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In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
Furthermore, if they are restricted to being in full disjunctive normal form, in which every variable appears exactly once in every conjunction, they can be checked in constant time (each conjunction represents one satisfying assignment).
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
[8] [9] This provides a procedure for converting between conjunctive normal form and disjunctive normal form. [10] Since the Disjunctive Normal Form Theorem shows that every formula of propositional logic is expressible in disjunctive normal form, every formula is also expressible in conjunctive normal form by means of effecting the conversion ...
The Blake canonical form is a special case of disjunctive normal form. The Blake canonical form is not necessarily minimal (upper diagram), however all the terms of a minimal sum are contained in the Blake canonical form. [ 3 ]
The existence of negation normal forms drives many applications, for example in digital circuit design, where it is used to manipulate the types of logic gates, and in formal logic, where it is needed to find the conjunctive normal form and disjunctive normal form of a formula.
Canonical normal form, a standardized formula which uniquely identifies the function: Algebraic normal form or Zhegalkin polynomial, as a XOR of ANDs of the arguments (no complements allowed) Full (canonical) disjunctive normal form, an OR of ANDs each containing every argument or complement
Greibach normal form; Kuroda normal form; Normal form (abstract rewriting), an element of a rewrite system which cannot be further rewritten; in logic: Normal form (natural deduction) Algebraic normal form; Canonical normal form; Clausal normal form; Conjunctive normal form; Disjunctive normal form; Negation normal form; Prenex normal form ...
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