Be careful with don´t cares

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.