Disjunctive normal form

related topics
{math, number, function}
{law, state, case}

In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more conjunctions of one or more literals. A DNF formula is in full disjunctive normal form, if each of its variables appears exactly once in every clause. As in conjunctive normal form (CNF), the only propositional operators in DNF are and, or, and not. The not operator can only be used as part of a literal, which means that it can only precede a propositional variable. For example, all of the following formulas are in DNF:

However, the following formulas are not in DNF:

Converting a formula to DNF involves using logical equivalences, such as the double negative elimination, De Morgan's laws, and the distributive law. Note that all logical formulas can be converted into disjunctive normal form. However, in some cases conversion to DNF can lead to an exponential explosion of the formula. For example, in DNF, logical formulas of the following form have 2n terms:

The following is a formal grammar for DNF:

Where term is any variable.

See also

External links

Full article ▸

related documents
Discrete probability distribution
Urysohn's lemma
Unit interval
Unitary matrix
Axiom of power set
Injective function
Inverse transform sampling
Irreducible fraction
Euler's identity
Algebraic closure
Parse tree
NP-equivalent
Bernoulli's inequality
Elias gamma coding
Klein four-group
Class (set theory)
Linear function
Earley parser
Complete graph
Inner automorphism
Regular graph
Connectedness
Null set
Minkowski's theorem
Cipher
Profinite group
Special functions
Just another Perl hacker
Automorphism
Subring