The paper is an annotated summary of Ehud Shapiro's report, “The Induction of Theories from Facts.” In the view of this author, Shapiro's report forms a very good foundation for work in the field of learning. It gives a clear definition of the term “learning” in a way which both is intuitively acceptable and renders learning algorithms amenable to precise analysis. It also establishes a paradigm for learning algorithms which is precise enough that it can serve as a benchmark for future development as well as for the analysis of presently available algorithms.

For the purposes of this paper self-improvement will be defined to be the automatic development of problem solving heuristics. The reason for such a narrow definition will be indicated. Precise formulation of the concepts of problem and game will form the basis for the discussion of self-improving programs and an attempt to deal with the question of their adequacies.

Using certain basic facts about finite fields and their use in the construction of linear shift registers of maximal period, a method has been described for the construction of arrays such that if one looks at different parts of the array through a fixed size "window," each configuration seen is distinct. The method has been exemplified in the case where the elements of the array are binary digits.