Mutation testing with hyperproperties.

We present a new method for model-based mutation-driven test case generation. Mutants are generated by making small syntactical modifications to the model or source code of the system under test. A test case kills a mutant if the behavior of the mutant deviates from the original system when running the test. In this work, we use hyperproperties-which allow to express relations between multiple executions-to formalize different notions of killing for both deterministic as well as non-deterministic models. The resulting hyperproperties are universal in the sense that they apply to arbitrary reactive models and mutants. Moreover, an off-the-shelf model checking tool for hyperproperties can be used to generate test cases. Furthermore, we propose solutions to overcome the limitations of current model checking tools via a model transformation and a bounded SMT encoding. We evaluate our approach on a number of models expressed in two different modeling languages by generating tests using a state-of-the-art mutation testing tool.

Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs.

Craig's interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants. In this paper, we generalise this system to propositional hyper-resolution proofs as well as clausal proofs. The latter are generated by contemporary SAT solvers. Finally, we show that, when applied to local (or split) proofs, our extension generalises two existing interpolation systems for first-order logic and relates them in logical strength.

Under-approximating loops in C programs for fast counterexample detection.

Many software model checkers only detect counterexamples with deep loops after exploring numerous spurious and increasingly longer counterexamples. We propose a technique that aims at eliminating this weakness by constructing auxiliary paths that represent the effect of a range of loop iterations. Unlike acceleration, which captures the exact effect of arbitrarily many loop iterations, these auxiliary paths may under-approximate the behaviour of the loops. In return, the approximation is sound with respect to the bit-vector semantics of programs. Our approach supports arbitrary conditions and assignments to arrays in the loop body, but may as a result introduce quantified conditionals. To reduce the resulting performance penalty, we present two quantifier elimination techniques specially geared towards our application. Loop under-approximation can be combined with a broad range of verification techniques. We paired our techniques with lazy abstraction and bounded model checking, and evaluated the resulting tool on a number of buffer overflow benchmarks, demonstrating its ability to efficiently detect deep counterexamples in C programs that manipulate arrays.