Monotonic Abstraction: On Efficient Verification of Parameterized Systems

Abstract

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.

Program Specialization for Verifying Infinite State Systems: An Experimental Evaluation

“…Finally, we would like to mention that our verification method can be regarded as complementary to the methods for the verification of infinite state systems based on abstractions [2,4,8,11,14,19,20]. These methods work by constructing approximations of the set of reachable states that satisfy a given property.…”

“…In particular, an extension of our method could be done by replacing the bottom-up, exact computation of the perfect model performed in Phase (2), by an approximated computation in the style of [4,14]. (As already mentioned, this extension would require the computation of both over-approximations and under-approximations of models, because of the presence of negation.)…”

“…In order to cope with this limitation, various decidable subclasses of systems and formulas have been identified (see, for instance, [1,15]). Other approaches enhance finite state model checking by using more general deductive techniques (see, for instance, [33,37]) or using abstractions, by which one can compute conservative approximations of the set of states verifying a given property (see, for instance, [2,6,8,11,19,20]). …”

“…In Phase (1) the CLP specification is specialized with respect to the initial state of the system and the temporal property to be verified, and in Phase (2) the construction of the perfect model of the specialized program is performed via a bottom-up evaluation. The main goal of Phase (1) is to derive a specialized program for which the bottom-up model construction of Phase (2) terminates. We have shown in an experimental way that, indeed, Phase (2) terminates in most examples without the need for abstractions.…”

“…The main goal of Phase (1) is to derive a specialized program for which the bottom-up model construction of Phase (2) terminates. We have shown in an experimental way that, indeed, Phase (2) terminates in most examples without the need for abstractions.…”