with up to 25 processes and 140 variable dependencies,and we checked safety as wellas liveness properties. W e compared verification under the pure three-valued approach (which has proven to be generally successfulfor concurrent systems in [17,14,15]) with verification under our novel approach with parameterisation. In several cases where the pure three-valued approach failed due to an out-of-memory exception,our new technique was capable of returning a definite verification result.…”