Regular Model Checking Without Transducers (On Efficient Verification of Parameterized Systems)

Abstract

Abstract. We give a simple and efficient method to prove safety properties for parameterized systems with linear topologies. A process in the system is a finite-state automaton, where the transitions are guarded by both local and global conditions. Processes may communicate via broadcast, rendez-vous and shared variables. The method derives an overapproximation of the induced transition system, which allows the use of a simple class of regular expressions as a symbolic representation. Compared to traditional regular model checking methods, the analysis does not require the manipulation of transducers, and hence its simplicity and efficiency. We have implemented a prototype which works well on several mutual exclusion algorithms and cache coherence protocols.

Handling Parameterized Systems with Non-atomic Global Conditions

“…All existing automatic verification methods (e.g., [12,4,6,8,9,3,2]) are defined for parameterized systems where universal and existential conditions are evaluated atomically. Non-atomic versions of parameterized mutual exclusion protocols such as the Bakery algorithm and two-phase commit protocol have been studied with heuristics to discover invariants, ad-hoc abstractions, or semi-automated methods in [5,13,16,7].…”

“…The method presented in this paper is related to those in [3,2] in the sense that they also rely on combining over-approximation with symbolic backward reachability analysis. However, the papers [3,2] assume atomic global conditions.…”

“…However, the papers [3,2] assume atomic global conditions. As described above, the passage from the atomic to the non-atomic semantics is not trivial.…”

“…The labels of the nodes encode the local states of the processes, while the labels of the edges carry information about the data flow between the processes. Our verification method consists of three ingredients each of which is implemented by a fully automatic procedure: (i) a preprocessing phase in which a refinement protocol is used to translate the behaviour of a parameterized system with global conditions into a system with graph configurations; (ii) a model checking phase based on symbolic backward reachability analysis of systems with graph configurations; and (iii) an overapproximation scheme inspired by the ones proposed for systems with atomic global conditions in [3] and [2]. The over-approximation scheme is extended here in a non-trivial manner in order to cope with configurations which have graph structures.…”

A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

“…Our approach allows in contrast to carry out pre-post reasoning, invariance checking, as well as bounded analysis, for a larger class of systems. Techniques like those used in [ADHR07,AHDR08] could be integrated into our framework in the future in order to discover (local) invariants automatically.…”