A Verification Toolkit for Numerical Transition Systems

1 Swiss Federal Institute of Technology Lausanne (EPFL) 2 Verimag, Grenoble, France 3 Uppsala University, Sweden Abstract. This paper reports on an effort to create benchmarks and a toolkit for rigorous verification problems, simplifying tool integration and eliminating ambiguities of complex programming language constructs. We focus on Integer Numerical Transition Systems (INTS), which can be viewed as control-flow graphs whose edges are annotated by Presburger arithmetic formulas. We describe the syntax, semantics, a front-end, and a first release of benchmarks for such transition systems. Furthermore, we present FLATA and ELDARICA, two new verification tools for INTS. The FLATA system is based on precise acceleration of the transition relation, while the ELDARICA system is based on predicate abstraction with interpolation-based counterexample-driven refinement. The ELDARICA verifier uses the PRINCESS theorem prover as a sound and complete interpolating prover for Presburger arithmetic. Both systems can solve several examples for which previous approaches failed and present a useful baseline for verifying integer programs. Our infrastructure is publicly available; we hope that it will spur further research, benchmarking, competitions, and synergistic communication between verification tools.