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In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always unambiguous and are used as specifications for performing calculations, data processing, automated reasoning, and other tasks.
In logic and computer science, the Boolean satisfiability problem is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make = TRUE. In contrast, "a AND NOT a" is unsatisfiable.
Computer science is the study of processes that interact with data and that can be represented as data in the form of programs. It enables the use of algorithms to manipulate, store, and communicate digital information. A computer scientist studies the theory of computation and the design of software systems.
Computational linguistics is an interdisciplinary field concerned with the statistical or rule-based modeling of natural language from a computational perspective, as well as the study of appropriate computational approaches to linguistic questions.
In computability theory, the Church–Turing thesis is a hypothesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by a Turing machine. The thesis is named after American mathematician Alonzo Church and the British mathematician Alan Turing. Before the precise definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil methods. In the 1930s, several independent attempts were made to formalize the notion of computability:
Multics is an influential early time-sharing operating system which is based on the concept of a single-level memory. Multics "has influenced all modern operating systems since, from microcomputers to mainframes."
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Data processing is, generally, "the collection and manipulation of items of data to produce meaningful information." In this sense it can be considered a subset of information processing, "the change (processing) of information in any manner detectable by an observer."
In artificial intelligence (AI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions. Evolution of the population then takes place after the repeated application of the above operators.
In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form which gives it useful properties for use in logic programming, formal specification, and model theory. Horn clauses are named for the logician Alfred Horn, who first pointed out their significance in 1951.
A cognitive model is an approximation to animal cognitive processes for the purposes of comprehension and prediction. Cognitive models can be developed within or without a cognitive architecture, though the two are not always easily distinguishable.
Robert Anthony Kowalski is a logician and computer scientist, whose research is concerned with developing both human-oriented models of computing and computational models of human thinking. He has spent most of his career in the United Kingdom.
The object-capability model is a computer security model. A capability describes a transferable right to perform one operations on a given object. It can be obtained by the following combination:
A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced by John von Neumann. The same name may also refer to quantum dot cellular automata, which are a proposed physical implementation of "classical" cellular automata by exploiting quantum mechanical phenomena. QCA have attracted a lot of attention as a result of its extremely small feature size and its ultra-low power consumption, making it one candidate for replacing CMOS technology.
In computability theory, super-recursive algorithms are a generalization of ordinary algorithms that are more powerful, that is, compute more than Turing machines. The term was introduced by Mark Burgin, whose book "Super-recursive algorithms" develops their theory and presents several mathematical models. Turing machines and other mathematical models of conventional algorithms allow researchers to find properties of recursive algorithms and their computations. In a similar way, mathematical models of super-recursive algorithms, such as inductive Turing machines, allow researchers to find properties of super-recursive algorithms and their computations.
In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
References
- Dennis, J. B., and Glasee, E. The structure of on-line information processing systems. Information Systems Sciences: Proc. Second Cong., Spartan Books, Baltimore, 1965, pp. 1–11
- J. B. Dennis and E. C. Van Horn. Programming Semantics for Multiprogrammed Computations . Communications of the ACM 9(3), March 1966.
- Levy, Henry M. (1984). "3". Capability-based computer systems. Maynard, Mass: Digital Press. ISBN 0-932376-22-3.
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