A Survey of Regular Model Checking

Abstract

Regular model checking is being developed for algorithmic verification of several classes of infinite-state systems whose configurations can be modeled as words over a finite alphabet. Examples include parameterized systems consisting of an arbitrary number of homogeneous finite-state processes connected in a linear or ring-formed topology, and systems that operate on queues, stacks, integers, and other linear data structures. The main idea is to use regular languages as the representation of sets of configurations, and finite-state transducers to describe transition relations. In general, the verification problems considered are all undecidable, so the work has consisted in developing semi-algorithms, and decidability results for restricted cases. This paper provides a survey of the work that has been performed so far, and some of its applications.

Proving Liveness by Backwards Reachability

“…We have implemented a verification method based on Corollary 1 and Theorem 2 in the framework of Regular Model Checking [7], and applied it to a number of well-known parameterized mutual exclusion protocols.…”

“…Dijkstra's algorithm takes significantly longer time to verify because it contains an action where a global variable is set. Computing the effect of arbitrarily many executions of such an action is relatively expensive in our current implementation [7]. Comparison with Related Work.…”

“…We describe an implementation of our method in the framework of Regular Model Checking [7]. For several examples, the proof rule of Section 4 computes a strict underapproximation of the set 3F ; therefore we also present a complementary rule which can prove termination for those examples.…”

“…Our example shows that backwards reachability analysis (which is guaranteed to terminate [5]) can prove liveness properties for some of these systems, although in general they are undecidable. Finally, we have implemented our technique in the framework of regular model checking [7]. We prove starvation-freedom for several parameterized mutual exclusion protocols; some of which we have previously not been able to prove starvation-freedom for using transitive closure computation [6].…”

CSL Model Checking Algorithms for Infinite-State Structured Markov Chains

“…However, there is related work on model checking infinite state systems, such as, e.g., Boucherie product processes [4], probabilistic lossy channel systems [18], regular model checking [1], recursive Markov chains [8] and probabilistic pushdown automata [5], as well as on transient analysis of queueing networks [14,10] and on transient analysis of infinite-state systems with uniformization [19,6]. None of this work, however, addresses the model checking questions that we address.…”