algebraic normal form

English

Etymology

"Algebraic" would refer to the fact that a two-element Galois field, ${𝔽}_2$ adjoined with some variables forms a polynomial algebra, ${𝔽}_2[x_1,\mathrm{...},x_n]$.

Noun

algebraic normal form (uncountable)

1. (algebra, logic) ring sum normal form
   • 2015 September 22, Magnus Gausdal Find, Joan Boyar, “Multiplicative Complexity of Vector Valued Boolean Functions”, in arxiv.org‎^[1], retrieved 10 August 2017:

         It is well known that every $(n,1)$-function $f$ can be written uniquely as a multilinear polynomial over ${𝔽}_2$
     $f(x_1,\mathrm{...},x_n)=\sum _{X\subseteq [n]}{\alpha }_X\prod _{i\in X}{x}_i$.
     This polynomial is called the Zhegalkin polynomial or the algebraic normal form (ANF) of $f$.

Synonyms

• ring sum normal form

See also

• Zhegalkin polynomial