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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)
Topics referred to by the same term
League All, Missouri, a community in the US All, a brand of Sun Products Albanian lek by ISO 4217 currency code ALL (complexity), the class of all decision
All
Branch of mathematical logic
needed to express the languages in them. For example, PH, the union of all complexity classes in the polynomial hierarchy, is precisely the class of languages
Descriptive_complexity_theory
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
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
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
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
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
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
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
the overall strategy of the company, 2) transparency over all costs and benefits of complexity, identifying the optimization benefits, 3) related measures
Complexity_management
Class of problems in computer science
probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity class was defined by Gill in 1977
PP_(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
P_(complexity)
or equivalently, threshold gates. For each fixed i, the complexity class TCi consists of all languages that can be recognized by a family of threshold
TC_(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
Complexity class used to classify decision problems
that verifies whether the guess is a solution to the problem. The complexity class P (all problems solvable, deterministically, in polynomial time) is contained
NP_(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
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)
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
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
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)
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)
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 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)
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
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
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)
Computer memory needed by an algorithm
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a
Space_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)
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)
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)
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
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
Topics referred to by the same term
theory Language complexity, a linguistic hypothesis All pages with titles beginning with Complexity Complex (disambiguation) Complexity theory (disambiguation)
Complexity_(disambiguation)
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(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)
Topics referred to by the same term
Complexity theory may refer to: Computational complexity theory, a field in theoretical computer science and mathematics Assembly theory, to quantify the
Complexity_theory
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
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
Class of computational complexity
unsolved problems in computer science In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine
PSPACE
Unsolved problem in computer science
problem, essentially all known proof techniques in computational complexity theory fall into one of the following classifications, all insufficient to prove
P_versus_NP_problem
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
2017 research paper by Google
large language models Gated recurrent units (2014) further reduced its complexity. Some architectures, such as RWKV (Receptance Weighted Key Value) or state
Attention_Is_All_You_Need
In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount
LH_(complexity)
System composed of many interacting components
and Complexity", exploring the diversity of problem types by contrasting problems of simplicity, disorganized complexity, and organized complexity. Weaver
Complex_system
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
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
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
In descriptive complexity, a query is a mapping from structures of one signature to structures of another vocabulary. Neil Immerman, in his book Descriptive
Query_(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
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits
CC_(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)
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)
Algorithm characteristic in computations
over all possible inputs. It is frequently contrasted with worst-case complexity which considers the maximal complexity of the algorithm over all possible
Average-case_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
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)
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, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t
SL_(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)
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)
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
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, the complexity class PPP (polynomial pigeonhole principle) is a subclass of TFNP. It is the class of search problems
PPP_(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
Information-based complexity (IBC) studies optimal algorithms and computational complexity for the continuous problems that arise in physical science,
Information-based_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)
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
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
computational complexity of an algorithm or a computational problem. It starts from an assumption about a probability distribution on the set of all possible
Probabilistic analysis of algorithms
Probabilistic_analysis_of_algorithms
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)
Measures of how efficiently algorithms use resources
respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function
Best,_worst_and_average_case
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
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
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)
Complexity class of bounded-depth circuits
(alternating circuit) is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families of circuits
AC0
Index of articles associated with the same name
Query complexity in computational complexity describes the number of queries needed to solve a computational problem for an input that can be accessed
Query_complexity
Unsolved problem on graph query complexity
vertices, but on the empty graph it tests all possible pairs before terminating. Therefore, the query complexity of this algorithm is ( n 2 ) = n ( n − 1
Aanderaa–Karp–Rosenberg conjecture
Aanderaa–Karp–Rosenberg_conjecture
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)
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
Quantum Merlin Arthur
for Quantum Merlin Arthur, refers to a complexity class in computational complexity theory. It is the set of all formal languages that satisfy the following
QMA
Topics referred to by the same term
described by RFC 2378 PH (complexity), the union of all complexity classes in the polynomial hierarchy in computational complexity theory Phot, or ph, a measurement
PH_(disambiguation)
Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics
Hamiltonian_complexity
Rules out assigning to arbitrary functions their computational complexity
computational complexity theory, Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about the complexity of computable
Blum's_speedup_theorem
Algorithm that employs a degree of randomness as part of its logic or procedure
known[as of?] if all algorithms can be derandomized without significantly increasing their running time. For instance, in computational complexity, it is unknown
Randomized_algorithm
Attribute of machine learning models
sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output
Sample_complexity
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
NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven, that P≠NP, it
NP-hardness
is estimating stationary distribution for an ergodic Markov chain. The complexity class is not known to equal PL, and an attempt to simulate PL through
PL_(complexity)
theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions. Given a Gödel numbering
Compression_theorem
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
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
Study of resources used by an algorithm
the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to
Analysis_of_algorithms
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
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
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
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
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
1988 studio album by Metallica
Association of America in 2003. ...And Justice for All was acclaimed for its depth and complexity, although its dry mix and nearly inaudible bass guitar
...And Justice for All (album)
...And_Justice_for_All_(album)
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
Type of computer science algorithm
In computational complexity theory, the strict definition of in-place algorithms includes all algorithms with O(1) space complexity, the class DSPACE(1)
In-place_algorithm
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ALL COMPLEXITY
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