Abstract
A finite automaton or, synonymously, a finite state machine is in the simplest case a triple (X,I,λ), whereby X is a finite set of states, I is a finite set of inputs, and λ is the next-state mapping, such that λ : X x I → X (cf. Arbib, 1969). For example, if x1 and x2 are two state variables each possessing two possible states, the whole automaton has four possible states, and λ specifies the transitions between these states in dependence on a given input. If the input is constant, one speaks of an autonomous automaton, otherwise of a nonautonomous automaton .
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