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Inherent difficulty of computational problems
theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage
Computational complexity theory
Computational_complexity_theory
Amount of resources to perform an algorithm
computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation
Computational_complexity
Algorithmic runtime requirements for matrix multiplication
problems in computer science In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Feature of systems that defy description
For instance, for many functions (problems), such a computational complexity as time of computation is smaller when multitape Turing machines are used
Complexity
Notion in combinatorial game theory
game positions, possible outcomes, and computational complexity of various game scenarios. The state-space complexity of a game is the number of legal game
Game_complexity
Measurement of computational complexity
computational complexity of algorithms and computational problems, commonly associated with the use of the big O notation. With respect to computational resources
Asymptotic computational complexity
Asymptotic_computational_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
Algorithmic runtime requirements for common math procedures
list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
American computer scientist (born 1981)
University of Texas at Austin. His primary areas of research are computational complexity theory and quantum computing. Aaronson grew up in the United States
Scott_Aaronson
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
Partition of a simple polygon into triangles
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set
Polygon_triangulation
Problem in combinatorial optimization
Problems". In R. E. Miller and J. W. Thatcher (editors). Complexity of Computer Computations. New York: Plenum. pp. 85–103 Kellerer, Hans; Pferschy, Ulrich;
Knapsack_problem
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
Subfield of computer science and mathematics
transmitted data. Computational complexity theory is a branch of the theory of computation that focuses on classifying computational problems according
Theoretical_computer_science
Type of computer science algorithm
in-place. In computational complexity theory, the strict definition of in-place algorithms includes all algorithms with O(1) space complexity, the class
In-place_algorithm
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 the philosophy of mathematics
problem International Workshop on Logic and Computational Complexity, Logic and Computational Complexity, Springer, 1995, p. 31. St. Iwan (2000), "On
Ultrafinitism
Computational complexity of quantum algorithms
computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as
Quantum_complexity_theory
Mathematical model describing how an output of a function is computed given an input
more specifically in computability theory and computational complexity theory, a model of computation is a model that describes how an output of a mathematical
Model_of_computation
Mathematical function generalizing the determinant and permanent
The computational complexity of evaluating an immanant depends strongly on the shape of the associated diagram. Early results in algebraic complexity theory
Immanant
Field in logic and theoretical computer science
proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are
Proof_complexity
Mathematical operation in linear algebra
square n×n matrices. Its computational complexity is therefore O ( n 3 ) {\displaystyle O(n^{3})} , in a model of computation for which the scalar operations
Matrix_multiplication
Appearing random but actually being generated by a deterministic, causal process
significant advantage. This notion of pseudorandomness is studied in computational complexity theory and has applications to cryptography. Formally, let S and
Pseudorandomness
Academic subfield of computer science
automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental
Theory_of_computation
Open problem on 3x+1 and x/2 functions
The Collatz and related conjectures are often used when studying computational complexity. The connection is made through the busy beaver function, where
Collatz_conjecture
Branch of chemistry
Computational chemists typically focus on developing and applying computer programs and methodologies to specific chemical questions. The complexity inherent
Computational_chemistry
In computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes
Structural_complexity_theory
Casual games by The New York Times
since 1991, just "Acrostic". Computer scientists have studied the computational complexity of solving several NYT Games. This allows one to understand, for
The_New_York_Times_Games
American computer scientist (1928–2022)
field of computational complexity theory." Their paper defined the foundational notion of a Complexity class, a way of classifying computational problems
Juris_Hartmanis
American computer scientist (born 1969)
1979), is an American theoretical computer scientist working in computational complexity theory and algorithms. Williams graduated from the Alabama School
Ryan Williams (computer scientist)
Ryan_Williams_(computer_scientist)
Academic conference in computer science
The Computational Complexity Conference (CCC) is an academic conference in the field of theoretical computer science whose roots date to 1986. It fosters
Computational Complexity Conference
Computational_Complexity_Conference
Branch of the discipline of sociology
science. In relevant literature, computational sociology is often related to the study of social complexity. Social complexity concepts such as complex systems
Computational_sociology
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)
Conceptual framework
databases. The emerging methods of socionics are a variant of computational sociology. Computational sociology is influenced by a number of micro-sociological
Social_complexity
Problem a computer might be able to solve
factor of n." is a computational problem that has a solution, as there are many known integer factorization algorithms. A computational problem can be viewed
Computational_problem
Rendering method
rendering algorithms for generating digital images. On a spectrum of computational cost and visual fidelity, ray tracing-based rendering techniques, such
Ray_tracing_(graphics)
Term describing difficult problems in AI
done by expert systems.[citation needed] Computational complexity theory deals with the relative computational difficulty of computable functions. By definition
AI-complete
Computational complexity
problems in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems
NL_(complexity)
Branch of computational complexity theory
computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their
Parameterized_complexity
Self-balancing binary search tree
Additionally, after finding a node for insertion and deletion, the amortized complexity of the tree restructuring operations is constant. Adding or deleting the
WAVL_tree
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
In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements
Element_distinctness_problem
Proof checkable by a randomized algorithm
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a
Probabilistically checkable proof
Probabilistically_checkable_proof
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
Hypothesis in computational complexity theory
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where
Computational hardness assumption
Computational_hardness_assumption
Branch of computer science
study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry
Computational_geometry
Measure of algorithmic complexity
the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size
Kolmogorov_complexity
Israeli computer scientist and mathematician
computational complexity", under the supervision of Richard Lipton. He is credited with significantly expanding the field of computational complexity
Avi_Wigderson
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Computer memory needed by an algorithm
complexity theory – Inherent difficulty of computational problems Computational resource – Aspect of computational complexity theory Time complexity –
Space_complexity
Type of hash function
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input
Rolling_hash
of algorithms is an approach to estimate the computational complexity of an algorithm or a computational problem. It starts from an assumption about a
Probabilistic analysis of algorithms
Probabilistic_analysis_of_algorithms
Determining whether a knot is the unknot
complexity class P. First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes
Unknotting_problem
Aspect of computational complexity theory
In computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems
Computational_resource
Mathematics award
including: All mathematical aspects of computer science, including computational complexity theory, logic of programming languages, analysis of algorithms
IMU_Abacus_Medal
Algorithm to multiply two numbers
integers. This is known as the computational complexity of multiplication. Usual algorithms done by hand have asymptotic complexity of O ( n 2 ) {\displaystyle
Multiplication_algorithm
American computer scientist
science at the University of California, San Diego, specializing in computational complexity theory. Impagliazzo received a BA in mathematics from Wesleyan
Russell_Impagliazzo
Written or spoken word game
Ghost (also known as ghosts or pig) is a written or spoken word game in which players take turns to extend the letters of a word without completing a valid
Ghost_(game)
List of unsolved computational problems
implications for fields such as cryptography, algorithm design, and computational theory. What is the relationship between BQP and NP? NC = P problem
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
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
Class of algorithms in computational geometry
In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities
Convex_hull_algorithms
Calculations of the game complexity of Go
use in Go). Generalized Go is played on n × n boards, and the computational complexity of determining the winner in a given position of generalized Go
Go_and_mathematics
Combinatorial optimization problem
problem in polynomial time, and even small instances may require long computation time. It was also proven that the problem does not have an approximation
Quadratic_assignment_problem
Combined real-and-virtual environment
Theory of computing Model of computation Stochastic Formal language Automata theory Computability theory Computational complexity theory Logic Semantics Algorithms
Extended_reality
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
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
NC_(complexity)
Set of objects whose state must satisfy limits
studied in computational complexity theory, finite model theory and universal algebra. It turned out that questions about the complexity of CSPs translate
Constraint satisfaction problem
Constraint_satisfaction_problem
Statistical method in data analysis
and can scale poorly as n {\displaystyle n} grows (see § Complexity above). In computational biology, single-cell technologies such as mass cytometry
Hierarchical_clustering
(2011-03-01). "Descriptional and computational complexity of finite automata—A survey". Information and Computation. 209 (3): 456–470. doi:10.1016/j.ic
Alternating_finite_automaton
Unsolved problem in computer science
relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources
P_versus_NP_problem
Computer system simulating intelligence
Recognized journals include Computational Intelligence, International Journal of Computational Intelligence Systems, Applied Computational Intelligence and Soft
Computational_intelligence
Topics referred to by the same term
generate it. Solomonoff–Kolmogorov–Chaitin complexity, the most widely used such measure. In computational complexity theory, although it would be a non-formal
Algorithmic_complexity
1998 non-fiction book
Complexity and Real Computation is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are
Complexity and Real Computation
Complexity_and_Real_Computation
Geometric graph with unit edge lengths
Welzl, Emo (1990), "Combinatorial complexity bounds for arrangements of curves and spheres", Discrete & Computational Geometry, 5 (2): 99–160, doi:10.1007/BF02187783
Unit_distance_graph
American-Canadian computer scientist, contributor to complexity theory
Department of Mathematics. Cook is considered one of the forefathers of computational complexity theory. He won the 1982 ACM Turing Award. Cook received his bachelor's
Stephen_Cook
Interactive proof system in computational complexity theory
In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin
Arthur–Merlin_protocol
NP-hard problem in combinatorial optimization
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances
Travelling_salesman_problem
Indian American professor of computer science (born 1957)
centered around the design of algorithms, together with work on computational complexity theory, cryptography, and algorithmic game theory. During the 1980s
Vijay_Vazirani
Method of determining a point in 3D space
estimation of some parameters. This means that both the computation time and the complexity of the operations involved may vary between the different
Triangulation (computer vision)
Triangulation_(computer_vision)
Computational benchmark
engineering task of building a powerful quantum computer and the computational-complexity-theoretic task of finding a problem that can be solved by that
Quantum_supremacy
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)
Area of mathematics
scientific computation The mathematics of scientific computation, in particular numerical analysis, the theory of numerical methods Computational complexity Computer
Computational_mathematics
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
PSPACE
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
NP_(complexity)
is called facet enumeration (see convex hull algorithms). The computational complexity of the problem is a subject of research in computer science. For
Vertex_enumeration_problem
Book by Stephen Wolfram
discusses how facts about the computational universe inform evolutionary theory, SETI, free will, computational complexity theory, and philosophical fields
A_New_Kind_of_Science
Decidable first-order theory of the natural numbers with addition
Presburger arithmetic is an interesting example in computational complexity theory and computation. Let n be the length of a statement in Presburger arithmetic
Presburger_arithmetic
Subfield of mathematical topology
topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and
Computational_topology
of agents from a computational perspective. In particular, computational social choice is concerned with the efficient computation of outcomes of voting
Computational_social_choice
Greek computer scientist
machine learning. He is known for work on the computational complexity of Nash equilibria, the complexity of multi-item auctions, and the behavior of the
Constantinos_Daskalakis
Algorithm that employs a degree of randomness as part of its logic or procedure
Papadimitriou (1993), Computational Complexity (1st ed.), Addison Wesley, ISBN 978-0-201-53082-7 Chapter 11: Randomized computation, pp. 241–278. Rabin
Randomized_algorithm
Board game
English draughts is 500,995,484,682,338,672,639 and it has a game-tree complexity of approximately 1040. By comparison, chess is estimated to have between
English_draughts
Symposium on Computational Geometry CIAA – International Conference on Implementation and Application of Automata CCC – Computational Complexity Conference
List of computer science conferences
List_of_computer_science_conferences
Computation model defining an abstract machine
theorists investigating questions in the theory of computation. In particular, computational complexity theory makes use of the Turing machine: Depending
Turing_machine
Standard form of Boolean function
contradictions, as well as valid CNFs. An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula
Conjunctive_normal_form
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
Technique in digital signal processing
calculations, which has computational complexity equivalent of sliding DFT), the Goertzel algorithm has a higher order of complexity than fast Fourier transform
Goertzel_algorithm
Two-player board game
The Game of the Amazons (in Spanish, El Juego de las Amazonas; often called Amazons for short) is a two-player abstract strategy game invented in 1988
Game_of_the_Amazons
Algorithm to multiply matrices
the computational complexity of matrix multiplication) remains unknown. As of September 2025[update], the best bound on the asymptotic complexity of a
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Subpermutation of a longer permutation
S2CID 1846959. Bruner, Marie-Louise; Lackner, Martin (2013), "The computational landscape of permutation patterns", Pure Mathematics and Applications
Permutation_pattern
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
Boy/Male
Indian, Sikh
Good Soul
Girl/Female
Biblical
Olive tree.
Girl/Female
Danish, German, Hindu, Indian, Latin, Swedish
Heavenly
Boy/Male
Australian, French, German
Guardian; Mighty with a Spear
Surname or Lastname
English (Worcestershire)
English (Worcestershire) : topographic name for someone living by a steep uphill path, from a derivative of Old English stigel, stigol ‘steep uphill path’. Compare Stiles.
Girl/Female
Hindu, Indian, Marathi
Graceful; Prosperous
Surname or Lastname
English
English : variant spelling of Toll.
Surname or Lastname
Cornish
Cornish : nickname for someone with white hair or a pale complexion, from Cornish gwnn ‘white’ + the definite article an.English : regional name for someone from Anjou, France (see Angevine).
Boy/Male
Tamil
Kameshwary | காமேஷà¯à®µà®¾à®°à¯à®¯
Kama God
Boy/Male
Muslim
An old Arabian tribe's name.
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
COMPUTATIONAL COMPLEXITY
v. i.
To make an enumeration or computation; to engage in numbering or computing.
v. t.
To exceed in reckoning or computation.
n.
Account; reckoning; computation.
n.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.
n.
Reckoning; computation.
n.
Erroneous computation; false reckoning.
n.
The difference of the results obtained by observation, and by computation from a formula.
n.
The act or process of computing; calculation; reckoning.
n.
Enumeration; computation.
a.
Proceeding by sixes; sextuple; -- applied especially to a system of arithmetical computation in which the base is six.
n.
The science of numbers; the art of computation by figures.
n.
The act or process, or the result, of calculating; computation; reckoning, estimate.
a.
Proceeding in computation by twelves; expressed in the scale of twelves.
a.
Capable of being measured; susceptible of mensuration or computation.
n.
The result of computation; the amount computed.
n.
The fifth month of the Jewish year according to the ecclesiastical reckoning, the eleventh by the civil computation, coinciding nearly with August.
n.
A reckoning; computation; calculation; enumeration; a record of some reckoning; as, the Julian account of time.
n.
An erroneous computation.
n.
The act or process of making mathematical computations or of estimating results.
n.
Computation.