Abstract

This chapter describes the finite deterministic automata. Automata are mathematical models of devices that process information by giving responses to inputs. Models for discrete deterministic computing devices possessing a finite memory are considered in the chapter. Their behavior at a particular time instant depends not only on the latest input but on the entire sequence of past inputs. They are capable of only a finite number of inputs, internal states, and outputs, and are, furthermore, deterministic in the sense that an input sequence uniquely determines the output behavior. A word over an alphabet I is a finite string consisting of zero, or more letters of I whereby the same letter may occur several times. The string consisting of zero letters is called the empty word, written λ. If P and Q are words over an alphabet I, then their catenation PQ is also a word over I. Catenation is an associative operation, and the empty word λ is an identity with respect to catenation.

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