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On Simplifying Truth Functions: A Preliminary Reduction of Coreless Formulas

The core of a truth function ø consists of those prime implicants of ø which are terms of every disjunctive normal formula equivalent to ø. The notion of core is generalized here: a class of prime implicants of ø is defined, called its "pseudo core." The pseudo core of ø consists of those prime implicants of ø which are terms of every one of a class Γ of normal equivalents of ø, where Γ includes a simplest normal equivalent. The pseudo core may be found easily and rapidly, plays the same role as the core in simplifying a formula, and may exist even in coreless formulas.