This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.

K.A.PATON 411 24 Centromere finding: some shape descriptors for small chromosome outlines.

INTRODUCTION The problem of reducing the line-like elements of a digitized picture to idealized thin lines is of general interest in pattern recognition. As early as 1957 the idea of obtaining a thin-line representation of certain patterns was suggested (Kirsch et al. 1957); recently McCormick (1963) and Narasimhan (1964) have described computer programs for doing this (for use in particular on bubble chamber photographs), and similar work has been done in character recognition, for example by Deutsch (1967). Blum (1964) has put forward an approach for dealing with more general shapes. In this the boundary of a shape is considered as being the source of a wavefront. The points at which wavefronts originating at different parts of the boundary first meet form a'skeleton' which, with a function giving the time taken for the wavefront to reach each point of the skeleton, completely defines the original shape. Programs for generating this skeleton for digitized pictures have been described by Rosenfeld and Pfaltz (1966), and also by Philbrick (1966).

Networks as models of word storage: G. R. Kiss

Theorem Proving Vision Robotics Information Processing Psychology Learning and Inductive Inference Planning and Related Problem-solving Techniques A. Natural Language Processing Ovnrview The most common way that human beings communicate Is by speaking or writing In one of the "natural" languages, like English, French, or Chinese. Computer programming languages, on the other hand, seem awkward to humans. These "artificial" languages are designed to have a rigid format, or syntax, so that a computer program reading and compiling code written In an artificial language can understand what the programmer means. In addition to being structurally simpler than natural languages, the artificial languages can express easily only those concepts that are important In programming: "Do this then do that," "See it such and such Is true," etc. The things that can be expressed In a language are referred to as the semantics of the language. The research on understanding natural language described in this section of the Handbook is concerned with programs that deal with the full range of meaning of languages like English.

ABSTReCT The research activities of the Heuristic Programming Project, for the four-year period ending July 31, 1977, are summarized in this report. Contributions to Knowledge Engineering research in the fields of knowledge acquisition (both interactive and automated), knowledge representation and knowledge utilization were reported in over thirty publications by members of the project. A summary of those publications is?resented here. The Al Handbook, an encyclopedic reference to the field of::tificial Intelligence, is described in the appendix, along with the excecteç table of contents and sample articles.

This chapter will discuss one example of how AI techniques are being integrated with, and extending, existing molecular biology sequence analysis methods. AI ideas of complex representations, pattern recognition, search, and machine learning have been applied to the task of inferring and recognizing structural patterns associated with molecular function. We wish to construct such patterns, and to recognize them in unknown molecules, based on information inferred solely from protein primary (amino acid) sequences.

Shortly after Watson and Crick's discovery of the structure of DNA, and at about the same time that the genetic code and the essential facts of gene expression were being elucidated, the field of linguistics was being similarly revolutionized by the work of Noam Chomsky [Chomsky, 1955, 1957, 1959, 1963, 1965]. Observing that a seemingly infinite variety of language was available to individual human beings based on clearly finite resources and experience, he proposed a formal representation of the rules or syntax of language, called generative grammar, that could provide finite--indeed, concise--characterizations of such infinite languages. Just as the breakthroughs in molecular biology in that era served to anchor genetic concepts in physical structures and opened up entirely novel experimental paradigms, so did Chomsky's insight serve to energize the field of linguistics, with putative correlates of cognitive processes that could for the first time be reasoned about 48 A

He then solves the simpler problem and uses the information obtained in the solution of the simpler problem in the solution of the original complex problem.

Methods of Approach At the outset it might be well to distinguish sharply between two general approaches to the problem of machine learning.