For the machine, time was considered to be discrete and its internal structure, at a given moment, was described simply as one of a finite set of states. In 1936 an English mathematician, Alan Mathison Turing, in a paper published in the Proceedings of the London Mathematical Society (“On Computable Numbers with an Application to the Entscheidungsproblem”), conceived a logical machine the output of which could be used to define a computable number. Thus, an automaton can be described as a logically defined entity that can be embodied in the form of a machine, with the term automaton designating both the physical and the logical constructions. This mode of abstraction yields mathematical systems that in certain respects resemble logical systems. In this way, an automaton may be considered, abstractly, as a set of physically unspecified states, inputs, outputs, and rules of operation, and the study of automata as the investigation of what can be accomplished with these.
The principles of their operation as a sequence of discrete states can, however, be understood independently of the nature or arrangement of their components. The components of automata consist of specific materials and devices, such as wires, transistors, levers, relays, gears, and so forth, and their operation is based on the mechanics and electronics of these parts. Nelson Nature and origin of modern automata The best known general automaton is the modern electronic computer, the internal states of which are determined by the data input and which operates to produce a certain output.Ī-B-C, 1-2-3… If you consider that counting numbers is like reciting the alphabet, test how fluent you are in the language of mathematics in this quiz. A thermostat, for instance, has an “on” or “off” state that depends on the temperature.
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The internal states of such devices are not determined solely by their initial state, as is the case of the pendulum clock, but may be determined by an input from a human operator, from another automaton, or by an event or series of events in the environment. For example, thermostats, automatic pilots of aircraft, missile guidance systems, telephone networks, and controls of certain kinds of automatic elevators are all forms of automata. More general automata are designed to respond to changes in external conditions or to other inputs. As long as such a clock is wound and its operation is not interfered with, it will continue to operate unaffected by outside influences except the effect of gravity on the pendulum. Each state, through the operation of the escapement, determines the next succeeding state, as well as a discrete output, which is displayed as the discrete positions of the hands of the clock. In such a mechanism the gears can assume only one of a finite number of positions, or states, with each swing of the pendulum. Real or hypothetical automata of varying complexity have become indispensable tools for the investigation and implementation of systems that have structures amenable to mathematical analysis.Īn example of a typical automaton is a pendulum clock.
SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!Īutomata theory, body of physical and logical principles underlying the operation of any electromechanical device (an automaton) that converts information from one form into another according to a definite procedure.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.
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