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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
Complexity class used to classify decision problems
in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
NP_(complexity)
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)
Branch of computational complexity theory
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according
Parameterized_complexity
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
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
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
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)
Complexity class (logarithmic space)
In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved
L_(complexity)
Complexity class
In computational complexity theory, the complexity class FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial
FP_(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
BPP_(complexity)
Unproven computational hardness assumption
In computational complexity theory, the exponential time hypothesis (ETH) states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved
Exponential_time_hypothesis
Feature of systems that defy description
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity
Complexity
Amount of resources to perform an algorithm
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus
Computational_complexity
Complexity class in computer science
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(complexity)
Model of computational complexity
functions is a popular approach to separating complexity classes. For example, a prominent circuit class P/poly consists of Boolean functions computable
Circuit_complexity
Randomized polynomial time class of computational complexity theory
In computational complexity theory, randomized polynomial time (RP) is the complexity class of decision problems for which a probabilistic Turing machine
RP_(complexity)
Computational complexity
computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(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
Concept in computational complexity theory
(Bounded-error Probabilistic Logarithmic-space Polynomial-time), is the complexity class of problems solvable in logarithmic space and polynomial time with
BPL_(complexity)
Complexity class
In computational complexity theory, SNP (from Strict NP) is a complexity class containing a limited subset of NP based on its logical characterization
SNP_(complexity)
Computer memory needed by an algorithm
input influencing space complexity. Analogously to time complexity classes DTIME(f(n)) and NTIME(f(n)), the complexity classes DSPACE(f(n)) and NSPACE(f(n))
Space_complexity
Transformation of one computational problem to another
forms a preorder, whose equivalence classes may be used to define degrees of unsolvability and complexity classes. There are two main situations where
Reduction_(complexity)
Complexity class
science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of
PPAD_(complexity)
Computational complexity class
NP-intermediate, neither having polynomial time nor likely to be NP-hard. The complexity class QP consists of all problems that have quasi-polynomial time algorithms
Quasi-polynomial_time
Computational input that relies on the length but not content of the input
the input, but not on the input itself. A decision problem is in the complexity class P/f(n) if there is a polynomial time Turing machine M with the following
Advice_(complexity)
Mathematical model of computation
several important complexity classes is allowing for an error probability of 1/3. For instance, the complexity class BPP is defined as the class of languages
Probabilistic_Turing_machine
Abstract machine used to study decision problems
R'} is in the relativized complexity class P R {\displaystyle {\mathsf {P}}^{R}} . Other relativized complexity classes such as N P R {\displaystyle
Oracle_machine
Computational complexity class
In computational complexity theory, the complexity class E is the set of decision problems that can be solved by a deterministic Turing machine in time
E_(complexity)
and specifically computational complexity theory and circuit complexity, TC (Threshold Circuit) is a complexity class of decision problems that can be
TC_(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
Computational complexity of quantum algorithms
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational
Quantum_complexity_theory
Type of computational problem
Counting complexity techniques have significant applications in clarifying the relation between complexity classes of P, NP, PH, etc, in circuit complexity, and
Counting_problem_(complexity)
Complexity class
would give polynomial time algorithms for all the problems in the complexity class NP. It is suspected, but unproven, that P≠NP and (therefore) that there
NP-hardness
Class in computational complexity theory
unsolved problems in computer science In computational complexity theory, the class NC (for Nick's class) is the set of decision problems decidable in polylogarithmic
NC_(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)
Algorithmic complexity class
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable
EXPTIME
Problem of determining if a Boolean formula could be made true
this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization
Boolean satisfiability problem
Boolean_satisfiability_problem
Type of randomized algorithm
be repeated and every time will generate different arrangement. The complexity class of decision problems that have Las Vegas algorithms with expected polynomial
Las_Vegas_algorithm
Class of computational complexity
is not in the language. PSPACE can be characterized as the quantum complexity class QIP. PSPACE is also equal to PCTC, problems solvable by classical computers
PSPACE
Type of randomized algorithm
algorithm k times and returning the majority function of the answers. The complexity class BPP describes decision problems that can be solved by polynomial-time
Monte_Carlo_algorithm
Interactive proof system in computational complexity theory
In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin
Arthur–Merlin_protocol
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
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)
Topics referred to by the same term
elements Pseudo-class, cascading style sheet (CSS) construct for defining formatting Complexity class, a set of problems of related complexity in computational
Class
In circuit complexity, AC is a complexity class hierarchy. Each class, ACi, consists of the languages recognized by Boolean circuits with depth O ( log
AC_(complexity)
Complexity class
In computational complexity theory, the complexity class #P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems
♯P
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)
Complexity class
In computational complexity theory, the complexity class PPP (polynomial pigeonhole principle) is a subclass of TFNP. It is the class of search problems
PPP_(complexity)
PR is the complexity class of all primitive recursive functions—or, equivalently, the set of all formal languages that can be decided in time bounded by
PR_(complexity)
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
Complexity class
In computational complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP. The name is somewhat
FNP_(complexity)
Computational complexity class of problems
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial
BQP
Method for solving one problem using another
reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes. The three most common types
Polynomial-time_reduction
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)
Complexity class consisting of all recursive languages
In computational complexity theory, R is the class of decision problems solvable by a Turing machine, which is the set of all recursive languages (also
R_(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
In computational complexity theory, the complexity class 𝖤𝖫𝖤𝖬𝖤𝖭𝖳𝖠𝖱𝖸 consists of the decision problems that can be solved in time bounded by
ELEMENTARY
Given more time, a Turing machine can solve more problems
time-bounded complexity class, there is a strictly larger time-bounded complexity class, and so the time-bounded hierarchy of complexity classes does not
Time_hierarchy_theorem
Topics referred to by the same term
peptide NP (complexity), Nondeterministic Polynomial, a computational complexity class NP-complete, a class of decision problems NP-hard, a class of problems
NP
Complexity class
computational complexity theory, the class QIP (which stands for Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class IP
QIP_(complexity)
Complexity class
In computational complexity theory, PPA is a complexity class, standing for "Polynomial Parity Argument" (on a graph). Introduced by Christos Papadimitriou
PPA_(complexity)
Complexity class
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 NP
Co-NP
Complexity class of problems
computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of
NP-intermediate
Topics referred to by the same term
PPP (complexity), a computational complexity class Precise Point Positioning, a GNSS data processing technique Public, private, protected, class member
PPP
Complexity class from interactive proofs
In computational complexity theory, the class IP (which stands for interactive proof) is the class of problems solvable by an interactive proof system
IP_(complexity)
Complexity class of approximable problems
In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time
APX
Classification of computer problems
science – whether P = NP – by showing that the complexity class P is not equal to the complexity class NP. The idea behind the approach is to adopt and
Geometric_complexity_theory
Proof checkable by a randomized algorithm
proofs give rise to many complexity classes depending on the number of queries required and the amount of randomness used. The class PCP[r(n), q(n)] refers
Probabilistically checkable proof
Probabilistically_checkable_proof
Standard model in theoretical computer science
In computational complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs
Arithmetic_circuit_complexity
Notion of the "hardest" or "most general" problem in a complexity class
In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or
Complete_(complexity)
Measure of complexity of real-valued functions
and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with respect to a probability distribution
Rademacher_complexity
whose expressive power coincides exactly with a given complexity class, so that membership in the class becomes a consequence of syntactic well-formedness
Implicit computational complexity
Implicit_computational_complexity
Complexity class
In computational complexity theory, Polynomial Local Search (PLS) is a complexity class that models the difficulty of finding a locally optimal solution
PLS_(complexity)
Computational complexity class
In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in
NE_(complexity)
Unsolved problem in computational complexity theory
the computational complexity class NP-intermediate. It is known that the graph isomorphism problem is in the low hierarchy of class NP, which implies
Graph_isomorphism_problem
In computability and complexity theory, ALL is the class of all decision problems. ALL contains all of the complex classes of decision problems, including
ALL_(complexity)
Measure of the structural complexity of a software program
after the first command. Cyclomatic complexity may also be applied to individual functions, modules, methods, or classes within a program. One testing strategy
Cyclomatic_complexity
In computational complexity theory, DLIN is the class of decision problems that can be solved by a multitape Turing machine in linear time, O(n). It is
DLIN
American-Canadian computer scientist, contributor to complexity theory
mathematics, complexity of higher type functions, complexity of analysis, and lower bounds in propositional proof systems. He named the complexity class NC after
Stephen_Cook
American computer scientist (1943–2021)
relationship between the NSPACE and DSPACE complexity classes. His work in establishing complexity classes has helped to create the background against
Walter_Savitch
Complexity class used in circuit complexity
specifically computational complexity theory and circuit complexity, TC0 (Threshold Circuit) is the first class in the hierarchy of TC classes. TC0 contains all
TC0
Concept in computational complexity theory
that is, if they lie in the complexity class P. In modern terms, it identifies tractable problems with the complexity class P. Formally, to say that a
Cobham's_thesis
Study of complexity classes
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
Complexity class
or "hash P complete") form a complexity class in computational complexity theory. The problems in this complexity class are defined by having the following
♯P-complete
Analysis of computer programs without executing them
outset specialized programming languages or methods that delineate a complexity class. Thus, SA's focus is on compile time, making no demand on the programmer;
Static_program_analysis
Type of approximation algorithm
means probability greater than 3/4, though as with most probabilistic complexity classes the definition is robust to variations in this exact value (the bare
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
complement of a complexity class, called the complement class, which is the set of complements of every problem in the class. If a class is called C, its
Complement_(complexity)
American computer scientist (born 1969)
the complexity class NEXP is not contained in ACC0 received the best paper award at the Conference on Computational Complexity in 2011. Complexity theorist
Ryan Williams (computer scientist)
Ryan_Williams_(computer_scientist)
In computational complexity theory, a language B (or a complexity class B) is said to be low for a complexity class A (with some reasonable relativized
Low_(complexity)
Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation: Combinatorial optimization problems and their approximability
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
In computational complexity theory, NP/poly is a complexity class, a non-uniform analogue of the class NP of problems solvable in polynomial time by a
NP/poly
Complexity class of bounded-depth circuits
AC0 (alternating circuit) is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families
AC0
complexity class contained in PP defined via GapP functions. The class often arises in the context of quantum computing. AWPP contains the complexity
AWPP
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits
CC_(complexity)
Topics referred to by the same term
in cardiology PR-104 Progesterone receptor, a protein PR (complexity), a complexity class pr (Unix), Unix command to paginate or columnate files for
PR
Overview of and topical guide to algorithms
includes their design, proof of correctness, efficiency, computational complexity, and implementation in computer programs. Algorithm — finite sequence
Outline_of_algorithms
Quantum Merlin Arthur
abbreviation for Quantum Merlin Arthur, refers to a complexity class in computational complexity theory. It is the set of all formal languages that satisfy
QMA
Every graph has evenly many odd vertices
problem the geometric properties of the formula commonly arise. The complexity class PPA encapsulates the difficulty of finding a second odd vertex, given
Handshaking_lemma
Algorithm that employs a degree of randomness as part of its logic or procedure
considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision problems for
Randomized_algorithm
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