I have to ask your forbearance for appearing here, since I am an outsider to most of the fields which form the subject of this conference. Even in the area in which I have some experience, that of the logics and structure of automata, my connections are almost entirely on one side, the mathematical side. The usefulness of what I am going to say, if any, will therefore be limited to this: I may be able to give you a picture of the mathematical approach to these problems, and to prepare you for the experiences that you will have when you come into closer contact with mathematicians. This should orient you as to the ideas and the attitudes which you may then expect to encounter. I hope to get your judgment of the modus procedendi and the distribution of emphasis that I am going to use. I feel that I need instruction even in the limiting area between our fields more than you do, and I hope that I shall receive it from your criticisms.