Zhegalkin algebra

Summary

In mathematics, Zhegalkin algebra is a set of Boolean functions defined by the nullary operation taking the value $1$, use of the binary operation of conjunction $\land$, and use of the binary sum operation for modulo 2 $\oplus$. The constant $0$ is introduced as $1 \oplus 1 = 0$. The negation operation is introduced by the relation $\neg x = x \oplus 1$. The disjunction operation follows from the identity $x \lor y = x \land y \oplus x \oplus y$.