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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)
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
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 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
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
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 complexity of real-valued functions
real valued functions. Given a set A ⊆ R m {\displaystyle A\subseteq \mathbb {R} ^{m}} , the Rademacher complexity of A is defined as follows: Rad ( A
Rademacher_complexity
Abstract machine used to study decision problems
of a certain problem R {\displaystyle R} in a single operation. The problem R {\displaystyle R} can be of any complexity class, or it can even
Oracle_machine
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
System composed of many interacting components
study of complex system, 2004. Chu, D.; Strand, R.; Fjelland, R. (2003). "Theories of complexity". Complexity. 8 (3): 19–30. Bibcode:2003Cmplx...8c..19C.
Complex_system
Attribute of a software system
Programming complexity (or software complexity) is a term that includes software properties that affect internal interactions. Several commentators distinguish
Programming_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)
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
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
String that certifies the answer to a computation
that R(x, y) In this definition, y is the certificate, or witness, for the membership of x in L. Certificates also give definitions for some complexity classes
Certificate_(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
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
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
American writer and television producer (born 1948)
Weekly writes of his ongoing epic fantasy A Song of Ice and Fire: "The complexity of characters such as Daenerys, Arya and the Kingslayer will keep readers
George_R._R._Martin
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 psychology
Cognitive complexity describes cognition along a simplicity-complexity axis. It is the subject of academic study in fields including personal construct
Cognitive_complexity
Data structures used in spatial indexing
(bulk-loaded) Priority R-tree variant of the R-tree is worst-case optimal, but due to its increased complexity it has remained confined to theoretical study
R-tree
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
Data structure used for indexing spatial information
objects and has little impact on the total complexity. The total insert complexity is still comparable to the R-tree: reinsertions affect at most one branch
R*-tree
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)
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
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)
Transformation of one computational problem to another
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently
Reduction_(complexity)
In computational complexity theory, the complexity class E L E M E N T A R Y {\displaystyle {\mathsf {ELEMENTARY}}} consists of the decision problems
ELEMENTARY
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
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
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
Function in algebraic graph theory
strongly on the value of x and has been intensively studied in computational complexity. When x is a natural number, this problem is normally viewed as computing
Chromatic_polynomial
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)
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)
Topics referred to by the same term
calls R (programming language), an environment for statistical computing and graphics R (complexity), the set of all recursive languages IBM System R, an
R_(disambiguation)
Measure of the level of consciousness
Perturbational Complexity Index (PCI) is a quantitative measure used in neuroscience to assess the level of consciousness based on the complexity of brain responses
Perturbational Complexity Index
Perturbational_Complexity_Index
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)
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)
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)
Complexity measure in computer science
The Lempel–Ziv complexity is a measure that was first presented in the article On the Complexity of Finite Sequences (IEEE Trans. On IT-22,1 1976), by
Lempel–Ziv_complexity
Complexity management is a business methodology that deals with the analysis and optimization of complexity in enterprises. Effective complexity management
Complexity_management
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
Stacey, R. (2006). The Science of Complexity: An Alternative Perspective for Strategic Change Processes. In R. MacIntosh et al (eds.). Complexity and Organization:
Business_agility
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
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
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
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)
Existential second order logic captures NP
oldest result of descriptive complexity theory, a branch of computational complexity theory that characterizes complexity classes in terms of logic-based
Fagin's_theorem
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
Proof checkable by a randomized algorithm
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 to
Probabilistically checkable proof
Probabilistically_checkable_proof
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)
American computer scientist and mathematician
major contributions to the fields of mathematical logic, complexity theory and proof complexity. He is currently a professor at the University of California
Samuel_Buss
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
Soviet-American mathematician
Albert R. Meyer. He is well known for his work in randomness in computing, algorithmic complexity and intractability, average-case complexity, foundations
Leonid_Levin
Model of computational complexity
In computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree,
Decision_tree_model
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
Unsolved problem in computer science
2307/2580891. JSTOR 2580891. R. Impagliazzo, "A personal view of average-case complexity", p. 134, 10th Annual Structure in Complexity Theory Conference (SCT'95)
P_versus_NP_problem
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
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
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
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
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
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
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 ) ) {\displaystyle O(\log ^{*}(n))} , the
Disjoint-set_data_structure
Country in East Asia
September 2025. Retrieved 20 June 2026. "Textiles". Observatory of Economic Complexity. 2024. Archived from the original on 10 August 2026. Retrieved 10 August
China
Attribute of machine learning models
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function
Sample_complexity
American businessman
coverage as “political activism, not journalism”. Lissack, Michael R. "Complexity: the science, its vocabulary, and its relation to organizations", Emergence
Michael_Lissack
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
strictly contained in R (Cooper 2004:88). On the other hand, we can "enumerate" any recursively enumerable set (see also its complexity class RE) by a primitive-recursive
PR_(complexity)
Reduction between decision problems that preserves strong NP-completeness
In computational complexity theory, a pseudo-polynomial transformation is a kind of reduction between decision problems that preserves strong NP-completeness
Pseudo-polynomial transformation
Pseudo-polynomial_transformation
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
Country in Eurasia from 1922 to 1991
2307/2494336. JSTOR 2494336. Tetlock, Philip E. (December 1985). "Integrative complexity of American and Soviet foreign policy rhetoric: A time-series analysis"
Soviet_Union
Indicator for how well data points fit a line or curve
the model and its complexity, which is shown as a u-shape curve on the right. For the adjusted R2 specifically, the model complexity (i.e. number of parameters)
Coefficient_of_determination
Quantified formulas with real-number variables
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the
Existential theory of the reals
Existential_theory_of_the_reals
English and American actor (born 1983)
wrote that despite an exceptional story, the film had glossed over the complexities in Cavendish's life, and thought that Garfield was "hampered by a role
Andrew_Garfield
Mathematical method of assigning a prior probability to a given observation
in Problemy Peredaci Informacii 9, pp. 115–116, 1973 Solomonoff, R., "Complexity-Based Induction Systems: Comparisons and Convergence Theorems," IEEE
Algorithmic_probability
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
Human Y-chromosome DNA haplogroup
haplogroups in populations of the world R-L21 R-L295 R-M124 R-M167 R-M17 R-M173 R-M207 R-M342 R-M420 R-M479 R-U106 According to Family Tree,[who?] they
Haplogroup_R1a
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
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
Concept in computational complexity theory
time; 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
Cobham's_thesis
Type of computational problem
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a
Counting_problem_(complexity)
Class of models and problems in circuit complexity
ACC, is a class of computational models and problems defined in circuit complexity, a field of theoretical computer science. The class is defined by augmenting
ACC0
In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for
Propositional_proof_system
American basketball player (born 1985)
with a concentration in Applied Cultural Thought. In 2021, J.R Smith signed with Complexity Gaming, and he has also played Warzone tournaments. In 2012
J._R._Smith
Complexity class used in circuit complexity
theoretical computer science, and specifically computational complexity theory and circuit complexity, TC0 (Threshold Circuit) is the first class in the hierarchy
TC0
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)
Theorem in computational complexity theory
computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class
PCP_theorem
Set of problems solved by small circuits
computational complexity theory, P/poly is a complexity class that can be defined in both circuit complexity and non-uniform complexity. Since the two
P/poly
Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , resource bounded measure gives a method to classify the size of subsets of complexity classes. For
Resource-bounded_measure
American social scientist (1942–2021)
Douglas R. White (1942 – 22 August 2021) was an American complexity researcher, social anthropologist, sociologist, and social network researcher at the
Douglas_R._White
Discrete Fourier transform algorithm
of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n 2 ) {\textstyle O(n^{2})} , which arises
Fast_Fourier_transform
Associative array for storing key–value pairs
probing sequence. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the
Hash_table
Prime Minister of India from 1984 to 1989
foreseen but unavoidable in the resolution of an issue of this magnitude and complexity, this Agreement represents the only way of safeguarding legitimate Tamil
Rajiv_Gandhi
Austrian nonprofit research organization
The Complexity Science Hub Vienna (CSH) is a Vienna-based research organisation with the aim to bundle, coordinate and advance the research of complex
Complexity_Science_Hub
Equivalence of average-case and expected complexity
In computational complexity theory, Yao's principle (also called Yao's minimax principle or Yao's lemma) relates the performance of randomized algorithms
Yao's_principle
Sports car manufactured by Japanese automobile manufacturer Nissan
drag for improved fuel efficiency. Initially, engineers expressed the complexity of achieving such an aerodynamic level, given a road car's high ground
Nissan_GT-R
Unsolved problem in computational complexity theory
time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem
Graph_isomorphism_problem
Geological theory of abrupt, severe change
Cambridge, Massachusetts: Perseus Publishing. ISBN 0-7382-0282-7. Lewin, R.; Complexity, Dent, London, 1993, p. 75 Palmer, T.; Catastrophism, Neocatastrophism
Catastrophism
travel, tourism, insurance
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