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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)
Topics referred to by the same term
sequence Ultrafilter on a set § Completeness Complete (complexity), a notion referring to a problem in computational complexity theory that all other problems
Completeness
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
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely
NP-completeness
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
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 used to classify decision problems
would exist for solving NP-complete, and by corollary, all NP problems. The complexity class NP is related to the complexity class co-NP, for which the
NP_(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
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
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 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
Complexity class
In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time
NP-hardness
Unsolved problem in computer science
An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is
P_versus_NP_problem
theory of the reals § Complete problems Karp's 21 NP-complete problems List of PSPACE-complete problems Reduction (complexity) Grigoriev & Bodlaender
List_of_NP-complete_problems
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, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits
CC_(complexity)
Term describing difficult problems in AI
The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of
AI-complete
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)
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
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)
Unsolved problem in computational complexity theory
be solvable in polynomial 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
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
Method for solving one problem using another
Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes. The three most
Polynomial-time_reduction
In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems
NL-complete
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
Computational complexity class of problems
APPROX-QCIRCUIT-PROB problem is complete for efficient quantum computation, and the version presented below is complete for the Promise-BQP complexity class (and not for
BQP
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)
Set of computational problems stated by Richard Karp (1973)
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
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 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
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)
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)
In computer science, FIXP is a complexity class introduced by Kousha Etessami and Mihalis Yannakakis at 2010. It represents problems that can be solved
FIXP
Class of computational complexity
}{=}}PSPACE}}} More unsolved problems in computer science In computational complexity theory, PSPACE is the set of all decision problems that can be solved
PSPACE
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)
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
In computational complexity, an NP-complete (or NP-hard) problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose
Weak_NP-completeness
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)
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 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)
even when given reasonably complete information about the project system. With a lens of systems thinking, project complexity can be defined as an intricate
Project_complexity
complexity of the Dyson Telescope Puzzle. Vol. Games of No Chance 3. Robert A. Hearn (2008). "Amazons, Konane, and Cross Purposes are PSPACE-complete"
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
1999 book by Neil Immerman
of a first-order query) and complexity theory (including formal languages, resource-bounded complexity classes, and complete problems). Chapter three begins
Descriptive_Complexity
Type of decision problem in computer science
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input
PSPACE-complete
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
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 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
Measurement of computational complexity
on NP-completeness, the term "computational complexity" (of algorithms) has become commonly used to refer to asymptotic computational complexity. Further
Asymptotic computational complexity
Asymptotic_computational_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)
Soviet-American mathematician
computational complexity. Levin was awarded the Knuth Prize in 2012 for his discovery of NP-completeness and the development of average-case complexity. He is
Leonid_Levin
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)
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is
Cook–Levin_theorem
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
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
Strategic board wargame
one smaller. The Wargamer Academy rates the complexity of CNA, on a scale of 1–10, as 10+. The complete campaign game takes 111 turns, each turn representing
The_Campaign_for_North_Africa
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
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
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
Computational property
In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational
Strong_NP-completeness
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Calculations of the game complexity of Go
harder complexity. Without ko, Go is PSPACE-hard. This is proved by reducing True Quantified Boolean Formula, which is known to be PSPACE-complete, to generalized
Go_and_mathematics
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)
American-Canadian computer scientist, contributor to complexity theory
who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor emeritus at the University
Stephen_Cook
In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an
UP_(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 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)
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)
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 complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
Concept in computational complexity theory
In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic
NEXPTIME
Computational problem
In computational complexity theory, generalized geography is a well-known PSPACE-complete problem. Geography is a children's game, where players take turns
Generalized_geography
When a finite set S of relations yields polynomial-time or NP-complete problems
because the complexity of the problem defined by S is either in P or is NP-complete, as opposed to one of the classes of intermediate complexity that is known
Schaefer's_dichotomy_theorem
Class in computational complexity theory
In computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be
P-complete
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
This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with
List of computability and complexity topics
List_of_computability_and_complexity_topics
Musical concept indicating to the speed of interpretation
are perceived in the simplest way. From the viewpoint of Kolmogorov's complexity theory, this means a representation of the data that minimizes the amount
Tempo
Reduction between decision problems that preserves strong NP-completeness
computational complexity theory, a pseudo-polynomial transformation is a kind of reduction between decision problems that preserves strong NP-completeness. It maps
Pseudo-polynomial transformation
Pseudo-polynomial_transformation
Complexity class consisting of all recursive languages
Steve Smale, (1989), "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines", Bulletin
R_(complexity)
Complexity class
In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in
Co-NP-complete
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
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
Vertex coloring where every color pairing appears at least once
In graph theory, a complete coloring is a (proper) vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices. Equivalently
Complete_coloring
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
In computational complexity, not-all-equal 3-satisfiability (NAE3SAT) is an NP-complete variant of the Boolean satisfiability problem, often used in proofs
Not-all-equal 3-satisfiability
Not-all-equal_3-satisfiability
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
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)
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
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)
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)
Set of decision problems
Ackermann-complete. It is EXPSPACE-complete to decide whether the reachability of a given vector addition system is finite. Game complexity Meyer, A.R
EXPSPACE
Aspect of music
increased complexity to disrupt the sense of a regular beat, leading eventually to the widespread use of irrational rhythms in New Complexity. This use
Rhythm
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
Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics
Hamiltonian_complexity
Algorithm used for pathfinding and graph traversal
major practical drawback is its O ( b d ) {\displaystyle O(b^{d})} space complexity where d is the depth of the shallowest solution (the length of the shortest
A*_search_algorithm
Yes/no problem in computer science
computational complexity theory to characterize complexity classes of decision problems. For example, the Boolean satisfiability problem is complete for the
Decision_problem
Game generalized so that it can be played on a board or grid of any size
position is EXPTIME-complete. Generalized chess, go (with Japanese ko rules), Quixo, and checkers are EXPTIME-complete. Game complexity Combinatorial game
Generalized_game
Variant of heap data structure
worst-case time complexity of O(log n). For a random heap, and for repeated insertions, the insertion operation has an average-case complexity of O(1). The
Binary_heap
1979 classic textbook on computational complexity theory
Johnson has the best introduction to computational complexity I have ever seen." List of NP-complete problems Garey, M. R.; Johnson, D. S. (1979). Victor
Computers_and_Intractability
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
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