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Standard form of Boolean function
In Boolean algebra, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause
Conjunctive_normal_form
Problem of determining if a Boolean formula could be made true
generalized conjunctive normal form formula, viz. as a conjunction of arbitrarily many generalized clauses, the latter being of the form R(l1,...,ln)
Boolean satisfiability problem
Boolean_satisfiability_problem
Standard form of a boolean function
philosophical logic — a cluster concept. The disjunctive normal form and its counterpart, the conjunctive normal form, are the most common standardized ways of representing
Disjunctive_normal_form
Standard forms of Boolean functions
canonical conjunctive normal form (CCNF), maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can
Canonical_normal_form
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
Logical formula with NOT only on variables
first 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
Negation_normal_form
Properties linking logical conjunction and disjunction
\varphi } in disjunctive normal form, the formula φ ¯ D {\displaystyle {\overline {\varphi }}^{D}} will be in conjunctive normal form, and given the result
Conjunction/disjunction duality
Conjunction/disjunction_duality
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
expert created manual conjunctive normal form queries has shown that searchonym expansion in the Boolean conjunctive normal form is much more effective
Vocabulary_mismatch
Problem in computational complexity theory
determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the
Maximum satisfiability problem
Maximum_satisfiability_problem
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
Operation in Boolean circuit theory
logic circuit and produces an equisatisfiable boolean formula in conjunctive normal form (CNF). The length of the formula is linear in the size of the circuit
Tseytin_transformation
Topics referred to by the same term
file extension .cnf, .conf, .cfg, .cf, or .ini Conjunctive normal form, also known as clausal normal form, in Boolean logic Constant weight without fins
CNF
NP-complete variant of the Boolean satisfiability problem
NP-complete variant of the Boolean satisfiability problem. Given a conjunctive normal form with three literals per clause, the problem is to determine whether
1-in-3-SAT
Computer program for the Boolean satisfiability problem
constraints. SAT solvers often begin by converting a formula to conjunctive normal form. They are often based on core algorithms such as the DPLL algorithm
SAT_solver
Type of search algorithm
deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem. It was introduced in 1961
DPLL_algorithm
Logic problem, AND of pairwise ORs
typically expressed as Boolean formulas of a special type, called conjunctive normal form (2-CNF) or Krom formulas. Alternatively, they may be expressed
2-satisfiability
Inference rule in logic, proof theory, and automated theorem proving
proved (the conjecture) are conjunctively connected. The resulting sentence is transformed into a conjunctive normal form with the conjuncts viewed as
Resolution_(logic)
Concept in the Boolean satisfiability problem
logic, given an unsatisfiable Boolean propositional formula in conjunctive normal form, a subset of clauses whose conjunction is still unsatisfiable is
Unsatisfiable_core
it 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
Switching_lemma
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
In mathematical logic, an atomic formula or its negation
definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two
Literal_(mathematical_logic)
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)
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
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
problem 3SAT (the Boolean satisfiability problem for expressions in conjunctive normal form (CNF) with exactly three variables or negations of variables per
Cook–Levin_theorem
Computational Formula that can be measured in terms of True or False
include: Detecting whether a clause in an unsatisfiable formula in conjunctive normal form belongs to some minimally unsatisfiable subset and whether a clause
True quantified Boolean formula
True_quantified_Boolean_formula
1969 non-fiction book by G. Spencer-Brown
depth does not exceed two. The result is a normal form, the primary algebra analog of the conjunctive normal form. LoF (T14–15) proves the primary algebra
Laws_of_Form
Protein-coding gene in humans
CCNF may also mean Canonical conjunctive normal form in Boolean algebra. G2/mitotic-specific cyclin-F is a protein that in humans is encoded by the CCNF
CCNF
Pair of logical equivalences
in 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
lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision list includes
Decision_list
has exactly k literals, each with distinct variables, and is in conjunctive normal form. These are called k-CNF formulas. The problem is to determine the
MAXEkSAT
special expressions, the conjunctive normal form and disjunctive normal form. For monotone functions these two special forms can also be restricted to
Monotone_dualization
Making other gates using just NOR gates
NOR gate. Alternatively, an XNOR gate is made by considering the conjunctive normal form ( A + B ¯ ) ⋅ ( A ¯ + B ) {\displaystyle (A+{\overline {B}})\cdot
NOR_logic
Unproven computational hardness assumption
problem in which the input to the problem is a Boolean expression in conjunctive normal form (that is, an and of ors of variables and their negations) with
Exponential_time_hypothesis
Normal form for modal logic formulas
These three forms are also called cpl-clauses, box-clauses and dia-clauses respectively. Note that any clause in conjunctive normal form (CNF) is also
Modal_clausal_form
Type of database query
formula in prenex normal form, thus this form is usually simply assumed. Thus conjunctive queries are of the following general form: ( x 1 , … , x k )
Conjunctive_query
Model in software development
in the diagram. Therefore, in case all elements are written in Conjunctive normal form (CNF), then the terms can easily be combined with logical AND and
Feature_model
negation of the corresponding conditional derive a theorem in conjunctive normal form in the methodical fashions described in text books. If, and only
Corresponding_conditional
Estimate of time taken for running an algorithm
is that 3SAT, the satisfiability problem of Boolean formulas in conjunctive normal form with at most three literals per clause and with n {\displaystyle
Time_complexity
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
Function returning one of only two values
arguments and their complements Conjunctive normal form, as an AND of ORs of the arguments and their complements Canonical normal form, a standardized formula
Boolean_function
Topics referred to by the same term
deciding the satisfiability of propositional logic formulae in conjunctive normal form Delay-locked loop, a device to reduce clock skew in digital circuits
DLL
Abstract strategy board game
by Reisch by reducing the quantified Boolean formula problem in conjunctive normal form to Hex. This result means that there is no efficient (polynomial
Hex_(board_game)
Propositional formula
(Prolog) query. If n > 1, the clause is no longer Horn. Conjunctive normal form Disjunctive normal form Horn clause Chang, Chin-Liang; Richard Char-Tung Lee
Clause_(logic)
validates both the clausification phase and the refutation of the conjunctive normal form. Along with proving theorems, Vampire has other related functionalities
Vampire_(theorem_prover)
Derivation of the laws of probability theory
equivalently rephrased using conjunction and negation alone (the conjunctive normal form), we can now handle any compound proposition. The laws thus derived
Cox's_theorem
Set of computational problems stated by Richard Karp (1973)
Satisfiability: the Boolean satisfiability problem for formulas in conjunctive normal form (often referred to as SAT) 0–1 integer programming (A variation
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
equisatisfiability are Skolemization and some translations into conjunctive normal form such as the Tseytin transformation. A translation from propositional
Equisatisfiability
Mathematical function conceived as a crude model
the AND and OR functions, and use them in the disjunctive or the conjunctive normal form. Researchers also soon realized that cyclic networks, with feedbacks
Artificial_neuron
Probabilistic graphical representation of causal relationships
as hard as counting the number of satisfying assignments of a conjunctive normal form formula (CNF)) and that approximate inference within a factor 2n1−ɛ
Bayesian_network
Standard form of Boolean function
near-optimal algorithm for computing the Blake canonical form of a formula in conjunctive normal form. Poretsky law Horn clause Quine–McCluskey algorithm Brown
Blake_canonical_form
Complexity class
satisfiability problem (SAT) where the formula is restricted to conjunctive normal form and to at most k literals per clause, where k is fixed. An analogous
SNP_(complexity)
Complexity class
problem) Are there any variable assignments that satisfy a given CNF (conjunctive normal form) formula? (Boolean satisfiability problem or SAT) Does a univariate
♯P
Stage of electronic circuit design verification
become highly popular because of their efficiency and versatility. Conjunctive Normal Form Satisfiability: SAT solvers returns an assignment to the variables
Formal_equivalence_checking
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
Algorithm that outputs all solutions to a problem
Boolean 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
Branch of mathematical logic
formulae in conjunctive normal form such that the first-order quantifiers are universal and the quantifier-free part of the formula is in Krom form, which
Descriptive_complexity_theory
Task of computing complete subgraphs
satisfiability problem. It describes how to translate Boolean formulas in conjunctive normal form (CNF) into equivalent instances of the maximum clique problem.
Clique_problem
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 a Boolean
Linear_separability
Replacing subterm in a formula with another term
based on term rewriting. In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as a rewriting system. For
Rewriting
SAT solving algorithm
consists in finding a satisfying assignment for a given formula in conjunctive normal form (CNF). An example of such a formula is: ( (not A) or (not C) )
Conflict-driven clause learning
Conflict-driven_clause_learning
Complexity class of approximable problems
satisfiability problem. In this problem, we have a Boolean formula in conjunctive normal form where each variable appears at most 3 times, and we wish to know
APX
Special type of Boolean function
if every prime implicant of the disjunctive normal form and every clause of the conjunctive normal form have exactly one variable in common. It is possible
Read-once_function
Algorithm component in computer science
(\exists y\forall x.p(x,y))} : the negation of that formula has the conjunctive normal form p ( X , f ( X ) ) ∧ ¬ p ( g ( Y ) , Y ) {\displaystyle p(X,f(X))\land
Occurs_check
Local search algorithm solving boolean satisfiability
formulae in Boolean logic that are in, or have been converted into conjunctive normal form. They start by assigning a random value to each variable in the
WalkSAT
Directed graph isomorphic to its own transpose graph
the 2-satisfiability problem, that is, a Boolean expression in conjunctive normal form with two variables or negations of variables per clause, may be
Skew-symmetric_graph
concerns the Boolean satisfiability problem for Boolean formulas in conjunctive normal form, with uniform clause size. These problems can be parameterized
Entropy_compression
16.3), the problem of determining whether a boolean formula in conjunctive normal form with two variables per clause is satisfiable. The problem of unique
NL-complete
Grammar of the Irish language
pronouns used: conjunctive forms, disjunctive forms, and emphatic forms (which may be used either conjunctively or disjunctively) The normal word order in
Irish_grammar
Computational problem
Pa wins if ψ ends up false. The formula ψ is assumed to be in conjunctive normal form. In this proof, we assume that the quantifier list starts and ends
Generalized_geography
Algorithm for the minimization of Boolean functions
near-optimal algorithm for finding all prime implicants of a formula in conjunctive normal form. Step two of the algorithm amounts to solving the set cover problem;
Quine–McCluskey_algorithm
Complexity class of problems
Boolean satisfiability problem for "intersecting monotone CNF": conjunctive normal form, with each clause containing only positive or only negative terms
NP-intermediate
Directed graph representing a Boolean expression
analyzing complex Boolean expressions. A 2-satisfiability instance in conjunctive normal form can be transformed into an implication graph by replacing each
Implication_graph
American mathematician (1928–2023)
deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e., for solving the CNF-SAT problem. The algorithm was a refinement
Martin_Davis_(mathematician)
deciding the satisfiability of propositional logic formula in conjunctive normal form, i.e. for solving the CNF-SAT problem Exact cover problem Min conflicts
List_of_algorithms
Classic NP-complete problem in computer science
the circuit a variable, then for each NAND gate, construct the conjunctive normal form clauses (v1 ∨ v3) ∧ (v2 ∨ v3) ∧ (¬v1 ∨ ¬v2 ∨ ¬v3), where v1 and
Circuit satisfiability problem
Circuit_satisfiability_problem
Method of automated theorem proving
clauses, i.e. clauses that are composed of a single literal, in conjunctive normal form. Because each clause needs to be satisfied, we know that this literal
Unit_propagation
Graph with a median for each three vertices
combinations of values. Usually such problems are expressed in conjunctive normal form, in which each clause is expressed as a disjunction and the whole
Median_graph
Problem of counting solutions to logic formulas
amounts to counting the number of solutions of the negation of a conjunctive normal form (CNF) formula. Intractability even holds in the case known as #PP2DNF
♯SAT
Classical information retrieval model
query Q {\displaystyle Q} is a Boolean expression, typically in conjunctive normal form: Q = ( t a ∨ t b ) ∧ ( ¬ t c ∨ t d ) ∧ … {\displaystyle Q=(t_{a}\lor
Boolean model of information retrieval
Boolean_model_of_information_retrieval
Theorem in mathematical logic
This can be verified by writing φ {\displaystyle \varphi } in conjunctive normal form: φ ≡ ( P ∨ ¬ R ) ∧ Q {\displaystyle \varphi \equiv (P\lor \lnot
Craig_interpolation
Computer scientist
Boolean satisfiability problem: its input is a Boolean formula in conjunctive normal form with at most one positive literal per clause, and the goal is to
Jean_Gallier
American computer scientist (born 1947)
satisfiability problem, of determining whether a logic formula in conjunctive normal form can be made true by a suitable assignment of its variables. In
Harry_R._Lewis
is 3-satisfiable with x1=x2=x3=x4=TRUE. Formally, generalized conjunctive normal forms with a ternary Boolean function R are employed, which is TRUE just
XOR-SAT
Function in Boolean algebra
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
Type of flowchart
only one node between any input and any output. See conjunctive normal form and disjunctive normal form. A cause–effect graph is useful for generating a
Causal_map
polynomial-time algorithms to convert any Boolean expression to conjunctive normal form such as Tseitin's algorithm, posing SAT problems in CNF does not
Boolean satisfiability algorithm heuristics
Boolean_satisfiability_algorithm_heuristics
Model of concept hierarchies
] F {\textstyle [X]_{F}} , which can be identified within the conjunctive normal form of η ( X ) {\textstyle \eta (X)} if exists. Likewise, for the RSL
General_Concept_Lattice
Abnormal yellowish skin colour caused by high level of bilirubin
in the conjunctival membranes overlying the avascular sclera. Thus, the proper term for the yellowing of "white of the eyes" is conjunctival icterus
Jaundice
random violated constraint. For propositional satisfiability of conjunctive normal form formulae, which is the original settings of this algorithm, every
Local search (constraint satisfaction)
Local_search_(constraint_satisfaction)
Character of the Japanese writing system
sometimes used to delimit choices. が is a Japanese case marker, as well as a conjunctive particle. It is used to denote the focus of attention in a sentence,
Ka_(kana)
formed from full words by the employment of certain formatives; the rest (nouns, pronouns, some relatives, some adverbs, all ideophones, conjunctives
Sotho_parts_of_speech
On the complexity classes of problems about satisfying a subset of boolean relations
arbitrary precision can also clearly be done in polynomial time. Conjunctive normal form is abbreviated CNF below. X(N)OR-SAT stands for a satisfiability
Max/min CSP/Ones classification theorems
Max/min_CSP/Ones_classification_theorems
Logical connective AND
if and only if (also known as iff) both of its operands are true. The conjunctive identity is true, which is to say that AND-ing an expression with true
Logical_conjunction
Verb form with the letter waw in order to change its tense or aspect
e.g. in the beginning of a narrative; or it may be combined with the conjunctive function. Weingreen gives the following example. If one considers two
Vav-consecutive
Type of logical formula
the resolution proof. Used in this way, goal clauses are similar to conjunctive queries in relational databases, and Horn clause logic is equivalent
Horn_clause
Medical condition
A pinguecula is a common type of conjunctival stromal degeneration in the eye. It appears as an elevated yellow-white plaque in the bulbar conjunctiva
Pinguecula
Jewish religious chanting practice
use. In particular, it was necessary to invent a range of different conjunctive accents to show how to introduce and elaborate the main motif in longer
Hebrew_cantillation
Element of Japanese language
favor and] use'). The gerund(ive) or ‑te form (て形, ‑te-kei) is yet another way to make adverbial or conjunctive clauses. It has various meanings that overlap
Japanese conjugation (ren'yōkei base)
Japanese_conjugation_(ren'yōkei_base)
Rule system for formal languages
described by a conjunctive grammar, which in turn also includes other non-context-free languages, such as the language of all words of the form anbncn. Every
Context-free_grammar
CONJUNCTIVE NORMAL-FORM
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CONJUNCTIVE NORMAL-FORM
CONJUNCTIVE NORMAL-FORM
CONJUNCTIVE NORMAL-FORM
CONJUNCTIVE NORMAL-FORM
CONJUNCTIVE NORMAL-FORM
CONJUNCTIVE NORMAL-FORM