Alonzo Church

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. Born in Washington, DC, he received a bachelor's degree from Princeton University in 1924, completing his Ph.D. there in 1927, under Oswald Veblen. After a postdoc at Göttingen, he taught at Princeton, 1929-67, and at ...

Including:

• Alonzo Church - Death
• Alonzo Church - Books

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In computer science, the Actor model, first published in 1973 (Hewitt et al. 1973), is a mathematical model of concurrent computation. The Actor model treats “Actors” as the universal primitives of concurrent digital computation: in response to a message that it receives, an Actor can make local decisions, create more Actors, send more messages, and determine how to respond to the next message received. The Actor model has been used both as a framework within which to develop a theor ...

Including:

• Actor model - History
• Actor model - Fundamental concepts
• Actor model - Formal systems
• Actor model - Applications
• Actor model - Models prior to the Actor model
• Actor model - Lambda calculus
• Actor model - Simula
• Actor model - Smalltalk
• Actor model - Petri nets
• Actor model - Message Passing Semantics
• Actor model - The unbounded nondeterminism controversy
• Actor model - Direct communication and asynchrony
• Actor model - Actor creation plus addresses in messages means variable topology
• Actor model - Inherently concurrent
• Actor model - No requirement on order of message arrival
• Actor model - Not sequentiality not buffering not synchrony and not fixed topology
• Actor model - Locality
• Actor model - Compositionality
• Actor model - Behaviors
• Actor model - Relationship to mathematical logic
• Actor model - Migration
• Actor model - Security
• Actor model - Synthesizing addresses of Actors
• Actor model - Why is the Actor model important now?
• Actor model - Actor researchers

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Turing machines are extremely basic symbol-manipulating devices which — despite their simplicity — can be adapted to simulate the logic of any computer that could possibly be constructed. They were described in 1936 by Alan Turing. Though they were intended to be technically feasible, Turing machines were not meant to be a practical computing technology, but a thought experiment about the limits of mechanical computation; thus they were not actually constructed. Studying their abstract properties yields many insights in computer s ...

Including:

• Turing machine - Definition
• Turing machine - Informal description
• Turing machine - Formal definition
• Turing machine - Example
• Turing machine - Deterministic and non-deterministic Turing machines
• Turing machine - Universal Turing machines
• Turing machine - Comparison with real machines
• Turing machine - Simulators

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Alan Mathison Turing (June 23, 1912 – June 7, 1954) was a British mathematician, logician, and cryptographer. Turing is often considered to be a father of modern computer science. With the Turing Test, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He provided an influential formalisation of the concept of algorithm and computation with the Turing machine, formulating the n ...

Including:

• Alan Turing - Childhood and youth
• Alan Turing - College and his work on computability
• Alan Turing - Cryptanalysis
• Alan Turing - Work on early computers and the Turing Test
• Alan Turing - Work on pattern formation and mathematical biology
• Alan Turing - Prosecution for homosexuality and Turing's death
• Alan Turing - Recognition
• Alan Turing - Turing biographies
• Alan Turing - Turing in fiction

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Plato (Greek: Πλάτων Plátōn) (ca. May 21? 427 BC – ca. 347 BC) was an immensely influential classical Greek philosopher, student of Socrates, teacher of Aristotle, writer of philosophical dialogues, and founder of the Academy in Athens. Plato lectured extensively at the Academy, and wrote on many philosophical issues. The most important writings of Plato are his dialogues, although a handful of epigrams also survive, and some letters have come down to us under his name. It is believed that all of Plato's authen ...

Including:

• Plato - Biography
• Plato - Work
• Plato - Themes
• Plato - Form and basis
• Plato - Metaphysics
• Plato - Epistemology
• Plato - The state
• Plato - Platonic scholarship
• Plato - Bibliography
• Plato - By tetralogy
• Plato - Stephanus pagination
• Plato - Loeb Classical Library

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In computability theory the Church–Turing thesis, Church's thesis, Church's conjecture or Turing's thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available. It is generally assumed that an algorithm must satisfy the following requirements: ...

Including:

• Church–Turing thesis - Church–Turing thesis
• Church–Turing thesis - History
• Church–Turing thesis - Success of the thesis
• Church–Turing thesis - Philosophical implications
• Church–Turing thesis - Reference

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In computer science, computability theory is the branch of the theory of computation that studies which problems are computationally solvable using different models of computation. Computability theory differs from the related discipline of computational complexity theory, which deals with the question of how efficiently a problem can be solved, rather than whether it is solvable at all. Computability theory computation - Introduction. A central question of computer science is to address the limits o ...

Including:

• Computability theory computation - Introduction
• Computability theory computation - Formal models of computation
• Computability theory computation - Power of computational models
• Computability theory computation - Power of finite state machines
• Computability theory computation - Power of push-down automata
• Computability theory computation - Power of Turing machines
• Computability theory computation - Unreasonable models of computation
• Computability theory computation - Infinite execution
• Computability theory computation - Oracle machines
• Computability theory computation - Limits of hypercomputation
• Computability theory computation - History of computability theory

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The 20th century lasted from 1901 to 2000 in the Gregorian calendar. Common usage sometimes regards it as lasting from 1900 to 1999. The 20th century is also sometimes known as the nineteen hundreds (1900s). However, a number of arguments have been used to justify the common usage. One advanced by Stephen Jay Gould is that the first decade had only nine years, thus contradicting the definition of decade equaled 10 years. Another argument is that the astronomical year numbering system for years does have a year zero, the ...

Including:

• 20th century - Overview
• 20th century - Important developments events and achievements
• 20th century - Science and technology
• 20th century - Wars and politics
• 20th century - Culture and entertainment
• 20th century - Disease and medicine
• 20th century - Natural resources and the environment
• 20th century - Significant people
• 20th century - World leaders
• 20th century - Scientists
• 20th century - Humanities
• 20th century - Business
• 20th century - Aerospace pioneers
• 20th century - Spiritual figures
• 20th century - Artists
• 20th century - Music
• 20th century - Film
• 20th century - Writers and poets
• 20th century - Sports figures
• 20th century - Decades and years

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John von Neumann (Neumann János) (December 28, 1903 – February 8, 1957) was a Jewish Hungarian-born mathematician and polymath who made important contributions in quantum physics, functional analysis, set theory, computer science, economics and many other mathematical fields. Most notably, von Neumann was a pioneer of the modern digital computer and the application of operator theory to quantum mechanics (see Von Neumann algebra), member of the Manhattan Project Team, creator of game theory and the concept of cellular automata. ...

Including:

• John von Neumann - Biography
• John von Neumann - Logic
• John von Neumann - Quantum Mechanics
• John von Neumann - Economics
• John von Neumann - Armaments
• John von Neumann - Computer Science
• John von Neumann - Politics and Social Affairs
• John von Neumann - Honors
• John von Neumann - Students

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In mathematics and computer science an algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a corresponding recognizable end-state. Algorithms can be implemented by computer programs. Informally, the concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). The concept of algorithms was formalized in 1936 by Alan Turing's Turing machines and Alonzo Church's lambda c ...

Including:

• Algorithm - Formalization of algorithms
• Algorithm - Implementation
• Algorithm - Example
• Algorithm - History
• Algorithm - Classes
• Algorithm - Classification by implementation
• Algorithm - Classification by design paradigm
• Algorithm - Classification by field of study
• Algorithm - Classification by complexity
• Algorithm - Sources
• Algorithm - Legal issues

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List of Princeton University people - Academia. See also: Notable Princeton professors, Mathematics and science Robert Goheen A.B. 1940, M.A. 1947, Ph.D. 1948 - former president of Princeton, former U.S. Ambassador to India Livingston Farrand A.B. 1888 - former president of Cornell University Alan Lightman A.B. 1970 - physicist and novelist, professor at MIT Gregory Mankiw A.B. 1980 - economist, professor at Harvard University Neil Rudenstine A.B. 1956 - for ...

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List of Princeton University people, List of Princeton University people - Alumni, List of Princeton University people - Academia, List of Princeton University people - Government / Law / Public policy, List of Princeton University people - Business, List of Princeton University people - Economics, List of Princeton University people - Mathematics and science, List of Princeton University people - Engineering/Technology, List of Princeton University people - Literature, List of Princeton University people - Pulitzer Prize winners, List of Princeton University people - Sports, List of Princeton University people - Entertainment, List of Princeton University people - Art, List of Princeton University people - Other, List of Princeton University people - Fictional, List of Princeton University people - Notable Princeton professors, List of Princeton University people - Architecture, List of Princeton University people - Economics and business, List of Princeton University people - Government law and public policy, List of Princeton University people - Humanities and literature, List of Princeton University people - Math and science

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History of computer science - Early computing. The earliest computers were, in fact, people, clerks who performed calculations. Computers would make astronomical calculations for calendars and also worked in commerce, government, and research. These computers often made use of calculating machines, which have a very long history. The earliest of these devices is the abacus, and it was thought to have been invented in Babylon circa 2400 BCE. Its original style of usage was by lines drawn in sand with pebbles. Abaci, of a m ...

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History of computer science, History of computer science - Early history, History of computer science - Early computing, History of computer science - Binary logic, History of computer science - The Analytical Engine, History of computer science - Emergence of a discipline, History of computer science - The theoretical groundwork, History of computer science - Shannon and Information Theory

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In the following: H refers to the source "Hodges" U refers to the source "Undecidable" W refers to definitions from Websters Ninth New Collegiate Dictionary Marriam-Webster Inc., Springfield Mass, 1990 PM refers to the source Principia Mathematica circa B.C.-- Pythagoras shows the existence of numbers that are not rational, i.e. numbers exist that are not the natural numbers or ratios of the counting numbers. Numbers that are either natural numbers or ...

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Halting problem, Halting problem - Formal statement, Halting problem - Importance and consequences, Halting problem - Sketch of proof, Halting problem - Common pitfalls, Halting problem - Formalization of the halting problem, Halting problem - Relationship with Gödel's incompleteness theorem, Halting problem - Can humans solve the halting problem?, Halting problem - Recognizing partial solutions, Halting problem - History of the Halting Problem, Halting problem - Footnotes

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Mathematical functions have great strengths in terms of flexibility and analysis. For example, if a function is known to be idempotent, then a call to a function which has its own output as its argument, and which is known to have no side-effects, may be efficiently computed without multiple calls. A function in this sense has zero or more parameters and a single return value. The parameters—or arguments, as they are sometimes called—are the inputs to the function, and the return value is the function's output. The definition of a ...

See also:

Functional programming, Functional programming - Introduction, Functional programming - History, Functional programming - Comparison with imperative programming, Functional programming - Functional programming languages, Functional programming - Higher-order functions, Functional programming - Speed and space considerations, Functional programming - Functional languages

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"We can all think clearly, more or less, some of the time, but von Neumann's clarity of thought was orders of magnitude greater than that of most of us, all the time. For von Neumann it seemed to be impossible to be unclear in thought or in expression." --Paul Halmos The oldest of three children, von Neumann was born Neumann Margittai János Lajos (two surnames, two given names respectively) in Budapest, Austria-Hungary (Osztrák-Magyar Monarchia) to Neumann Miksa (Max Neumann), a lawyer who worked in a bank, and ...

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John von Neumann, John von Neumann - Biography, John von Neumann - Logic, John von Neumann - Quantum Mechanics, John von Neumann - Economics, John von Neumann - Armaments, John von Neumann - Computer Science, John von Neumann - Politics and Social Affairs, John von Neumann - Honors, John von Neumann - Students

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Kripke's three lectures constitute an attack on the descriptivist (Fregean, Russellian) theory of reference with respect to proper names, according to which a name refers to an object by virtue of the name's being associated with a description that the object in turn satisfies. He gave several examples purporting to render descriptivism implausible (e.g., surely Aristotle could have died at age two and so not satisfied any of the descriptions we associate with his name, and yet it would seem wrong to deny that he was Aristotle). As an altern ...

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Saul Kripke, Saul Kripke - Biography, Saul Kripke - Work, Saul Kripke - Modal logic, Saul Kripke - Naming and necessity, Saul Kripke - Wittgenstein, Saul Kripke - Truth

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See also: List of Presidents of Mexico See also: List of Mexican state governors Miguel Alemán Valdés Miguel Alemán Velasco Eduardo Bours Felipe Calderón Cuauhtémoc Carlos Castañeda Cuauhtémoc Cárdenas Lázaro Cárdenas Batel Lázaro Cárdenas del Río Luis Donaldo Colosio Porfirio Díaz Vicente Fox Carlos Hank González Jorge Hank Rhon Miguel Hidalgo y Costilla Enrique Jack ...

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List of Mexicans, List of Mexicans - Arts, List of Mexicans - Authors, List of Mexicans - Beauty queens, List of Mexicans - Businesspeople, List of Mexicans - Cartoonist, List of Mexicans - Composers, List of Mexicans - Criminals, List of Mexicans - Entertainment, List of Mexicans - Journalism, List of Mexicans - Military, List of Mexicans - Politics, List of Mexicans - Religion, List of Mexicans - Science and technology, List of Mexicans - Sports

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Formally, we start with a countably infinite set of identifiers, say {a, b, c, ..., x, y, z, x1, x2, ...}. The set of all lambda expressions can then be described by the following context-free grammar in BNF: <expr> ::= <identifier> <expr> ::= (λ <identifier>. <expr>) <expr ...

See also:

Lambda calculus, Lambda calculus - History, Lambda calculus - Informal description, Lambda calculus - Formal definition, Lambda calculus - α-conversion, Lambda calculus - β-reduction, Lambda calculus - η-conversion, Lambda calculus - Arithmetic in lambda calculus, Lambda calculus - Logic and predicates, Lambda calculus - Recursion, Lambda calculus - Computable functions and lambda calculus, Lambda calculus - Undecidability of equivalence, Lambda calculus - Lambda calculus and programming languages

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List of University of California Los Angeles people - Nobel Laureates. Ralph Bunche - Peace, 1950 Bruce Merrifield - Chemistry, 1984 Glenn T. Seaborg - Chemistry, 1951 William Sharpe - Economics, 1990 List of University of California Los Angeles people - Academia Science and Technology. William Arveson - mathematician; professor of mathematics at University of California, Berkeley Paul Baran - Internet pioneer Mich ...

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List of University of California Los Angeles people, List of University of California Los Angeles people - Notable Alumni, List of University of California Los Angeles people - Nobel Laureates, List of University of California Los Angeles people - Academia Science and Technology, List of University of California Los Angeles people - Arts Film and Literature, List of University of California Los Angeles people - Athletics, List of University of California Los Angeles people - Business and Law, List of University of California Los Angeles people - Politics, List of University of California Los Angeles people - Miscellaneous, List of University of California Los Angeles people - Notable UCLA Faculty, List of University of California Los Angeles people - Nobel Laureates, List of University of California Los Angeles people - Social Science Arts and Humanities, List of University of California Los Angeles people - Science and Technology, List of University of California Los Angeles people - Athletics, List of University of California Los Angeles people - Politics, List of University of California Los Angeles people - Medicine, List of University of California Los Angeles people - Business and Law

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The thesis can be stated as: "Every 'function which would naturally be regarded as computable' can be computed by a Turing machine." Due to the vagueness of the concept of a "function which would naturally be regarded as computable", the thesis cannot formally be proven. Disproof would be possible only if humanity found ways of building hypercomputers whose results should "naturally be regarded as computable". Any computer program can be translated into a Turing machine, and any Turing machine can be ...

See also:

Church–Turing thesis, Church–Turing thesis - Church–Turing thesis, Church–Turing thesis - History, Church–Turing thesis - Success of the thesis, Church–Turing thesis - Philosophical implications, Church–Turing thesis - Reference

Read more here: » Church–Turing thesis: Encyclopedia II - Church–Turing thesis - Church–Turing thesis