Philipp Wendler

Dirk Beyer, Matthias Dangl, Philipp Wendler

Bounded model checking (BMC) is a well-known and successful technique for finding bugs in software. k-induction is an approach to extend BMC-based approaches from falsification to verification. Automatically generated auxiliary invariants can be used to strengthen the induction hypothesis. We improve this approach and further increase effectiveness and efficiency in the following way: we start with light-weight invariants and refine these invariants continuously during the analysis. We present and evaluate an implementation of our approach in the open-source verification-framework CPAchecker. Our experiments show that combining k-induction with continuously-refined invariants significantly increases effectiveness and efficiency, and outperforms all existing implementations of k-induction-based software verification in terms of successful verification results.

Dirk Beyer, Stefan Löwe, Philipp Wendler

Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement. Because the interpolants have a significant influence on the quality of the abstraction, and thus, the effectiveness of the verification, an algorithm for deriving the best possible interpolants is desirable. We present an analysis-independent technique that makes it possible to extract several alternative sequences of interpolants from one given infeasible error path, if there are several reasons for infeasibility in the error path. We take as input the given infeasible error path and apply a slicing technique to obtain a set of error paths that are more abstract than the original error path but still infeasible, each for a different reason. The (more abstract) constraints of the new paths can be passed to a standard interpolation engine, in order to obtain a set of interpolant sequences, one for each new path. The analysis can then choose from this set of interpolant sequences and select the most appropriate, instead of being bound to the single interpolant sequence that the interpolation engine would normally return. For example, we can select based on domain types of variables in the interpolants, prefer to avoid loop counters, or compare with templates for potential loop invariants, and thus control what kind of information occurs in the abstraction of the program. We implemented the new algorithm in the open-source verification framework CPAchecker and show that our proof-technique-independent approach yields a significant improvement of the effectiveness and efficiency of the verification process.

Dirk Beyer, Stefan Löwe, Evgeny Novikov et al.

Continuous testing during development is a well-established technique for software-quality assurance. Continuous model checking from revision to revision is not yet established as a standard practice, because the enormous resource consumption makes its application impractical. Model checkers compute a large number of verification facts that are necessary for verifying if a given specification holds. We have identified a category of such intermediate results that are easy to store and efficient to reuse: abstraction precisions. The precision of an abstract domain specifies the level of abstraction that the analysis works on. Precisions are thus a precious result of the verification effort and it is a waste of resources to throw them away after each verification run. In particular, precisions are small and thus easy to store; they are easy to process and have a large impact on resource consumption. We experimentally show the impact of precision reuse on industrial verification problems, namely, 59 device drivers with 1119 revisions from the Linux kernel.