Tautology checking using cross-controllability and cross-observability relations

Abstract

A novel method is described for verifying the equivalence between a combinational circuit and its specification, when both are given in a modular (e.g., factored) form. It is based on the notion of cross-controllability and cross-observability relations that exist between the internal logic values across a cut of the joint composition of the circuit and the specification. It is proven that even after abstracting input and other internal variables the relations are sufficient to verify the equivalence. The abstraction allows reduction of the size of the relation, thus permitting the verification of much larger circuits. A report is presented on the verification of an 8*8 parallel multiplier using at most 527 BDD (binary decision diagram) cells of 21 variables. Extensions to sequential circuits are also discussed.