automata theory
-
What is automata theory?
Automata theory explores abstract machines and the problems they can solve. It treats an automaton as a logically defined entity that can be embodied as a machine. Automata consist of materials and devices such as wires, transistors, levers, and gears; their operation relies on the mechanics and electronics of these parts.
Alan Turing conceived a logical machine whose output could define a computable number. The Turing machine continues to be a standard reference point in basic discussions of automata theory, and many mathematical theorems concerning computability have been proven within the framework of Turing’s original proposal.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What is an automaton in automata theory?
In automata theory, an automaton is an electromechanical device that transforms information from one form to another through a definite procedure. It can be understood abstractly as a set of physically unspecified states, inputs, outputs, and operational rules. The study of automata investigates what can be accomplished using these components.
The best-known automaton is the modern electronic computer, whose internal states are determined by the input data, which operates to produce a certain output. The principles of their operation as a sequence of discrete states can be understood independently of the nature or arrangement of their components.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What is a finite automaton and how does it work?
A finite automaton is an acceptor that moves a tape to the left, reading symbols and erasing them. These automata share the same capabilities as McCulloch-Pitts automata and accept regular sets.
The input of the acceptor is written on tape, and the tape is blank at the computation's end. The acceptance of the input word is represented by a final state. A word x from alphabet S is accepted by A if A computes, beginning in an initial state q_0 with x on tape and halts in a final state with the tape entirely blank.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How do automata recognize patterns in sequences of symbols?
Automata, particularly finite-state acceptors, recognize patterns by "accepting" specific sequences of symbols, known as "words," from a defined alphabet. An acceptor processes an input word on tape, starting from an initial state, and transitions through a series of states based on the symbols it reads.
If the automaton halts in a designated "final state" after reading the entire word, the word is considered accepted, indicating that the automaton recognizes the pattern represented by that sequence of symbols. Finite-state acceptors have the same capabilities as McCulloch-Pitts automata and accept sets called regular sets. These acceptors move the tape to the left only, reading and erasing symbols.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How is automata theory used in computer science and mathematics?
Automata theory is a field that explores the principles behind electromechanical devices converting information based on defined procedures. It has become an indispensable tool in computer science and mathematics for analyzing and implementing systems with structures amenable to mathematical analysis.
Automata are used to design, build, and analyze computing systems, such as compilers, operating systems, and other software. In mathematics, automata theory provides abstract models for computation and is closely related to the theory of formal languages. Automata can be described as logically defined entities that can be embodied in the form of a machine.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.
automata 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. 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.
An example of a typical automaton is a pendulum 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. 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. 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.
More general automata are designed to respond to changes in external conditions or to other inputs. 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.
" height="20" alt="HEW Logo">
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. A thermostat, for instance, has an “on” or “off” state that depends on the temperature. 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.
Nature and origin of modern automata
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. The principles of their operation as a sequence of discrete states can, however, be understood independently of the nature or arrangement of their components. 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. This mode of abstraction yields mathematical systems that in certain respects resemble logical systems. 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.
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. 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. It performed its functions by scanning an unbounded tape divided into squares, each of which either contained specific information in the form of one of a finite number of symbols or was blank. It could scan only one square at a time, and, if in any internal state except one called “passive,” it was capable of moving the tape forward or backward one square at a time, erasing a symbol, printing a new symbol if the square was blank, and altering its own internal state. The number it computed was determined by symbols (the “program”) provided on a finite portion of the tape and the rules of operation, which included stopping when the passive state was reached. The output number was then interpreted from the symbols remaining on the tape after the machine stopped.
Automata theory since the middle of the 20th century has been extensively refined and has often found practical application in civilian and military machines. The memory banks of modern computers can store large (though finite) amounts of information. (For further information on computers and their applications, see information processing.) The original Turing machine had no limit to the memory bank because each square on the unbounded tape could hold information. The Turing machine continues to be a standard reference point in basic discussions of automata theory, and many mathematical theorems concerning computability have been proved within the framework of Turing’s original proposal.
The trusted destination for professionals, college students, and lifelong learners.
SUBSCRIBE
