Be careful with don't cares

Abstract

It is commonly expected that any correct implementation can replace its specification inside a larger design without violating the correctness of the whole design. This property (called replaceability) is automatically satisfied in the absence of don't cares because `correctness' by definition implies that specification and implementation compute the identical function. However, don't cares allow an implementation to compute a different function, and thus make it difficult to ensure replaceability. Whether this problem occurs depends on the exact meaning of `don't care' and the associated definition of `correctness'. We will consider three meanings of `don't care' and for each give conditions under which correct implementations may replace their specifications.