Section: New Results

Automated Deduction

We develop general techniques which allow us to re-use available tools in order to build a new generation of solvers offering a good trade-off between expressiveness, flexibility, and scalability. We focus on the careful integration of combination techniques and rewriting techniques to design decision procedures for a wide range of verification problems.

Building and verifying decision procedures

Participants : Alain Giorgetti, Olga Kouchnarenko, Christophe Ringeissen, Elena Tushkanova.

We have developed a methodology to build decision procedures by using superposition calculi which are at the core of equational theorem provers. We are interested in developing automated deduction techniques to prove properties about these superposition-based decision procedures. To this aim, we plan to further investigate the use of schematic superposition, which has been already applied to check the termination and the combinability of superposition-based procedures. We have been working on the development of a framework for specifying and verifying superposition-based procedures. In [52] , we present an implementation in Maude of the two inference systems corresponding to superposition and schematic superposition. Thanks to this implementation we automatically derive termination of superposition for a couple of theories of interest in verification.

Until now, schematic superposition was only studied for standard superposition. In [62] , we introduce a schematic superposition calculus modulo a fragment of arithmetics, namely the theory of Integer Offsets. This new schematic calculus is used to prove the decidability of the satisfiability problem for some theories extending Integer Offsets. We illustrate our theoretical contribution on theories representing extensions of classical data structures, e.g., lists and records. Our Maude-based implementation has been extended to incorporate this new schematic superposition calculus modulo Integer Offsets. It enables automatic decidability proofs for theories of practical use.