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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
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
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
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
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)
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
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)
Set of the elements not in a given subset
In set theory, the complement of a set A, often denoted by Ac (or A′), is the set of elements not in A. When all elements in the universe, i.e. all elements
Complement_(set_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
Concept in computational complexity theory
for complementation problems", SIAM Journal on Computing, 18 (3): 559–578, doi:10.1137/0218038 Nisan, N. (1994), "RL ⊆ SC", Computational Complexity, 4
BPL_(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
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
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
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
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
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)
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
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)
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
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
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(complexity)
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. NP is short for "nondeterministic
NP-completeness
Algorithm to multiply two numbers
by every digit in the second and adding the results. This has a time complexity of O(n2), where n is the number of digits. When done by hand, this may
Multiplication_algorithm
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)
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)
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
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)
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
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
Notion of equality in type theory
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Identity_type
Identities and relationships involving sets
of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides
Algebra_of_sets
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
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
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)
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)
Graph formed by complementation and disjoint union
cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint
Cograph
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
System that converts an analog signal into a digital signal
magnitude of the voltage or current. Typically, the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities
Analog-to-digital_converter
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
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
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
Mathematical game
Combinatorial explosion Determinacy Disjunctive sum First/Second-player win Game complexity Game tree Impartial game Misère Partisan game Solved game Sprague–Grundy
Guess_2/3_of_the_average
Foundational Heyting algebra Homogeneous Idempotent Lattice Bounded Complemented Complete Distributive Join and meet Partially ordered set Chain-complete
Series-parallel_partial_order
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
Branch of chemistry
descriptions of quantum mechanical systems. Computational results may complement information obtained by chemical experiments or predict unobserved chemical
Computational_chemistry
language of an input AFA non-empty?), the universality problem (is the complement of the language of an input AFA empty?), and the equivalence problem (do
Alternating_finite_automaton
Complexity class in computer science
BPL. Complexity Zoo: RL A. Borodin, S.A. Cook, P.W. Dymond, W.L. Ruzzo, and M. Tompa. Two applications of inductive counting for complementation problems
RL_(complexity)
Collection of mathematical objects
also called the complement of B in A. When all sets that are considered are subsets of a fixed universal set U, the complement U∖A is often called
Set_(mathematics)
Situation where total gains match total losses
Combinatorial explosion Determinacy Disjunctive sum First/Second-player win Game complexity Game tree Impartial game Misère Partisan game Solved game Sprague–Grundy
Zero-sum_game
Generic-case complexity is a subfield of computational complexity theory that studies the complexity of computational problems on "most inputs". Generic-case
Generic-case_complexity
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)
Mathematical set formed from two given sets
A×(B∖C)=(A×B)∖(A×C), (A×B)∁=(A∁×B∁)∪(A∁×B)∪(A×B∁), where A∁ denotes the absolute complement of A. Other properties related with subsets are: if A⊆B, then A×C⊆B×C;
Cartesian_product
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
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
Theorem in computational complexity theory
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
studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Hardness of approximation complements the study of approximation
Hardness_of_approximation
languages are not closed under complement (as intersection can be constructed by de Morgan's laws out of union and complement). Greibach, Sheila (October
Linear_grammar
Vertex coloring where every color pairing appears at least once
1016/0020-0190(89)90221-4, hdl:1874/16576. Manlove, D.; McDiarmid, C. (1995), "The complexity of harmonious coloring for trees", Discrete Applied Mathematics, 57 (2–3):
Complete_coloring
Mechanical pocket calculator
nines complement math, essentially subtracting by adding. The nines' complement math breakthrough eliminated the significant mechanical complexity created
Curta
Standard for assessing computer system vulnerabilities
changes are the new base metric Attack Requirements which complement the metric Attack Complexity with an assessment of what conditions at the target site
Common Vulnerability Scoring System
Common_Vulnerability_Scoring_System
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
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
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
Notable football skills and tactics
goalkeeper, which makes passing an integral part of the game. In terms of complexity, lower levels of the game such as youth, amateur, and semi-professional
Association_football_tactics
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
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)
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)
Game theory concept
game theory, the decisions of two or more players are called strategic complements if they mutually reinforce one another, and they are called strategic
Strategic_complements
Hospital that provides tertiary care
following:[citation needed] a major hospital that usually has a full complement of services including pediatrics, obstetrics, general medicine, gynecology
Tertiary_referral_hospital
Family of formal knowledge representation
logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used
Description_logic
number of function evaluations. However, it is crucial in analyzing the complexity of this problem that both the CNF and DNF representations are output.
Monotone_dualization
Mathematical-logic system
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
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
Science-fiction board game
received for its replayability, tension, and components, but its high complexity was met with criticism. A base-game expansion, Aftermath, was released
Nemesis_(board_game)
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
In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an
UP_(complexity)
Cooked dough food in Italian cuisine
with the rolling and cutting method or by extruding. They are generally complemented with thinner toppings to prevent chunks of meat or vegetables in a thick
Pasta
American singer, songwriter, and dancer (born 1966)
blow, she whispers ... Jackson's confectionary vocals are masterfully complemented by gentle harmonies and balanced out by pulsing rhythms, so she's never
Janet_Jackson
English author and journalist (1903–1950)
London. This was a much larger establishment with 200 pupils and a full complement of staff. He acquired a motorcycle and took trips through the surrounding
George_Orwell
Israeli computer scientist
investigates determinization and complementation of finite automata over infinite strings, in particular, the complexity of such translation for Büchi automata
Shmuel_Safra
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
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
Theorem for proving more complex theorems
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Lemma_(mathematics)
Operation in graph theory
algorithm can, with the same time complexity, recover a sequence of at most 3 n / 2 {\displaystyle 3n/2} local complementations transforming G 1 {\displaystyle
Local_complementation
Graph coloring with equal color classes
this conjecture by applying the conjecture for larger values of k to the complement graph of a given graph, and using as color classes contiguous subsequences
Equitable_coloring
Decision rule used for minimizing the possible loss for a worst-case scenario
Combinatorial explosion Determinacy Disjunctive sum First/Second-player win Game complexity Game tree Impartial game Misère Partisan game Solved game Sprague–Grundy
Minimax
Intersection graph for curves in the plane
each subtree by a string that traces around the subtree's edges. The complement graph of every comparability graph (also known as the cocomparability
String_graph
Lutz's resource-bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure
Resource-bounded_measure
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)
Distributed architecture framework for data management
privacy-related topics. Nevertheless, a cross-domain steering unit can only complement and support the federated governance structure and may grow obsolete with
Data_mesh
Embedding a graph in a topological space, often Euclidean
{\displaystyle G} is embedded on a closed surface Σ {\displaystyle \Sigma } , the complement of the union of the points and arcs associated with the vertices and edges
Graph_embedding
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
Lemma in constructibility theory
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Condensation_lemma
Subset of a graph's nodes such that all other nodes link to at least one
input K; it is a classical NP-complete decision problem in computational complexity theory. Therefore it is believed that there may be no efficient algorithm
Dominating_set
Directed-energy weapon, Laser weapon
deployment in 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
Political ideology promoting free-market capitalism
invisible hand of the market and the iron fist of the state combine and complement each other to make the lower classes accept desocialized wage labor and
Neoliberalism
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
Computer architecture bit width
−32,768 (−1 × 215) through 32,767 (215 − 1) for representation as two's complement. Since 216 is 65,536, a processor with 16-bit memory addresses can directly
16-bit_computing
Data structure for Boolean functions
compactly, using complemented edges, also known as complement links. The resulting BDD is sometimes known as a typed BDD or signed BDD. Complemented edges are
Binary_decision_diagram
travel, tourism, insurance
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
COMPLEMENT COMPLEXITY
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