On The Theory Of Boolean Formulas
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On the Theory of Boolean Formulas
The theory of substitutions for Boolean formulas developed in a previous report is applied here to the determination of those s-tuples of formulas that may be allowable replacements for s -tuples of sub-formulas of given Boolean formulas. The criteria of allowability are very general and flexible, yet may be expressed with great precision and ease. The results formalize and extend various known isolated instances. They may be used for the study of a large number of problems in the theory and application of Boolean formulas and functions.
On the Theory of Boolean Formulas
Substitution operators for subformulas of Boolean formulas are introduced and investigated.
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.