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In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently
Complement_(complexity)
Topics referred to by the same term
called an antonym) Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Complement (complexity), relating to decision
Complement
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
Computer memory needed by an algorithm
under complementation. This shows another qualitative difference between time and space complexity classes, as nondeterministic time complexity classes
Space_complexity
Concept in theoretical computer science
computational complexity of the complementation operation: given an automaton, how efficiently can we compute a complement automaton, e.g., in time complexity? State
Complementation_of_automata
Class of problems in computer science
In complexity theory, PP, or PPT is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability
PP_(complexity)
Measure of algorithmic complexity
theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer
Kolmogorov_complexity
Algebraic manipulation of "true" and "false"
enters via complement ¬ as follows. The complement operation is defined by the following two laws. Complementation 1 x ∧ ¬ x = 0 Complementation 2 x ∨ ¬
Boolean_algebra
Set of the elements not in a given subset
In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the
Complement_(set_theory)
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Complexity class
In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time
NP-hardness
Complexity class
computational complexity theory, co-NP is a complexity class. A decision problem X is a member of co-NP if and only if its complement X is in the complexity class
Co-NP
Notion in combinatorial game theory
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position)
Game_complexity
Unsolved problem in computer science
could be automated. The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation
P_versus_NP_problem
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t
SL_(complexity)
Concept in computer science
In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable
BPP_(complexity)
Algorithm that employs a degree of randomness as part of its logic or procedure
Carlo algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision
Randomized_algorithm
Class of problems solvable in polynomial time
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can
P_(complexity)
Randomized polynomial time class of computational complexity theory
be wrong, as a YES-instance can return a NO-answer. The complexity class co-RP is the complement, where a YES-answer might be wrong while a NO-answer is
RP_(complexity)
Branch of mathematical logic
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic
Descriptive_complexity_theory
Sequence of characters that forms a search pattern
expression of length about 850 such that its complement has a length about 232 can be found at File:RegexComplementBlowup.png. "Regular expressions for deciding
Regular_expression
Method for algorithm analysis in computer science
science, amortized analysis is a method for analyzing a given algorithm's complexity, or how much of a resource, especially time or memory, it takes to execute
Amortized_analysis
such a class a physical complexity class. Note that being self-low is a stronger condition than being closed under complement. Informally, a class being
Low_(complexity)
Argument by proponents of intelligent design
Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were
Irreducible_complexity
Model of computation
of integers and the gates compute set union, set intersection, and set complement, as well as the arithmetic operations addition and multiplication. A circuit
Circuit_(computer_science)
Closure of nondeterministic space under complementation
computational complexity theory, the Immerman–Szelepcsényi theorem states that nondeterministic space complexity classes are closed under complementation. It was
Immerman–Szelepcsényi_theorem
Solution of the traveling salesman problem
only a constant factor. The Held–Karp algorithm has exponential time complexity Θ ( 2 n n 2 ) {\displaystyle \Theta (2^{n}n^{2})} , significantly better
Held–Karp_algorithm
In computational complexity theory, SP 2 is a complexity class, intermediate between the first and second levels of the polynomial hierarchy. A language
S2P_(complexity)
The polynomial hierarchy is contained in probabilistic Turing machine in polynomial time
Toda's theorem is a result in computational complexity theory that was proven by Seinosuke Toda in his paper "PP is as Hard as the Polynomial-Time Hierarchy"
Toda's_theorem
State complexity is an area of theoretical computer science dealing with the size of abstract automata, such as different kinds of finite automata. The
State_complexity
Concept in computational complexity theory
In computational complexity theory, BPL (Bounded-error Probabilistic Logarithmic-space), sometimes called BPLP (Bounded-error Probabilistic Logarithmic-space
BPL_(complexity)
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(complexity)
Mathematical set formed from two given sets
complement }&A_{2}^{\complement }&\dots &A_{n}^{\complement }\\B_{1}^{\complement }&B_{2}^{\complement }&\dots &B_{n}^{\complement }\end{array}}\right[}
Cartesian_product
Inequality in information theory
A ¯ = Ω ∖ A {\displaystyle {\bar {A}}=\Omega \smallsetminus A} is the complement of A {\displaystyle A} . Indeed, by definition of the total variation
Bretagnolle–Huber_inequality
In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an
UP_(complexity)
Determining whether a knot is the unknot
complexity class P. First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes
Unknotting_problem
Class of computational complexity
}{=}}PSPACE}}} More unsolved problems in computer science In computational complexity theory, PSPACE is the set of all decision problems that can be solved
PSPACE
American singer and songwriter (born 1966)
the expression of a fully-formed human being with contradictions and complexities." Jackson's music encompasses a broad range of genres, including R&B
Janet_Jackson
Western music created during the Middle Ages
transmit musical ideas more easily, although notation coexisted with and complemented oral tradition. Medieval music was created for a number of different
Medieval_music
Type of search algorithm
problem is important both from theoretical and practical points of view. In complexity theory it was the first problem proved to be NP-complete, and can appear
DPLL_algorithm
Problem in graph theory
objective is to maximize the total weight of the edges between S and its complement rather than the number of the edges. The weighted max-cut problem allowing
Maximum_cut
Statement that is taken to be true
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Axiom
Mathematical model
automata. closed under intersection. not closed under complement. The computational complexity of some problems related to timed automata is now given
Timed_automaton
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely
NP-completeness
Graph with edges of length one, able to be drawn without crossings
Hiroshi (2008), "Planar unit-distance graphs having planar unit-distance complement", Discrete Mathematics, 308 (10): 1973–1984, doi:10.1016/j.disc.2007.04
Matchstick_graph
Computer science concept
computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize
Polynomial_hierarchy
Algorithm to multiply two numbers
by every digit in the second and adding the results. This has a time complexity of O ( n 2 ) {\displaystyle O(n^{2})} , where n is the number of digits
Multiplication_algorithm
Situation where total gains match total losses
explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game tree Impartial game Misère Partisan game Solved game Sprague–Grundy
Zero-sum_game
Fictional universe created by Iain M. Banks
reasonable to assume that all Minds have such features, as well as a complement of drones and other remote sensors as also described. Other equipment
The_Culture
Complexity class
In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can
RE_(complexity)
Paradox in set theory
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Russell's_paradox
US-based software and services company
Apollo | Continuous deployment is achievable at scale — no matter the complexity or constraints". Palantir. Archived from the original on February 2, 2024
Palantir
1999 book by Neil Immerman
Descriptive Complexity is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an
Descriptive_Complexity
Parasitic disease that results in diarrhea
available as diagnostic tools, although are not widely used due to methods complexity and costs. Prevention may be improved through proper personal hygiene
Giardiasis
Wireless networking standard in development
during the development of 802.11be but were postponed due to specification complexity, so 802.11bn continues this direction. In short, Multi-AP leverages the
Wi-Fi_8
Mathematical-logic system based on functions
own Gödel number, a contradiction results. The notion of computational complexity for the lambda calculus is a bit tricky, because the cost of a β-reduction
Lambda_calculus
British wildlife artists
working with. They value the complexity of mixing art and science and strive to show that the two can coexist and complement one another. On their website
Olly_and_Suzi
Abstract machine that models computation
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two
Interactive_proof_system
Partition of a graph's nodes into cliques
set in the complement of G, so a partition of the vertices of G is a clique cover of G if and only if it is a coloring of the complement of G. The clique
Clique_cover
Task of computing complete subgraphs
instance, Tarjan & Trojanowski (1977), an early work on the worst-case complexity of the maximum clique problem. Also in the 1970s, beginning with the work
Clique_problem
Laser air defense system
actually deployed December 2025. It has a range of up to 10 km (6.2 mi), complementing the Iron Dome system which was designed to intercept missiles launched
Iron_Beam
Standard for assessing computer system vulnerabilities
changes are the new base metric Attack Requirements which complement the metric Attack Complexity with an assessment what conditions at the target side are
Common Vulnerability Scoring System
Common_Vulnerability_Scoring_System
Theorem in topology
cohomology of its complement. If X is an n-dimensional compact connected submanifold of Rn+1 (or Sn+1) without boundary, its complement has 2 connected
Jordan_curve_theorem
Process of generalization
(1995) "What is complexity? Remarks on simplicity and complexity by the Nobel Prize-winning author of The Quark and the Jaguar" Complexity states the 'algorithmic
Abstraction
Logical incompatibility between two or more propositions
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Contradiction
2011 book by Daniel Kahneman
triggers associated with each type of thinking process, and how they complement each other, starting with Kahneman's own research on loss aversion. From
Thinking,_Fast_and_Slow
Form of computing using molecular biology
and affinity than an interaction between a DNA strand and its reverse complement. However, unlike DNA computing, this model is yet to be practically realized
Peptide_computing
Mathematical set containing no elements
{\displaystyle X} . Since the complement of an open set is closed and the empty set and X {\displaystyle X} are complements of each other, the empty set
Empty_set
Sequence of words formed by specific rules
languages). In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets
Formal_language
Hidden Markov model algorithm
1 {\displaystyle 1} to t {\displaystyle t} . The backward algorithm complements the forward algorithm by taking into account the future history if one
Forward_algorithm
Type of infinite structure
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
O-minimal_theory
Finding an optimal algorithm for playing chess
solved at least weakly. Calculated estimates of game-tree complexity and state-space complexity of chess exist which provide a bird's eye view of the computational
Solving_chess
Quality of an individual or group influencing or guiding others
of leadership have produced theories involving (for example) traits, complexity, collective intelligence, situational interaction, function, behavior
Leadership
Country in Eurasia from 1922 to 1991
Eastern Europe during the Cold War. The Warsaw Pact was the military complement to the Comecon, the regional economic organization for the socialist states
Soviet_Union
1993 studio album by Tool
AllMusic saw the album's success in the "striking, haunting visuals that complemented the album's nihilistic yet wistful mood." As of 2021, Undertow has been
Undertow_(Tool_album)
Japanese manga series
there, Andō wrote the lyrics to convey Miko's bright personality and complement the music, which she felt already set a bright mood. She mixed slang expressions
This_Monster_Wants_to_Eat_Me
Geometric graph with unit edge lengths
Hiroshi (2008), "Planar unit-distance graphs having planar unit-distance complement", Discrete Mathematics, 308 (10): 1973–1984, doi:10.1016/j.disc.2007.04
Unit_distance_graph
Concept in computer science
In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists
ZPP_(complexity)
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(complexity)
Hierarchy of complexity classes for formulas defining sets
Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is
Arithmetical_hierarchy
Impossible task in computing
decidable problems. Furthermore, the decidable problems can be divided into a complexity hierarchy. Aristotelian logic considers 4 kinds of sentences: "All p are
Entscheidungsproblem
Undecidability of equality of real numbers
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Richardson's_theorem
2000 film by Mary Harron
Harron described Cale's work as "a soulful, even melancholy sound to complement the soundtrack's poppy brightness". Cale was uninvolved with the selection
American_Psycho_(film)
Proposition in mathematical logic
is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940. The generalized continuum hypothesis
Continuum_hypothesis
American rapper and songwriter (born 1987)
sometimes upend[ing] them completely" on a record that "brims with comedy, complexity and the many voices in [Lamar's] head." The album debuted at number two
Kendrick_Lamar
DNA or RNA sequence that matches its complement when read backwards
equal to its reverse complement. For example, the DNA sequence ACCTAGGT is palindromic with its nucleotide-by-nucleotide complement TGGATCCA because reversing
Palindromic_sequence
Form of logic that allows quantification over predicates
intimately tied to computational complexity theory. The field of descriptive complexity studies which computational complexity classes can be characterized
Second-order_logic
Consistency of the axioms of arithmetic
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Hilbert's_second_problem
Argentine television series
scanned and projected environments were then sent to foreign studios to "complement the work". International visual effects vendors included DNEG in London
The_Eternaut_(TV_series)
Logical operation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition
Negation
Fundamental theorem in mathematical logic
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Gödel's_completeness_theorem
Subset of a graph's vertices, including at least one endpoint of every edge
computational complexity theory. Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in parameterized complexity theory
Vertex_cover
{\displaystyle \complement _{A}B=A\setminus B} . 2. Without a subscript, denotes the absolute complement; that is, ∁ A = ∁ U A {\displaystyle \complement A=\complement
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
American diplomat and politician (1923–2023)
In a 2023 interview, Kissinger said soccer was "at the highest level complexity masquerading as simplicity." Since his childhood, Kissinger had been a
Henry_Kissinger
2023 cultural phenomenon
attention to each film's critique of power, self-awareness, and existential complexity, noting Barbie's feminist messaging delivered through joy rather than
Barbenheimer
equipment, fuel, and ammunition. As the war progressed, the strength, complexity, and significance of the air force gradually increased. In 1915, the fortress
Imperial German Army in World War I
Imperial_German_Army_in_World_War_I
Axioms for the natural numbers
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Peano_axioms
portrayals of Black people in comics and has started to reflect the complexities of Black people across the diaspora. Starting in the 1870s Currier and
Portrayal of black people in comics
Portrayal_of_black_people_in_comics
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
Girl/Female
Indian
Competent.
Boy/Male
Muslim
Competent. Well disposed.
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Muslim
Competent
Boy/Male
Muslim
Compliments, Happiness
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Hindu
Competent, Powerful
Girl/Female
Tamil
Fit, Competent, Administrator
Boy/Male
Indian, Sanskrit
Competent
Girl/Female
Indian
Competent
Boy/Male
Hindi
Competent.
Boy/Male
Japanese
Complacent; satisfied.
Boy/Male
Indian
Compliments, Happiness
Boy/Male
Tamil
Sakshain | ஸாகà¯à®·à¯€à®¨
Competent, Powerful
Sakshain | ஸாகà¯à®·à¯€à®¨
Boy/Male
Muslim/Islamic
Compliments happiness
Boy/Male
Muslim
Competent. Well disposed.
Boy/Male
Anglo Saxon
Competent.
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Arabic, Muslim
Competent
Girl/Female
Hindu
Fit, Competent, Administrator
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
Male
English
Pet form of English Chester, CHET means "soldier's camp."
Girl/Female
Hindu, Indian
Best Girl; Responsible; Expressive; Inspirational; Friendly Personality
Boy/Male
Irish
Fire; fiery; white fire.
Girl/Female
Indian
Allahs blessing, Dignity
Boy/Male
Hindu
One of the kauravas
Girl/Female
Hindu
Sweet fragrance, The celestial cow, Wish yielding cow
Boy/Male
Arabic, Muslim
Evidence; Clear; Manifest; Present; Attested; Proved
Boy/Male
Australian, Danish, Gaelic, German, Irish, Norse, Swedish
Little Hills; God of Thunder
Surname or Lastname
German and Jewish (Ashkenazic)
German and Jewish (Ashkenazic) : from Middle High German kint, German Kind ‘child’, hence a nickname for someone with a childish or naive disposition, or an epithet used to distinguish between a father and his son. In some cases it may be a short form of any of various names ending in -kind, a patronymic ending of Jewish surnames.Dutch : variant spelling of Kint, cognate with 1, also found in such forms as ’t Kind and compounds such as Jongkind.English : nickname from Middle English kind (Old English gecynde) in any of its many senses: ‘legitimate’, ‘dutiful’, ‘benevolent’, ‘loving’, ‘gracious’.
Female
English
Anglicized form of Greek HÅsanna, HOSANNA means "deliver us." In the bible, this was the cry of the people who recognized Jesus as the Messiah when he entered Jerusalem.
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
v. t.
To provide with an implement or implements; to cause to be fulfilled, satisfied, or carried out, by means of an implement or implements.
v. t.
A second quantity added to a given quantity to make it equal to a third given quantity.
n.
An expression, by word or act, of approbation, regard, confidence, civility, or admiration; a flattering speech or attention; a ceremonious greeting; as, to send one's compliments to a friend.
v. t.
To compliment.
v. t.
A compliment.
n. pl.
Respects; compliments.
v. t.
Something added for ornamentation; an accessory.
n.
The nest complement of eggs of a bird.
a.
Self-satisfied; contented; kindly; as, a complacent temper; a complacent smile.
v. t.
To supply a lack; to supplement.
v. t.
Full quantity, number, or amount; a complete set; completeness.
v. t.
That which fills up or completes; the quantity or number required to fill a thing or make it complete.
v. t.
The interval wanting to complete the octave; -- the fourth is the complement of the fifth, the sixth of the third.
n.
Union; combination; a coupling; a pair.
v. t.
The whole working force of a vessel.
v. t.
To praise, flatter, or gratify, by expressions of approbation, respect, or congratulation; to make or pay a compliment to.
v. i.
To pass compliments; to use conventional expressions of respect.
v. t.
That which is required to supply a deficiency, or to complete a symmetrical whole.
n.
Compilation.
n.
Compliments; greetings.