Editing Algebraic normal form (section)

== Common uses ==
ANF is a [[canonical form (Boolean algebra)|canonical form]], which means that two [[logically equivalent]] formulas will convert to the same ANF, easily showing whether two formulas are equivalent for [[automated theorem proving]]. Unlike other normal forms, it can be represented as a simple list of lists of variable names—[[conjunctive normal form|conjunctive]] and [[disjunctive normal form|disjunctive]] normal forms also require recording whether each variable is negated or not. [[Negation normal form]] is unsuitable for determining equivalence, since on negation normal forms, equivalence does not imply equality: a &or; ¬a is not reduced to the same thing as 1, even though they are logically equivalent.

Putting a formula into ANF also makes it easy to identify [[linearity|linear]] functions (used, for example, in [[linear-feedback shift register]]s): a linear function is one that is a sum of single literals.  Properties of nonlinear-feedback [[shift register]]s can also be deduced from certain properties of the feedback function in ANF.