Abstract

. We present a technique for proving properties of recursively defined circuits using Stalmarck's method. We consider instances of circuits defined according to a particular inductive scheme and show how extra definitions of fresh propositional variables can be added automatically in such a way that an automatic theorem prover is able to find short proofs of correctness of the resulting circuits. We show how regular circuits, such as adders and multipliers, fit into the inductive scheme. 1 Introduction Stalmarck's method is an effective algorithm for proving formulas in propositional logic extended with some arithmetic. The method was patented by Stalmarck in 1992 and has since been used to verify complex systems in many real industrial projects, particularly in the area of railway signalling [4]. Stalmarck defines a notion of proof hardness, the number of simultaneously free assumptions in a proof. It turns out that many real verification problems have easy proofs (hardness 0 or 1), a...