Zhegalkin (also Žegalkin, Gégalkine or Shegalkin) polynomials (Russian: полиномы Жегалкина), also known as algebraic normal form, are a representation...

y} . Using Zhegalkin Algebra, any perfect disjunctive normal form can be uniquely converted into a Zhegalkin polynomial (via the Zhegalkin Theorem). x...

interpolation, using multivariate polynomials with two or three variables Zhegalkin polynomial, a multilinear polynomial over F 2 {\displaystyle \mathbb...

which uniquely identifies the function: Algebraic normal form or Zhegalkin polynomial, as a XOR of ANDs of the arguments (no complements allowed) Full...

&r=p+q{\pmod {2}}\\\end{matrix}}} The description of a Boolean function as a polynomial in F 2 {\displaystyle \mathbb {F} _{2}} , using this basis, is called...

Disjunctive x y {\displaystyle xy} Conjunctive x y {\displaystyle xy} Zhegalkin polynomial x y {\displaystyle xy} Post's lattices 0-preserving yes 1-preserving...

Conjunctive x ¯ + y ¯ {\displaystyle {\overline {x}}+{\overline {y}}} Zhegalkin polynomial 1 ⊕ x y {\displaystyle 1\oplus xy} Post's lattices 0-preserving no...

sufficient operator Symmetric Boolean function Symmetric difference Zhegalkin polynomial Boolean domain Complete Boolean algebra Interior algebra Two-element...

Conjunctive x ¯ ⋅ y ¯ {\displaystyle {\overline {x}}\cdot {\overline {y}}} Zhegalkin polynomial 1 ⊕ x ⊕ y ⊕ x y {\displaystyle 1\oplus x\oplus y\oplus xy} Post's...

\left(a\land b\land c\right)} Formulas written in ANF are also known as Zhegalkin polynomials and Positive Polarity (or Parity) Reed–Muller expressions (PPRM)...