Chapter 3 – STRING ACCEPTORS

Publisher Summary This chapter defines various types of formal machines—automata—that can recognize the various given classes of pictures. The chapter presents a collection of propositions and theorems about one-dimensional machines; many of these are standard, while others are given as preparation for presenting their two-dimensional analogs. The chapter also presents informal proofs of many of these results. It describes computational models, which are not all of equal utility; some of them are potentially of practical interest, for example, bounded cellular automata, while others are much less. However, even the impractical models are pedagogically useful, as they provide a standard framework for breaking computations down into small steps. Informally, a cellular automaton is a string of bugs or cells, each of which, at any given time, is in some state. The cells operate in a sequence of discrete time steps, at each of which every cell reads the states of its left and right neighbors and changes to a possibly new state.