Boolean derivative

Noun

Meaning

Boolean derivative (plural Boolean derivatives)

(algebra) With respect to a Boolean variable




x

i




{\displaystyle x_{i}}

: The XOR-sum of the positive and negative Shannon cofactors of the given derived function with respect to




x

i




{\displaystyle x_{i}}

. In symbols:






∂
f


∂

x

i





(



x
→



)
=

f


x

i




(



x
→



)
⊕

f





x
¯




i




(



x
→



)


{\displaystyle {\partial f \over \partial x_{i}}({\vec {x}})=f_{x_{i}}({\vec {x}})\oplus f_{{\bar {x}}_{i}}({\vec {x}})}

.

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