In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes and deduce valid inferences, achieving automation eventually. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".
In computability theory, the Church–Turing thesis is a thesis 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:
Douglas Richard Hofstadter is an American cognitive and computer scientist whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, strange loops, artificial intelligence, and discovery in mathematics and physics. His 1979 book Gödel, Escher, Bach: An Eternal Golden Braid won the Pulitzer Prize for general nonfiction, and a National Book Award for Science. His 2007 book I Am a Strange Loop won the Los Angeles Times Book Prize for Science and Technology.
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.
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. 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, such as turning off power via a switch or pulling a plug. It may be intentional.
Iteration is the repetition of a process in order to generate a sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration.
Structure and Interpretation of Computer Programs (SICP) is a computer science textbook by Massachusetts Institute of Technology professors Harold Abelson and Gerald Jay Sussman with Julie Sussman. It is known as the "Wizard Book" in hacker culture. It teaches fundamental principles of computer programming, including recursion, abstraction, modularity, and programming language design and implementation.
Arthur John Robin Gorell Milner was a British computer scientist, and a Turing Award winner.
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. He 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 programming language family Lisp, significantly influenced the design of the language ALGOL, popularized time-sharing, and invented garbage collection.
The Devil's Dictionary is a satirical dictionary written by American journalist 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 has made pioneering contributions to programming languages and distributed computing. Her notable work includes the introduction of abstract data types and the accompanying principle of data abstraction, along with the Liskov substitution principle, which applies these ideas to object-oriented programming, subtyping, and inheritance. Her work was recognized with the 2008 Turing Award, the highest distinction in computer science.
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. 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.
Eric Allen Brewer is professor emeritus of computer science at the University of California, Berkeley and vice-president of infrastructure at Google. His research interests include operating systems and distributed computing. He is known for formulating the CAP theorem about distributed network applications in the late 1990s.
The history of the Church–Turing thesis ("thesis") involves the history of the development of the study of the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose values are algorithmically computable. It is an important topic in modern mathematical theory and computer science, particularly associated with the work of Alonzo Church and Alan Turing.
In computability theory, super-recursive algorithms are posited as a generalization of hypercomputation: hypothetical algorithms that are more powerful, that is, compute more than Turing machines.
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 (BBN), 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.
