On The Theory Of Boolean Formulas Minimal Including Sums I
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On the Theory of Boolean Formulas
The notion of prime implicant is defined and studied at a high level of generality. All the usual results are preserved and deepened and some new ones obtained. Paramount are those relating prime implicants and shortest sums. This theoretical development may be applied to the minimization of Boolean formulas built from formulas of an arbitrarily given set S (for example, the set of formulas realized by devices of a particular kind) and representing a given incomplete switching function. Several computational processes are briefly discussed. The general theory is supplemented by results particular to the 'classical' case in which S is the set of the products of literals.