In Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing logical formulas in one of three subforms:
The entire formula is purely true or false:10One or more variables are ANDed together into a term, then one or more terms are XORed together into ANF. No NOTs are permitted:a ⊕ b ⊕ ab ⊕ abcor in standard propositional logic symbols: a ⊻ b ⊻ ( a ∧ b ) ⊻ ( a ∧ b ∧ c ) {\displaystyle a\veebar b\veebar \left(a\wedge b\right)\veebar \left(a\wedge b\wedge c\right)} The previous subform with a purely true term:1 ⊕ a ⊕ b ⊕ ab ⊕ abcFormulas written in ANF are also known as Zhegalkin polynomials (Russian: полиномы Жегалкина) and Positive Polarity (or Parity) Reed–Muller expressions (PPRM).
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