Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, given any computer algorithm, a Turing machine capable of simulating that algorithm's logic can be constructed; the machine operates on an infinite memory tape divided into discrete "cells". The machine positions its "head" over a cell and "reads" or "scans" the symbol there; as per the symbol and its present place in a "finite table" of user-specified instructions, the machine writes a symbol in the cell either moves the tape one cell left or right either proceeds to a subsequent instruction or halts the computation. The Turing machine was invented in 1936 by Alan Turing, who called it an "a-machine". With this model, Turing was able to answer two questions in the negative: Does a machine exist that can determine whether any arbitrary machine on its tape is "circular", thus by providing a mathematical description of a simple device capable of arbitrary computations, he was able to prove properties of computation in general—and in particular, the uncomputability of the Entscheidungsproblem.

Thus, Turing machines prove fundamental limitations on the power of mechanical computation. While they can express arbitrary computations, their minimalistic design makes them unsuitable for computation in practice: real-world computers are based on different designs that, unlike Turing machines, use random-access memory. Turing completeness is the ability for a system of instructions to simulate a Turing machine. A programming language, Turing complete is theoretically capable of expressing all tasks accomplishable by computers. A Turing machine is a general example of a CPU that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data. More it is a machine capable of enumerating some arbitrary subset of valid strings of an alphabet. A Turing machine has a tape of infinite length on which it can perform write operations. Assuming a black box, the Turing machine cannot know whether it will enumerate any one specific string of the subset with a given program.

This is due to the fact that the halting problem is unsolvable, which has major implications for the theoretical limits of computing. The Turing machine is capable of processing an unrestricted grammar, which further implies that it is capable of robustly evaluating first-order logic in an infinite number of ways; this is famously demonstrated through lambda calculus. A Turing machine, able to simulate any other Turing machine is called a universal Turing machine. A more mathematically oriented definition with a similar "universal" nature was introduced by Alonzo Church, whose work on lambda calculus intertwined with Turing's in a formal theory of computation known as the Church–Turing thesis; the thesis states that Turing machines indeed capture the informal notion of effective methods in logic and mathematics, provide a precise definition of an algorithm or "mechanical procedure". Studying their abstract properties yields many insights into computer science and complexity theory. In his 1948 essay, "Intelligent Machinery", Turing wrote that his machine consisted of:...an unlimited memory capacity obtained in the form of an infinite tape marked out into squares, on each of which a symbol could be printed.

At any moment there is one symbol in the machine. The machine can alter the scanned symbol, its behavior is in part determined by that symbol, but the symbols on the tape elsewhere do not affect the behavior of the machine. However, the tape can be moved back and forth through the machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore have an innings; the Turing machine mathematically models a machine. On this tape are symbols, which the machine can read and write, one at a time, using a tape head. Operation is determined by a finite set of elementary instructions such as "in state 42, if the symbol seen is 0, write a 1. In the original article, Turing imagines not a mechanism, but a person whom he calls the "computer", who executes these deterministic mechanical rules slavishly. More a Turing machine consists of: A tape divided into cells, one next to the other; each cell contains a symbol from some finite alphabet. The alphabet contains one or more other symbols.

The tape is assumed to be arbitrarily extendable to the left and to the right, i.e. the Turing machine is always supplied with as much tape as it needs for its computation. Cells that have not been written before are assumed to be filled with the blank symbol. In some models the tape has a left e

Computer science

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 and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems, its fields can be divided into practical disciplines. Computational complexity theory is abstract, while computer graphics emphasizes real-world applications. Programming language theory considers approaches to the description of computational processes, while computer programming itself involves the use of programming languages and complex systems. Human–computer interaction considers the challenges in making computers useful and accessible; the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, aiding in computations such as multiplication and division.

Algorithms for performing computations have existed since antiquity before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623. In 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner, he may be considered the first computer scientist and information theorist, among other reasons, documenting the binary number system. In 1820, Thomas de Colmar launched the mechanical calculator industry when he released his simplified arithmometer, the first calculating machine strong enough and reliable enough to be used daily in an office environment. Charles Babbage started the design of the first automatic mechanical calculator, his Difference Engine, in 1822, which gave him the idea of the first programmable mechanical calculator, his Analytical Engine, he started developing this machine in 1834, "in less than two years, he had sketched out many of the salient features of the modern computer".

"A crucial step was the adoption of a punched card system derived from the Jacquard loom" making it infinitely programmable. In 1843, during the translation of a French article on the Analytical Engine, Ada Lovelace wrote, in one of the many notes she included, an algorithm to compute the Bernoulli numbers, considered to be the first computer program. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information. In 1937, one hundred years after Babbage's impossible dream, Howard Aiken convinced IBM, making all kinds of punched card equipment and was in the calculator business to develop his giant programmable calculator, the ASCC/Harvard Mark I, based on Babbage's Analytical Engine, which itself used cards and a central computing unit; when the machine was finished, some hailed it as "Babbage's dream come true". During the 1940s, as new and more powerful computing machines were developed, the term computer came to refer to the machines rather than their human predecessors.

As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. In 1945, IBM founded the Watson Scientific Computing Laboratory at Columbia University in New York City; the renovated fraternity house on Manhattan's West Side was IBM's first laboratory devoted to pure science. The lab is the forerunner of IBM's Research Division, which today operates research facilities around the world; the close relationship between IBM and the university was instrumental in the emergence of a new scientific discipline, with Columbia offering one of the first academic-credit courses in computer science in 1946. Computer science began to be established as a distinct academic discipline in the 1950s and early 1960s; the world's first computer science degree program, the Cambridge Diploma in Computer Science, began at the University of Cambridge Computer Laboratory in 1953. The first computer science degree program in the United States was formed at Purdue University in 1962.

Since practical computers became available, many applications of computing have become distinct areas of study in their own rights. Although many believed it was impossible that computers themselves could be a scientific field of study, in the late fifties it became accepted among the greater academic population, it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM 704 and the IBM 709 computers, which were used during the exploration period of such devices. "Still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, you would have to start the whole process over again". During the late 1950s, the computer science discipline was much in its developmental stages, such issues were commonplace. Time has seen significant improvements in the effectiveness of computing technology. Modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base.

Computers were quite costly, some degree of humanitarian aid was needed for efficient use—in part from professional computer operators. As computer adoption became more widespread and affordable, less human assistance was needed for common usage. Despite its short history as a formal academic discipline, computer science has made a number of fundamental contributions to science and society—in fact, along with electronics, it is