Implicant

In Boolean logic, the term implicant has either a generic or a particular use. In the generic use, it refers to the hypothesis of an implication (implicant). In the particular use, a product term (i.e., a conjunction of literals) P is an implicant of a Boolean function F, denoted P \le F, if P implies F (i.e., whenever P takes the value 1 so does F). For instance, implicants of the function f(x,y,z,w)=xy+yz+w include the terms xy, xyz, xyzw, w, as well as some others.

== Prime implicant == A prime implicant of a function is an implicant (in the above particular sense) that cannot be covered by a more general (more reduced, meaning with fewer literals) implicant. W. V. Quine defined a prime implicant to be an implicant that is minimal—that is, the removal of any literal from P results in a non-implicant for F. An essential prime implicant (also known as core prime implicant) is a prime implicant that covers an input combination, for which the function is true (i.e. outputs 1), that no combination of other prime implicants is able to cover.