
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 2^{n} 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 
NPequivalent 
Bernoulli's inequality 
Elias gamma coding 
Klein fourgroup 
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 
