Regular Abstractions for Array Systems

Verifying safety and liveness over array systems is a highly challenging problem. Array systems naturally capture parameterized systems such as distributed protocols with an unbounded number of processes. Such distributed protocols often exploit process IDs during their computation, resulting in array systems whose element values range over an infinite domain. In this paper, we develop a novel framework for proving safety and liveness over array systems. The crux of the framework is to overapproximate an array system as a string rewriting system (i.e. over a finite alphabet) by means of a new predicate abstraction that exploits the so-called indexed predicates. This allows us to tap into powerful verification methods for string rewriting systems that have been heavily developed in the last few decades (e.g. regular model checking). We demonstrate how our method yields simple, automatically verifiable proofs of safety and liveness properties for challenging examples, including Dijkstra's self-stabilizing protocol and the Chang-Roberts leader election protocol

Counting dynamically synchronizing processes

We address the problem of automatically establishing correctness for programs generating an arbitrary number of concurrent processes and manipulating variables ranging over an infinite domain. The programs we consider can make use of the shared variables to count and synchronize the spawned processes. This allows them to implement intricate synchronization mechanisms, such as barriers. Automatically verifying correctness, and deadlock freedom, of such programs is beyond the capabilities of current techniques. For this purpose, we make use of counting predicates that mix counters referring to the number of processes satisfying certain properties and variables directly manipulated by the concurrent processes. We then combine existing works on counter, predicate, and constrained monotonic abstraction and build a nested counter example based refinement scheme for establishing correctness (expressed as non-reachability of configurations satisfying counting predicates formulas). We have implemented a tool (Pacman, for predicated constrained monotonic abstraction) and used it to perform parameterized verification on several programs whose correctness crucially depends on precisely capturing the number of processes synchronizing using shared variables.Funding agencies: 12.04 CENIIT project</p