In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of specific 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 contrast, a heuristic is a technique used in problem solving that uses practical methods and/or various estimates in order to produce solutions that may not be optimal but are sufficient given the circumstances.
Computer science is the study of algorithmic processes, computational machines and computation itself. As a discipline, computer science spans a range of topics from theoretical studies of algorithms, computation and information to the practical issues of implementing computational systems in hardware and software.
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:
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program.
In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive.
In computability theory, a primitive recursive function is roughly speaking a function that can be computed by a computer program whose loops are all "for" loops. Primitive recursive functions form a strict subset of those general recursive functions that are also total functions.
Recursion occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances, it is often done in such a way that no infinite loop or infinite chain of references can occur.
Stanley Bootle, known as Stan Kelly-Bootle, was a British author, academic, singer-songwriter and computer scientist.
In computer programming, an infinite loop is a sequence of instructions that, as written, will continue endlessly, unless an external intervention occurs. It may be intentional.
Arthur John Robin Gorell Milner, known as Robin Milner or A. J. R. G. Milner, was a British computer scientist, and a Turing Award winner.
In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum key value and the minimum key value, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. It is often used as a subroutine in radix sort, another sorting algorithm, which can handle larger keys more efficiently.
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
John McCarthy was an American computer scientist and cognitive scientist. McCarthy was one of the founders of the discipline of artificial intelligence. He co-authored the document that coined the term "artificial intelligence" (AI), developed the Lisp programming language family, significantly influenced the design of the ALGOL programming language, popularized time-sharing, and invented garbage collection.
The Devil's Dictionary is a satirical dictionary written by American Civil War soldier, journalist, and writer Ambrose Bierce consisting of common words followed by humorous and satirical definitions. The lexicon was written over three decades as a series of installments for magazines and newspapers. Bierce's witty definitions were imitated and plagiarized for years before he gathered them into books, first as The Cynic's Word Book in 1906 and then in a more complete version as The Devil's Dictionary in 1911.
Barbara Liskov is an American computer scientist who is an Institute Professor at the Massachusetts Institute of Technology and Ford Professor of Engineering in its School of Engineering's electrical engineering and computer science department.
In computer science, recursion is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem. Such problems can generally be solved by iteration, but this needs to identify and index the smaller instances at programming time. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.
The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number of computations can be described by a finite recursive program, even if this program contains no explicit repetitions.
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.
The Jargon File is a glossary and usage dictionary of slang used by computer programmers. The original Jargon File was a collection of terms from technical cultures such as the MIT AI Lab, the Stanford AI Lab (SAIL) and others of the old ARPANET AI/LISP/PDP-10 communities, including Bolt, Beranek and Newman, Carnegie Mellon University, and Worcester Polytechnic Institute. It was published in paperback form in 1983 as The Hacker's Dictionary, revised in 1991 as The New Hacker's Dictionary.
In mathematics and computer science, an algorithmic technique is a general approach for implementing a process or computation.
