Constrained Monotonic Abstraction: A CEGAR for Parameterized Verification

Abstract

Abstract. In this paper, we develop a counterexample-guided abstraction refinement (CEGAR) framework for monotonic abstraction, an approach that is particularly useful in automatic verification of safety properties for parameterized systems. The main drawback of verification using monotonic abstraction is that it sometimes generates spurious counterexamples. Our CEGAR algorithm automatically extracts from each spurious counterexample a set of configurations called a "Safety Zone" and use it to refine the abstract transition system of the next iteration. We have developed a prototype based on this idea; and our experimentation shows that the approach allows to verify many of the examples that cannot be handled by the original monotonic abstraction approach.

Abstracting and Counting Synchronizing Processes

“…In this work, we build on such methods and strengthen the obtained transition systems using automatically generated invariants in order to obtain counter machines that over-approximate the concurrent program behavior and still faithfully capture the barriers semantics. We then build on our work on constrained monotonic abstraction [4] in order to decide state reahability by automatically generating and refining monotonic over-approximations for such systems.…”

“…We generate these invariants using classical thread modular analysis techniques [14]. 4. We leverage on existing constrained monotonic abstraction techniques [17,4] to implement the inner loop and to address the state reachability problem.…”

“…4. We leverage on existing constrained monotonic abstraction techniques [17,4] to implement the inner loop and to address the state reachability problem. 5.…”

“…In [16], the authors adopt symbolic representations that can track inter-thread predicates. This yields a non monotonic system and the authors force monotonicity as in [17,4]. They however do not explain how to refine the obtained decidable monotonic abstraction for an undecidable problem.…”

“…In addition, and as stated earlier, over-approximating the concurrent programs we target with (monotonic) well structured transition systems would result in spurious runs. The works that seem most closely related are [4,10]. We introduced (constrained) monotonic abstraction in [17,4].…”