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Standard form of a boolean function
In boolean logic, a disjunctive normal form (DNF) is a normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described
Disjunctive_normal_form
Properties linking logical conjunction and disjunction
{\displaystyle \varphi } in disjunctive normal form, the formula φ ¯ D {\displaystyle {\overline {\varphi }}^{D}} will be in conjunctive normal form, and given the
Conjunction/disjunction duality
Conjunction/disjunction_duality
Problem of determining if a Boolean formula could be made true
problem to disjunctive normal form; to obtain an example, exchange "∧" and "∨" in the above exponential blow-up example for conjunctive normal forms. Another
Boolean satisfiability problem
Boolean_satisfiability_problem
Topics referred to by the same term
logic: Normal form (natural deduction) Algebraic normal form Canonical normal form Clausal normal form Conjunctive normal form Disjunctive normal form Negation
Normal_form
Standard form of Boolean function
conjunction of one or more disjunctions of one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or ( ∨ {\displaystyle
Conjunctive_normal_form
Boolean polynomials as sums of monomials
Unlike other normal forms, it can be represented as a simple list of lists of variable names—conjunctive and disjunctive normal forms also require recording
Algebraic_normal_form
Formalism of first-order logic
with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a canonical normal form useful in
Prenex_normal_form
Logical formula with NOT only on variables
example is also in conjunctive normal form, the next two are in both conjunctive normal form and disjunctive normal form, but the last example is in neither
Negation_normal_form
Standard forms of Boolean functions
Boolean function can be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction
Canonical_normal_form
follows that a formula in conjunctive normal form (that is, an AND of ORs) becomes a formula in disjunctive normal form (an OR of ANDs) under random restriction
Switching_lemma
Logic constructed only from NAND gates
NAND gate. Alternatively, an XOR gate is made by considering the disjunctive normal form A ⋅ B ¯ + A ¯ ⋅ B {\displaystyle A\cdot {\overline {B}}+{\overline
NAND_logic
Scripting language created in 1994
implement both the Traversable and Countable interfaces), and disjunctive normal form (DNF) types in PHP 8.2 (unions of intersections, such as
PHP
In logic, a statement which is always true
A {\displaystyle \neg \neg A\to A} Algebraic normal form Conjunctive normal form Disjunctive normal form Logic optimization Weisstein, Eric W. "Tautology"
Tautology_(logic)
Type of electronic component
of the CPLD is a macrocell, which contains logic implementing disjunctive normal form expressions and more specialized logic operations. Some of the
Complex programmable logic device
Complex_programmable_logic_device
normal form and disjunctive normal form. For monotone functions these two special forms can also be restricted to be monotone: The conjunctive normal
Monotone_dualization
Standard representation of a mathematical object
fundamental form. Negation normal form Conjunctive normal form Disjunctive normal form Algebraic normal form Prenex normal form Skolem normal form Blake canonical
Canonical_form
Boolean algebra concept
y=x\land y\oplus x\oplus y} . Using Zhegalkin Algebra, any perfect disjunctive normal form can be uniquely converted into a Zhegalkin polynomial (via the
Zhegalkin_algebra
Logic formula
that have simpler forms, known as normal forms. Some common normal forms include conjunctive normal form and disjunctive normal form. Any propositional
Propositional_formula
decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision
Decision_list
Simplification technique in mathematical logic
{\displaystyle F} is a quantifier-free formula, we can write it in disjunctive normal form ⋁ j = 1 m ⋀ i = 1 n L i j , {\displaystyle \bigvee _{j=1}^{m}\bigwedge
Quantifier_elimination
Pair of logical equivalences
formal logic, where it is needed to find the conjunctive normal form and disjunctive normal form of a formula. Computer programmers use them to simplify
De_Morgan's_laws
is frequently used is the one where Boolean combinations are in disjunctive normal form so that, e.g., { { q 1 } , { q 2 , q 3 } } {\displaystyle \{\{q_{1}\}
Alternating_finite_automaton
Topics referred to by the same term
(software), a package manager for RPM-based Linux distributions Disjunctive normal form, a standardization of a logical formula in boolean logic DNF (The
DNF
Number with all digits equally frequent
but a disjunctive sequence need not be normal. A rich number in base b is one whose expansion in base b is disjunctive: one that is disjunctive to every
Normal_number
results. normal form In logic, a standardized way of expressing logical formulas, such as conjunctive normal form (CNF) or disjunctive normal form (DNF)
Glossary_of_logic
Subfield of automated reasoning and mathematical logic
a number of methods. Gilmore's program used conversion to disjunctive normal form, a form in which the satisfiability of a formula is obvious. Depending
Automated_theorem_proving
Function returning one of only two values
functions: Negation normal form, an arbitrary mix of AND and ORs of the arguments and their complements Disjunctive normal form, as an OR of ANDs of
Boolean_function
Standard form of Boolean function
implicants of f. The Blake canonical form is a special case of disjunctive normal form. The Blake canonical form is not necessarily minimal (upper diagram)
Blake_canonical_form
Application of model-based design
the disjunctive normal form approach wherein the logical expressions describing the system's behavior are transformed into the disjunctive normal form. Constraint
Model-based_testing
Propositional formula
of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive
Clause_(logic)
Problem of counting solutions to logic formulas
parsimonious. Therefore, this problem is #P-complete as well. For disjunctive normal form (DNF) formulas, counting the solutions is also #P-complete, even
♯SAT
Logical operation
\}} , which is shown to be truth-functionally complete by the Disjunctive Normal Form Theorem. Expressed in terms of NAND ↑ {\displaystyle \uparrow }
Sheffer_stroke
Operation in combinatorial game theory
parallel games, at which point (in normal play) the last player to move wins. This operation may be extended to disjunctive sums of any number of games, again
Disjunctive_sum
Special type of Boolean function
and only if every prime implicant of the disjunctive normal form and every clause of the conjunctive normal form have exactly one variable in common. It
Read-once_function
Concept in mathematical logic
functionally complete. (Its functional completeness is also proved by the Disjunctive Normal Form Theorem.) But this is still not minimal, as ∨ {\displaystyle \lor
Functional_completeness
Book by Marvin Minsky and Seymour Papert
\psi _{i}} be supported on set A {\textstyle A} . Write it in disjunctive normal form, with one clause for each subset of A {\textstyle A} on which ψ
Perceptrons_(book)
Binary operation that is true if and only if both operands are false
\}} , which is shown to be truth-functionally complete by the Disjunctive Normal Form Theorem. This may also be seen from the fact that Logical NOR does
Logical_NOR
not apply, because the di are not coprime in pairs. The use of disjunctive normal form is a standard technique for Boolean manipulations. It here allows
Rogers_sieving_theorem
Topics referred to by the same term
CDNF may refer to: Canonical disjunctive normal form, a form of expression in Boolean algebra Cerebral dopamine neurotrophic factor, a protein encoded
CDNF
Computer programming testing tool
Currently,[when?] Fastest supports the following testing tactics: Disjunctive Normal Form (DNF). It is the only testing tactic applied by default (regardless
Fastest
Branch of mathematical logic
formulae in disjunctive normal form such that the first-order quantifiers are all universal and the quantifier-free part of the formula is in Horn form, which
Descriptive_complexity_theory
Representation of a game in game theory
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent
Normal-form_game
{\displaystyle E(a_{i+1},\ell ,c(a,\ell ,\nu ))} is in disjunctive normal form, i.e. it is of the form ⋁ i = 1 n ⋀ j = 1 m i ( ℓ i , j , r i , j ) {\displaystyle
Alternating_timed_automaton
Complexity class
problems. Determining the satisfiability of a Boolean formula in disjunctive normal form is easy: such a formula is satisfiable if and only if it contains
♯P-complete
Interdisciplinary research area
1\}^{n}} . For example, the concept class could be the set of disjunctive normal form (DNF) formulas on n bits or the set of Boolean circuits of some
Quantum_machine_learning
Graph representing an implementation of the logical functionality of a network
"sum-of-product" (ΣoΠ) form,[citation needed] that is, the canonical form in Boolean algebra known as the disjunctive normal form (DNF). The BDD and DNF
And-inverter_graph
algebra Algebraic normal form Boolean conjunctive query Canonical form (Boolean algebra) Conjunctive normal form Disjunctive normal form Formal system And-inverter
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Computational complexity class
problems of converting logical formulas between conjunctive and disjunctive normal form, listing all minimal hitting sets of a family of sets, or listing
Quasi-polynomial_time
Algorithm that outputs all solutions to a problem
functions, e.g., a Boolean formula written in conjunctive normal form or disjunctive normal form, a binary decision diagram such as an OBDD, or a Boolean
Enumeration_algorithm
Algorithm for the minimization of Boolean functions
Czort, Sebastian Lukas Arne (1999). The complexity of minimizing disjunctive normal form formulas (Master's thesis). University of Aarhus. Umans, Christopher;
Quine–McCluskey_algorithm
Algebraization of first-order logic
Translate the matrices of the most deeply nested quantifiers into disjunctive normal form, consisting of disjuncts of conjuncts of terms, negating atomic
Predicate_functor_logic
= {A1, A3} A logical expression is an OR-table of AND-sets (a disjunctive normal form): A1 & B3 | A1 & B2 & C4 | C2 => [ { A 1 B 3 } { A 1 B 2 C 4 }
Virtual_finite-state_machine
Quantifier elimination for semi-algebraic sets
standard logical (disjunctive normal form) and algebraic manipulations, it is straightforward to show that a semialgebraic set in Rn is formed by taking a finite
Tarski–Seidenberg_theorem
essentially the modern idea of truth-functions and their expression in disjunctive normal form. Boole's system admits of two interpretations, in class logic,
History_of_logic
Form of literature
1177/0963947005051287. S2CID 170517936. Gilbert, Richard (2004). "The Disjunctive Dragonfly". Modern Haiku. 35 (2): 21–44. Hollander 1981, pp. 37–46 Fussell
Poetry
Informal fallacy involving falsely limited alternatives
the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among
False_dilemma
Łukasiewicz logic. A ground logical rule is transformed into its disjunctive normal form. Let I + {\displaystyle I^{+}} be the set of indices of the variables
Probabilistic_soft_logic
Theorem about complexity measures of Boolean functions
Saket; Sen, Sandeep (2016). "On the Sensitivity Conjecture for Disjunctive Normal Forms". 36th IARCS Annual Conference on Foundations of Software Technology
Sensitivity_theorem
(Michalski, 1973), a supervised system for learning concepts in disjunctive normal form (DNF). Experience with these earlier systems and others, to include
Incremental_decision_tree
On the complexity classes of problems about satisfying a subset of boolean relations
satisfies all clauses, it is in PO. If all clauses, when converted to disjunctive normal form, have two terms, one consisting of all positive (unnegated) variables
Max/min CSP/Ones classification theorems
Max/min_CSP/Ones_classification_theorems
Function in Boolean algebra
functions for which all disjunctive normal forms have the maximal number of 2 n − 1 monomials of length n and all conjunctive normal forms have the maximal number
Parity_function
Form of personal pronoun
French disjunctive pronouns). In Portuguese, Spanish, Italian, and Romanian, prepositions generally combine with pronouns that are identical in form to nominative
Prepositional_pronoun
for all subformulas in A, and expressing the result in the full disjunctive normal form. It is thus sufficient to construct a decision algorithm for admissibility
Admissible_rule
simple or compound expression specified in either conjunctive or disjunctive normal form. The action part of the rule can be a set of actions that must
Policy-based_management
Grammar of the Irish language
used: conjunctive forms, disjunctive forms, and emphatic forms (which may be used either conjunctively or disjunctively) The normal word order in Irish
Irish_grammar
Model of concept hierarchies
in [ X ] F {\textstyle [X]_{F}} , which can be found within the disjunctive normal form of ρ ( X ) {\textstyle \rho (X)} , see Fig 3. For instance, from
General_Concept_Lattice
TTF are the following: Disjunctive Normal Form (DNF). By applying this tactic the operation is written in Disjunctive Normal Form and the test class is
Test_Template_Framework
Russian mathematician (1935–2022)
proof for lack of local unsolvability for constructing the minimal disjunctive normal form. In 1959, he moved to Novosibirsk, where he pursued government-sponsored
Yuri Zhuravlyov (mathematician)
Yuri_Zhuravlyov_(mathematician)
Type of flowchart
node between any input and any output. See conjunctive normal form and disjunctive normal form. A cause–effect graph is useful for generating a reduced
Causal_map
Jewish religious chanting practice
motifs only for the disjunctives and render the conjunctives in a monotone. It is notable that the Yemenite Jews have only eight disjunctive motifs, thus clearly
Hebrew_cantillation
Generalization of the real numbers
the disjunctive sum of those smaller games, and the theorem states that the method of addition we defined is equivalent to taking the disjunctive sum
Surreal_number
Logical connective OR
sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula S ∨ W {\displaystyle S\lor W} , assuming that S {\displaystyle
Logical_disjunction
Rule of inference of propositional logic
or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the
Disjunction_elimination
Type of logical formula
who first pointed out their significance in 1951. A Horn clause is a disjunctive clause (a disjunction of literals) with at most one positive, i.e. unnegated
Horn_clause
Concept in combinatorial game theory
the set of all disjunctive position sums in A {\displaystyle A} , and that this is true regardless of whether the game is played in normal or misere play
Indistinguishability_quotient
True when either but not both inputs are true
function's algebraic normal form. Disjunction is often understood exclusively in natural languages. In English, the disjunctive word "or" is often understood
Exclusive_or
Transcendental number(s) with all positive integers in order
≥ 2 {\displaystyle b\geq 2} . The Champernowne word is a disjunctive sequence. A disjunctive sequence is an infinite sequence (over a finite alphabet
Champernowne_constant
Mathematical models of strategic interactions
presented in extensive form. Every extensive-form game has an equivalent normal-form game, however, the transformation to normal form may result in an exponential
Game_theory
Type of non-monotonic logic
{\displaystyle \Box x\rightarrow x} supports the initial assumption. Disjunctive default logic the consequence of a default is a set of formulae instead
Default_logic
Clause type associated with questions
using a word like which, who, how, etc. An intermediate form is the choice question, disjunctive question or alternative question, which presents a number
Interrogative
Simultaneous movement of eyes in binocular vision
Vergence movements are closely connected to accommodation of the eye. Under normal visual conditions, looking at an object at a different distance will automatically
Vergence
Wide-ranging representation of a game in game theory
representations differ from normal-form in that they provide a more complete description of the game in question, whereas normal-form simply boils down the
Extensive-form_game
Part of speech that defines a noun or pronoun
such as Tagalog, follow their adjectival orders as rigidly as English. The normal adjectival order of English may be overridden in certain circumstances,
Adjective
Concept in game theory
be minmaxed ruling out any form inductive strategy. Heap games are a subclass of impartial games that involve the disjunctive sum of various single-heap
Impartial_game
Philosophical thought experiment
own output) and the "disembodied" brain would continue to have perfectly normal conscious experiences, like those of a person with an embodied brain, without
Brain_in_a_vat
Programming language evaluation rules
the right expression if the result can be determined—for example, in a disjunctive expression (OR) where true is encountered, or in a conjunctive expression
Evaluation_strategy
Variant of Nash equilibrium in game theory
extensive form game where no extensive-form trembling hand perfect equilibrium is admissible, i.e., the sets of extensive-form and normal-form trembling
Trembling hand perfect equilibrium
Trembling_hand_perfect_equilibrium
Syntax of the Irish language
for person or number, and pronouns appear in the disjunctive form. The copula, which has the realis form is, is used for identification and definition:
Irish_syntax
Game theory concept
Nash equilibrium for a Bayesian game, which is derived from the ex-ante normal form game associated with the Bayesian framework. In a traditional (non-Bayesian)
Bayesian_game
Classification of verbs by regularity of inflection
the forms most commonly made in irregular fashion. About 200 verbs in normal use have irregularities in one or other (or usually both) of these forms. They
Regular_and_irregular_verbs
Concept in game theory
versions of the battle of the sexes game, shown in extensive form. Below, the normal form for both of these games is shown as well. The first game is simply
Information_set_(game_theory)
Game of strategy
played in parallel with other normal play impartial games (see disjunctive sum). While all normal-play impartial games can be assigned a nim value, that is
Nim
pleasure, etc.) the players are allocated by the end of the game. A game in normal form is a function: π : ∏ i ∈ N Σ i → R N {\displaystyle \pi \ :\prod
Glossary_of_game_theory
Geometric property of a pair of sets of points in Euclidean geometry
co-NP-complete to decide whether a Boolean function given in disjunctive or conjunctive normal form is linearly separable. A linear threshold logic gate is
Linear_separability
Verb that is active in meaning but takes its form from a different voice
flatter'), and many more. The forms regularly follow those of the passive of normal verbs: Deponents have all the participles normal verbs do, although those
Deponent_verb
Part of speech that connects two words, sentences, phrases, or clauses
('because') is subordinating. The clause after the coordinating conjunction has normal word order, but the clause after the subordinating conjunction has verb-final
Conjunction_(grammar)
Various systems of symbolic logic
Classically, the statement above is moreover equivalent to a more disjunctive form discussed further below. Constructively, existence claims are however
Intuitionistic_logic
Complex syntactic structure linking two or more elements
and precedes the right-most square bracket. The coordinator appears in normal script between the conjuncts. [Sarah] and [Xolani] went to town. - N + N
Coordination_(linguistics)
Pronoun having no referent
weather verbs can control the subject of an adjunct clause, just like a "normal" subject. For example, compare: She brushes her teeth before having a bath
Dummy_pronoun
Grammatical construct in which a noun modifies another noun
each form tends to adhere to a certain sense; thus "face mask" is the normal term in hockey, and "facial mask" is heard more often in spa treatments
Noun_adjunct
DISJUNCTIVE NORMAL-FORM
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DISJUNCTIVE NORMAL-FORM
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