The algebra of Boolean formulas: Some criteria for minimaity

Several algorithms are presented, more or less directly related to the "minimization" theory of Boolean formulas. They give solutions to the following specific problems: computation of the sum of all the "prime implicants", starting with any "normal" formula; verification of the equivalence F a/ for "normal" formulas F; determination of some or all of the minimal F-including sets. The last problem is a two-fold generalization of the determination of the "irredundant normal formulas". More precisely if F, F1, F2,..., Fn are Boolean formulas such that F is included in ("implies") SigmaFi, a minimal F-including set is a collection of Fi such that their sum includes F, but no subcollection has the same property. Although these algorithms are of obvious practical importance, they are viewed here more as a theoretical contribution. Examples are included; the theory of Boolean formulas on which this paper is based is presented elsewhere.