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. 1

We present the class of binary automaton, a new representation for the subsets of N^m that naturally extends the NDD ([25], [10]). We prove that the affine hull of the set of vectors represented by a binary automaton is computable in polynomial time. As application, we show that the set of place invariants [11] of a counter system (an extension of the Broadcast Protocols [16], [13], [12], the Reset/Transfer Petri Nets [15],[11] and the linear systems [18]), is computable in polynomial time.

We present an approach to verification of parameterized systems, which is based on program transformation technique known as supercompilation. In this approach the statements about safety properties of a system to be verified are translated into the statements about properties of the program that simulates and tests the system. The supercompilation is used then to establish the required properties of the program. In this paper we show that reachability analysis performed by supercompilation can be seen as the proof of a correctness condition by induction. We formulate suitable induction principles and proof strategies and illustrate their use by examples of verification of parameterized protocols.

In the paper we explain the technique of verification via supercompliation taking as an example verification of the parameterised Load Balancing Monitor system. We demonstrate detailed executable specification of the Load Balancing Monitor protocol in a functional programming language REFAL and discuss the result of its supercompilation by the supercompiler SCP4. This case study is interesting both from the point of view of verification and program specialization. From the point of view of verification, a new type of non-determinism is involved in the protocol, which has not been covered yet in previous applications of the technique. With regard to program specialization, we argued earlier that our approach to program verification may be seen as specialization of interpreters with respect to data [25]. We showed that by supercompilation of an interpreter of a simplest purely imperative programming language. The language corresponding to the Load Balancing Monitor protocol that we consider here has some features both of imperative and functional languages.

Abstract not found

We introduce the simple and efficient method of monotonic abstraction 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 over finite domains. The method of monotonic abstraction derives an over-approximation of the induced transition system that 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 that works well on several mutual exclusion algorithms and cache coherence protocols. 1.