In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.
A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of 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 the seven Millennium Prize Problems,[1] is part of the field of computational complexity.
Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically.
^"P vs NP Problem | Clay Mathematics Institute". www.claymath.org. Archived from the original on July 6, 2018. Retrieved July 6, 2018.
and 24 Related for: Computational complexity theory information
theoretical computer science and mathematics, computationalcomplexitytheory focuses on classifying computational problems according to their resource usage...
computationalcomplexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation...
three major branches: automata theory and formal languages, computability theory, and computationalcomplexitytheory, which are linked by the question:...
In computationalcomplexitytheory, asymptotic computationalcomplexity is the usage of asymptotic analysis for the estimation of computational complexity...
Quantum complexitytheory is the subfield of computationalcomplexitytheory that deals with complexity classes defined using quantum computers, a computational...
Complexitytheory may refer to: Computationalcomplexitytheory, a field in theoretical computer science and mathematics Complex systems theory, the study...
problems in computer science) In theoretical computer science, the computationalcomplexity of matrix multiplication dictates how quickly the operation of...
In computationalcomplexitytheory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly...
science, and more specifically in computability theory and computationalcomplexitytheory, a model of computation is a model which describes how an output of...
usage of the term complexity specifically refers to sociologic theories of society as a complex adaptive system, however, social complexity and its emergent...
list the computationalcomplexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing...
the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size...
the time complexity is the computationalcomplexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly...
Descriptive complexity is a branch of computationalcomplexitytheory and of finite model theory that characterizes complexity classes by the type of logic...
transmitted data. Computationalcomplexitytheory is a branch of the theory of computation that focuses on classifying computational problems according...
important factor of complexity. In several scientific fields, "complexity" has a precise meaning: In computationalcomplexitytheory, the amounts of resources...
used by an algorithm Computational complexitytheory – Inherent difficulty of computational problems Computational resource – Something a computer needs...
University of Texas at Austin. His primary areas of research are computationalcomplexitytheory and quantum computing. Aaronson is married to computer scientist...
of n. Computational problems are one of the main objects of study in theoretical computer science. The field of computationalcomplexitytheory attempts...
theory is also sometimes used (a working is shown for this particular example here). In addition, the computational cost and computationalcomplexity...
Carlo algorithm repeatedly till a correct answer is obtained. Computationalcomplexitytheory models randomized algorithms as probabilistic Turing machines...
scientific computation The mathematics of scientific computation, in particular numerical analysis, the theory of numerical methods Computationalcomplexity Computer...
computer science, in particular, computational geometry and computationalcomplexitytheory. A primary concern of algorithmic topology, as its name suggests...
computer science, parameterized complexity is a branch of computationalcomplexitytheory that focuses on classifying computational problems according to their...