Abstract: A decomposition technique, for solving combinational constraint expressions, is presented. Decomposing a set of constraints can increase the opportunities for dividing them into independent sets that do not need to be conjoined in a constraint-solving process using a BDD representation. An AND decomposition, relying on a Theorem 1, is presented. An OR decomposition, relying on a corollary of Theorem 1, is presented. Theorem 1 provides an operation to test for, and create, a pair of sub-constraints G and H which are independent in any two variables x0 and x1. A decomposition procedure is presented for separating as many variables as possible, of an input constraint, into disjoint sub-constraints. A merging procedure is presented, that can be used if a decomposition does not only contain constraints whose support sets are disjoint from each other. The decomposition procedure can also be used to identify hold constraints.

Abstract: In the design of digital integrated circuits, it is often desirable to formally verify whether an implementation design is equivalent to a reference design. The present invention facilitates such formal verification by determining “necessary correspondences” between inputs or outputs of the two circuits to be compared for equivalency. Necessary correspondences are so called because while they establish necessary conditions for equivalency to occur, they are not sufficient to determine that equivalency actually exists. Once such necessary correspondences have been determined, algorithms to determine actual equivalency can be more strategically applied. It is often cost-effective (i.e. more efficient), as part of an equivalency-determining circuit design tool, to first apply the teachings of the present invention in order to lessen subsequent application of an equivalency determining method.