Automated Verification by Induction with Associative-Commutative Operators

Theories with associative and commutative (AC) operators, such as arithmetic, process algebras, boolean algebras, sets, : : : are ubiquitous in software and hardware veriication. These AC operators are diicult to handle by automatic deduction since they generate complex proofs. In this paper, we present new techniques for combining induction and AC reasoning, in a rewrite-based theorem prover. The resulting system has proved to be quite successful for veriication tasks. Thanks to its careful rewriting strategy, it needs less interaction on typical veriica-tion problems than well known tools like NQTHM, LP or PVS. We also believe that our approach can easily be integrated as an eecient tactic in other proof systems.