Tests, Proofs and Refinements

Abstract

Counter-example driven refinement using predicate abstraction has been successfully used to find bugs and verify properties in programs [1]. We describe two recent advances in counter-example driven refinement:

- We present a counter-example driven refinement technique that combines verification and testing [4]. In our approach, we simultaneously use testing and proving, with the goal of either finding a test that demonstrates that P violates ϕ, or a proof that demonstrates that all executions of P satisfy ϕ. The most interesting aspect of the approach is that unsuccessful proof attempts are used to generate tests, and unsuccessful attempts to generate tests are used to refine proofs. Besides being theoretically elegant, the approach has practical advantages –precise alias information obtained during tests can be used to greatly aid the efficiency of constructing proofs [5].

- In the past, counter-example driven refinement schemes have worked with a particular form of abstraction called predicate abstraction [1]. We present approaches to refine any abstract interpretation automatically using counterexamples. Several challenges arise: refining using disjunctions leads to powerset domains, and the use of joins forces us to consider counterexample DAGs instead of counterexample traces. We present our solutions to these problems [3,2]. We also present experiences implementing our techniques in a tool Dagger.