Automata and Finite Automata

The invention of modern computers seems to have been anticipated by many years by Turing. 1 Vet it is remarkable how little the progress of computers has been influenced by Turing's work. There is, perhaps, a basic difference in viewpoint that may account for this lack of convergence. Turing looked at machines from the point of view of their internal behavior. Although Turing originated the concept of universal machines, his idea seems to correspond much closer to that of our special-purpose machines. Every machine, by virtue of its state description, performs a specific task; a machine is altered only if its internal structure is altered. Computers, on the other hand, are generally specified in terms of their external capabilities. Their internal structure remains more or less fixed once they come into being. A computer is then a universal machine in disguise, and every Turing machine corresponds to a particular computer program. One may therefore study the behavior and structure of programs rather than work with states. The first step in this direction was perhaps taken by Wang, 2 who based his ideas of machines on a computer (which he called a B-machine) that 12G7