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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)
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
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)
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
Measure of the structural complexity of a software program
Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent
Cyclomatic_complexity
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
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
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
Computational complexity class
definition, it is contained in NEXPTIME. NE, unlike NEXPTIME, is not closed under polynomial-time many-one reductions. E (complexity) Complexity Zoo: NE v t e
NE_(complexity)
Inherent difficulty of computational problems
their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such
Computational complexity theory
Computational_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)
Computational complexity of quantum algorithms
relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two
Quantum_complexity_theory
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
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)
Complexity of sending information in a distributed algorithm
In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem
Communication_complexity
Application of complexity science to economics
Complexity economics, or economic complexity, is the application of complexity science to the problems of economics. It relaxes several common assumptions
Complexity_economics
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(complexity)
Measure of complexity of real-valued functions
A\subseteq \mathbb {R} ^{m}} , the Rademacher complexity of A is defined as follows: Rad ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] {\displaystyle
Rademacher_complexity
Topics referred to by the same term
(theorem prover), a modern, high performance prover for first-order logic E (complexity), a set of decision problems solvable by a Turing machine in a specific
E_(disambiguation)
Algorithmic runtime requirements for common math procedures
the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing computations
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Class of computational complexity
P S P A C E {\displaystyle {\mathsf {P{\overset {?}{=}}PSPACE}}} More unsolved problems in computer science In computational complexity theory, PSPACE
PSPACE
System composed of many interacting components
Copernicus, New York, U.S. Colander, D. (2000). The Complexity Vision and the Teaching of Economics, E. Elgar, Northampton, Massachusetts. Stoop, Ruedi;
Complex_system
Model of computational complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according
Circuit_complexity
Measurement of computational complexity
computational complexity theory, asymptotic computational complexity is the use of asymptotic analysis for the estimation of the computational complexity of algorithms
Asymptotic computational complexity
Asymptotic_computational_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
Person's perceived knowledge of themself
Self-complexity is a person's perceived knowledge of themself, based upon the number of distinct cognitive structures, or self-aspects, they believe to
Self-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)
Transformation of one computational problem to another
of the required computational resources in a given context (e.g., higher time complexity, greater memory requirement, need for extra hardware processor
Reduction_(complexity)
Computational input that relies on the length but not content of the input
In computational complexity theory, an advice string is an extra input to a Turing machine that is allowed to depend on the length n of the input, but
Advice_(complexity)
American computer scientist
the University of California, San Diego, specializing in computational complexity theory. Impagliazzo received a BA in mathematics from Wesleyan University
Russell_Impagliazzo
In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount
LH_(complexity)
Complexity class consisting of all recursive languages
recursive functions and universal machines", Bulletin of the American Mathematical Society, New Series, 21 (1): 1-46. Complexity Zoo: Class R v t e
R_(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)
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)
Research psychometric
Integrative complexity is a research psychometric that refers to the degree to which thinking and reasoning involve the recognition and integration of
Integrative_complexity
(assuming, e.g., reductions that belong to ELEMENTARY). The PR class can be divided into an infinite hierarchy of increasingly large complexity levels, according
PR_(complexity)
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 measure in computer science
and Jacob Ziv. This complexity measure is related to Kolmogorov complexity, but the only function it uses is the recursive copy (i.e., the shallow copy)
Lempel–Ziv_complexity
Model of computation
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal
Boolean_circuit
Given more time, a Turing machine can solve more problems
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally
Time_hierarchy_theorem
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)
Class in computational complexity theory
}{=}}{\mathsf {P}}} More unsolved problems in computer science In computational complexity theory, the class NC (for Nick's class) is the set of decision problems
NC_(complexity)
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
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits
CC_(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)
Effective complexity is a measure of complexity defined in a 1996 paper by Murray Gell-Mann and Seth Lloyd that attempts to measure the amount of non-random
Effective_complexity
Topics referred to by the same term
Algorithmic complexity may refer to: In algorithmic information theory, the complexity of a particular string in terms of all algorithms that generate
Algorithmic_complexity
languages that are neither RE nor co-RE. It is the largest complexity class, containing all other complexity classes. Complexity Zoo: Class ALL v t e
ALL_(complexity)
Field in logic and theoretical computer science
science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational
Proof_complexity
Application of complexity theory to strategy
Complexity theory and organizations, also called complexity strategy or complex adaptive organizations, is the use of the study of complexity systems
Complexity theory and organizations
Complexity_theory_and_organizations
Axioms in computational complexity theory
In computational complexity theory the Blum axioms or Blum complexity axioms are axioms that specify desirable properties of complexity measures on the
Blum_axioms
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
Conceptual framework
sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in
Social_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
Attribute of machine learning models
discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal
Sample_complexity
In computational complexity theory, the complexity class FL is the set of function problems that can be solved by a deterministic Turing machine in a
FL_(complexity)
Lens mount designed by Sony for their camcorders and mirrorless cameras
while maintaining vignetting with 35mm sensors. E-mount achieves this by: Minimising mechanical complexity, removing mechanical aperture and focus drive
Sony_E-mount
1977 scholarly article by Donald Knuth
"The Complexity of Songs" is a scholarly article by computer scientist Donald Knuth published in 1977 as an in-joke about computational complexity theory
The_Complexity_of_Songs
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)
Mathematic definition
In convex geometry and polyhedral combinatorics, the extension complexity of a convex polytope P {\displaystyle P} is the smallest number of facets among
Extension_complexity
Concept in psychology
Cognitive complexity describes cognition along a simplicity-complexity axis. It is the subject of academic study in fields including personal construct
Cognitive_complexity
Model of computational complexity
computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree, i.e. a sequence
Decision_tree_model
Classification of computer problems
Geometric complexity theory (GCT), is a research program in computational complexity theory proposed by Ketan Mulmuley and Milind Sohoni. The goal of the
Geometric_complexity_theory
American professional electronic sports organization
Complexity Gaming, formerly stylized as compLexity, was an American esports franchise headquartered in Frisco, Texas. The franchise was founded in 2003
Complexity_Gaming
Creationist argument by William Dembski
Specified complexity is a creationist intelligent design argument introduced by William Dembski. According to Dembski, the concept can formalize a property
Specified_complexity
Algorithm that employs a degree of randomness as part of its logic or procedure
unconditionally, i.e. without relying on any complexity-theoretic assumptions, assuming the convex body can be queried only as a black box. A more complexity-theoretic
Randomized_algorithm
isomorphic structures 𝔄 and 𝔅. Neil, Immerman (1999). Descriptive Complexity. New York, NY: Springer New York. ISBN 9781461205395. OCLC 853271745. v t e
Query_(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
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)
has vertex complexity at most v, if P can be represented as conv(V)+cone(E), where V and E are finite sets, such that each point in V or E has encoding
N-dimensional_polyhedron
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)
Subfield of computational complexity theory
Fine-grained complexity is a subfield of computational complexity theory that studies the time required to solve computational problems, especially those
Fine_grained_complexity
Complexity management is a business methodology that deals with the analysis and optimization of complexity in enterprises. Effective complexity management
Complexity_management
Complexity class
In computational complexity theory, SC (Steve's Class, named after Stephen Cook) is the complexity class of problems solvable by a deterministic Turing
SC_(complexity)
Concept in linguistics
Language complexity is a topic in linguistics which can be divided into several sub-topics such as phonological, morphological, syntactic, and semantic
Language_complexity
Unsolved problem in computer science
(1979). "The complexity of enumeration and reliability problems". SIAM Journal on Computing. 8 (3): 410–421. doi:10.1137/0208032. Ladner, R.E. (1975). "On
P_versus_NP_problem
In modern computer science and statistics, the complexity index of a function denotes the level of informational content, which in turn affects the difficulty
Complexity_index
2015 Italian film
The Complexity of Happiness (Italian: La felicità è un sistema complesso [la felitʃiˈta ˌɛ un siˈstɛːma komˈplɛsso]) is a 2015 comedy film written and
The_Complexity_of_Happiness
Base of natural logarithms
method uses binary splitting to compute e with fewer single-digit arithmetic operations and thus reduced bit complexity. Combining this with fast Fourier transform-based
E_(mathematical_constant)
Concept in topology
In mathematics, topological complexity of a topological space X (also denoted by TC(X)) is a topological invariant closely connected to the motion planning
Topological_complexity
Deterministic time, in computational complexity theory
O(f(n))} , the problem is in the complexity class D T I M E ( f ( n ) ) {\displaystyle {\mathsf {DTIME}}(f(n))} (or T I M E ( f ( n ) ) {\displaystyle
DTIME
Complexity class
computational complexity theory, the class QIP (which stands for Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class
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)
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
Measure of complexity regarding algorithmic entropy
theory, sophistication is a measure of complexity related to algorithmic entropy. When K is the Kolmogorov complexity and c is a constant, the sophistication
Sophistication (complexity theory)
Sophistication_(complexity_theory)
Algorithm analysis method
theoretical computer science, smoothed analysis is a way of measuring the complexity of an algorithm. Since its introduction in 2001, smoothed analysis has
Smoothed_analysis
Numerical measure of program structure
better known for introducing cyclomatic complexity. McCabe defined essential complexity as the cyclomatic complexity of the reduced CFG (control-flow graph)
Essential_complexity
Number and type of nodes and alternative paths that exist within a computer network
Network complexity is the number of nodes and alternative paths that exist within a computer network, as well as the variety of communication media, communications
Network_complexity
Complexity class
In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP, sometimes also written 2EXPTIME) is the set of all decision
2-EXPTIME
American social scientist
Scott E. Page (Q7436275). Scott E. Page is an American social scientist and John Seely Brown Distinguished University Professor of Complexity, Social
Scott_E._Page
1986 paper on software project management
different types of complexity: accidental complexity and essential complexity. This is related to Aristotle's classification. Accidental complexity relates to
No_Silver_Bullet
by D. Baccarini in 1996. Complexity can be: Structural complexity (also known as detail complexity, or complicatedness), i.e. consisting of many varied
Project_complexity
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
Implicit computational complexity (ICC) is a subfield of computational complexity theory that characterizes programs by constraints on the way in which
Implicit computational complexity
Implicit_computational_complexity
Data structure for storing non-overlapping sets
Bernard A. Galler and Michael J. Fischer in 1964. In 1973, their time complexity was bounded to O(log∗(n)), the iterated logarithm of n, by Hopcroft and
Disjoint-set_data_structure
Forecasting complexity is a measure of complexity put forward (under the original name of) by the physicist Peter Grassberger. It was later renamed "statistical
Forecasting_complexity
An algorithmic complexity attack (ACA) is a form of attack in which an attacker sends a pattern of requests to a computer system that triggers the worst-case
Algorithmic_complexity_attack
counterpart, NLIN. Balcazar, Jose Luis; Diaz, Josep; Gabarro, Joaquim (1990). Structural Complexity II. Springer Verlag. ISBN 3-540-52079-1., Theorem 3.9 v t e
DLIN
Algorithmic runtime requirements for matrix multiplication
in computer science In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Algorithm characteristic in computations
In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the
Average-case_complexity
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