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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)
Measure of algorithmic complexity
particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than P's own length (see section
Kolmogorov_complexity
Complexity class used to classify decision problems
science P = ? N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} More unsolved problems in computer science In computational complexity theory
NP_(complexity)
Inherent difficulty of computational problems
the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do. The P versus NP problem, one of
Computational complexity theory
Computational_complexity_theory
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
Mathematic definition
extension complexity of a convex polytope P {\displaystyle P} is the smallest number of facets among convex polytopes Q {\displaystyle Q} that have P {\displaystyle
Extension_complexity
Model of computational complexity
Proving that N P ⊈ P / p o l y {\displaystyle {\mathsf {NP}}\not \subseteq {\mathsf {P/poly}}} would separate P and NP (see below). Complexity classes defined
Circuit_complexity
"statistical complexity" by James P. Crutchfield and Karl Young. Grassberger, P. (1986). "Toward a quantitative theory of self-generated complexity". International
Forecasting_complexity
Class of computational complexity
P = ? P S P A C E {\displaystyle {\mathsf {P{\overset {?}{=}}PSPACE}}} More unsolved problems in computer science In computational complexity theory
PSPACE
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
Topics referred to by the same term
The P convention in communication p-value, in statistical hypothesis testing P (complexity), a complexity class in computational complexity theory #P complexity
P_(disambiguation)
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
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
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
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
Adage in human-computer interaction
The law of conservation of complexity, also known as Tesler's Law, or Waterbed Theory, is an adage in human–computer interaction stating that every application
Law of conservation of complexity
Law_of_conservation_of_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 theory, SP 2 is a complexity class, intermediate between the first and second levels of the polynomial hierarchy. A language L is in S 2 P
S2P_(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)
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)
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
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)
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)
Computer memory needed by an algorithm
complexity classes PSPACE and NPSPACE allow f {\displaystyle f} to be any polynomial, analogously to P and NP. That is, P S P A C E = ⋃ c ∈ Z + D S P
Space_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)
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
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
Class in computational complexity theory
C = ? P {\displaystyle {\mathsf {NC}}{\overset {?}{=}}{\mathsf {P}}} More unsolved problems in computer science In computational complexity theory
NC_(complexity)
Measure in information theory
Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can
Logical_depth
Measure of complexity of real-valued functions
learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with
Rademacher_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
Classification of computer problems
problem in computer science – whether P = NP – by showing that the complexity class P is not equal to the complexity class NP. The idea behind the approach
Geometric_complexity_theory
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
String that certifies the answer to a computation
In computational complexity theory, a certificate (also called a witness) is a string that certifies the answer to a computation, or certifies the membership
Certificate_(complexity)
Immerman, in his book Descriptive Complexity, "use[s] the concept of query as the fundamental paradigm of computation" (p. 17). Given signatures σ {\displaystyle
Query_(complexity)
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)
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
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
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
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, 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
relationships with classic complexity classes are: P ⊆ B P P ⊆ B Q P ⊆ A W P P ⊆ P P ⊆ P S P A C E ⊆ E X P {\displaystyle {\mathsf {P\subseteq BPP\subseteq
BQP
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
Computational input that relies on the length but not content of the input
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)
Abstract machine used to study decision problems
in the relativized complexity class P R {\displaystyle {\mathsf {P}}^{R}} . Other relativized complexity classes such as N P R {\displaystyle {\mathsf
Oracle_machine
Complexity class
science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass
PPAD_(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
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
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)
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
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits
CC_(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)
Topics referred to by the same term
field of p-adic numbers Quadratic programming, a special type of mathematical optimization problem Quasi-polynomial time, relating to time complexity in computer
QP
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
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)
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)
Notion of the "hardest" or "most general" problem in a complexity class
(or "most expressive") problems in the complexity class. More formally, a problem p is called hard for a complexity class C under a given type of reduction
Complete_(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)
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
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)
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
System composed of many interacting components
M. (1995). What is Complexity? Complexity 1/1, 16-19 Dorogovtsev, S.N.; Mendes, J.F.F. (2003). Evolution of Networks. Vol. 51. p. 1079. arXiv:cond-mat/0106144
Complex_system
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
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
kinds of complexity are closely related: If P has facet complexity at most f, then P has vertex complexity at most 4 n2 f. If P has vertex complexity at most
N-dimensional_polyhedron
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)
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
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(complexity)
Complexity class
time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time
NP-hardness
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 management is a business methodology that deals with the analysis and optimization of complexity in enterprises. Effective complexity management
Complexity_management
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
Complexity class
#P-complete problems (pronounced "sharp P complete", "number P complete", or "hash P complete") form a complexity class in computational complexity theory
♯P-complete
Eighth letter of the Greek alphabet
Incorporated. p. 2. ISBN 978-1-119-01162-0. Θ (time decay): the price change of an option in relation to time; "Complexity Zoo:P - Complexity Zoo". complexityzoo
Theta
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
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)
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, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount
LH_(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)
Problem of determining whether polynomials are identical
that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computational complexity required for polynomial identity
Polynomial_identity_testing
Conversion calculation in petroluem refinery
The Nelson complexity index (NCI) is a measure to compare the secondary conversion capacity of a petroleum refinery with the primary distillation capacity
Nelson_complexity_index
Concept in topology
→ P X . {\displaystyle s_{i}:\,U_{i}\to \,PX.} The topological complexity: TC(X) = 1 if and only if X is contractible. The topological complexity of
Topological_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
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)
Length of expression as combination of 1s
In number theory, the complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions,
Integer_complexity
In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an
UP_(complexity)
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
Holistic measure of the productive capabilities of large economic systems
The Economic Complexity Index (ECI) is a holistic measure of the productive capabilities of large economic systems, usually cities, regions, or countries
Economic_Complexity_Index
Concept of art that can be described by a computer program
Low-complexity art was described by Jürgen Schmidhuber in 1997, defined as art that can be described by a short computer program (that is, a computer program
Low-complexity_art
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 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)
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)
On collapse of the polynomial hierarchy if NP is in non-uniform polynomial time class
time problems, can be contained in the non-uniform polynomial time complexity class P/poly, then this assumption implies the collapse of the polynomial
Karp–Lipton_theorem
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)
Topic in systems theory
Complex Societies, Cambridge, New York u.a. 1988, S. 42ff. Landau, J.-P.: Complexity and the financial crisis, Introductory remarks at the Conference on
Singularity_(systems_theory)
Function that counts distinct factors of a string
In computer science, the complexity function of a word or string (a finite or infinite sequence of symbols from some alphabet) is the function that counts
Complexity_function
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)
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)
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
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
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