English Dictionary

consensus theorem

名詞

(logic) The following theorem of Boolean algebra: XY+X'Z+YZ=XY+X'Z where YZ, the algebraically redundant term, is called the "consensus term", or its dual form (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z), in which case Y+Z is the consensus term. (Note: X+Y,X'+Z⊢Y+Z is an example of the resolution inference rule (replacing the + with ∨ and the prime with prefix ¬ might make this more evident).)

日本語の意味

コンセンサス定理（合意定理とも呼ばれる）とは、ブール代数における定理で、論理式 XY + X'Z + YZ = XY + X'Z （またはその双対形式 (X+Y)(X'+Z)(Y+Z) = (X+Y)(X'+Z)）が成立することを示す。この定理において、YZ（または Y+Z）は余分な項（コンセンサス項）と呼ばれ、論理式の簡略化に寄与する。

In digital circuit optimization, applying the consensus theorem can simplify a sum-of-products expression by removing the algebraically redundant YZ term.

デジタル回路の最適化では、コンセンサス定理を適用することで、代数的に冗長なYZ項を取り除いて積和形の式を簡略化できます。

意味（1）

(logic) The following theorem of Boolean algebra: XY+X'Z+YZ=XY+X'Z where YZ, the algebraically redundant term, is called the "consensus term", or its dual form (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z), in which case Y+Z is the consensus term. (Note: X+Y,X'+Z⊢Y+Z is an example of the resolution inference rule (replacing the + with ∨ and the prime with prefix ¬ might make this more evident).)