Programming and the Theory of Automata )

Abstract

This chapter discusses the programming and the theory of automata. Two different types of computing units are discussed. First, a tape consisting of an indefinite number of squares, each capable of storing a single symbol. The second type of unit is a finite control automaton with a “tape head,” that is, a finite automaton, which can scan and read a square of the tape, erase that square or write in it, and at the next step scan the square to the left or the right of the square just scanned. A Turing machine consists of a finite-control automaton connected to a tape. A finite-control automaton is active and has the power to interpret a program, while a tape is passive and can do nothing by itself. The organization of the machine provides the basis for the structure of the machine language. The chapter reviews how one could use the proposed machine design language. It would be more effective when applied to a problem capable of analog treatment, that is, whose structure may be paralleled by the structure of a special-purpose. In such a case the mathematical equation describes the behavior of a physical model. To specify the solution of this equation the machine design language describes a special-purpose computer, which would operate analogously to the given physical model. The description of this special-purpose computer is supplied to a general- purpose computer, which translates it into its own machine language and then solves the problem.