Finite Automata

Abstract

In this chapter we consider how far finite-state automata, such as the machine for quality control described in the introduction, are able to carry out simple computations. As with all the machines to be discussed in this book, these automata are regarded as functions that respond to a given input tape by producing a certain output tape; more precisely, each symbol of input received by the machine in a given state produces one symbol of output and may cause the machine to change its state. The state of the machine may correspond to some information stored or remembered in the course of the calculation, such as ‘the last item was defective’. We do not study what mechanical process inside the automaton leads to the printing of output and change of state; the automaton is considered as a ‘black box’ (figure 1.1).