Many problems in artificial intelligence involve the searching of large trees of alternative possibilities--for example, game-playing and theorem-proving. The problem of efficiently searching large trees is discussed. A new method called "dynamic ordering" is described, and the older minimax and Alpha-Beta procedures are described for comparison purposes. Performance figures are given for six variations of the game of kalah. A quantity called "depth ratio" is derived which is a measure of the efficiency of a search procedure.

The problem discussed in this paper, namely that of finding a function to satisfy a given argument-value table, is by no means new to computing science, or to mathematics. Thus, for example, the problem of fitting a curve to a set of points is a part of numerical analysis. However, I am concerned with finding a function over a non-metric space, and so my work is closer to that of Feldman et al. (1969) in what they call, 'grammatical inference' or to the automaton-synthesizing programs described by Fogel, Owens and Walsh (1966).

A robot, in order to act intelligently, must be able to reason from facts which its sensors detect to conclusions which govern its actions. This reasoning process is so central to human intelligence that it seems immediately relevant to the problems of robot design to consider its properties, how it might be analysed and imitated.

This paper is a survey and discussion of research work relevant to the task of constructing some kind of reasoning robot. The emphasis is entirely on the organization of the reasoning processes, in particular planning, rather than on hardware. In practice the reasoning would most probably be carried out within a digital computer. My objective is to clarify the relationship between some superficially rather disparate approaches to this task, and simultaneously to indicate what seem to be the key problem areas. No new experimental results are presented, but the approach to the subject which I have adopted is a consequence of earlier experimentation with a simple computer simulation of a robot (Doran 1968a, 1969).

A minimal:robot,Icnown as Freddy, has been constructed with the aim of connecting a usable device online to the Department's lc L 4130, under the Multi-Pop time-sharing system, and discovering the snags. (See figure 1). Various technical problems arise when such a device runs free. It is much easier to anchor it and allow it to push its world about. Our present world is a three-foot diameter sandwich of hardboard and polystyrene which is light and rigid.

It seems most unlikely that one could in general write purely applicative Schonfmkel descriptions', like (5), of functions already known to one in some other form. Fortunately there is a general procedure -- the Schonfmkel procedure -- which, when applied to any expression written in the more intuitive lambda-calculus notation, will produce a correct translation of it into the Schonfinkel notation.

Institut Blaise Pascal, C.N.R.S., 23, Rue du Maroc, 75, Paris XIX, France We study some aspects of a general game-playing program. Such a program receives as data the rules of a game: an algorithm enumerating the moves and an algorithm indicating how to win. The program associates to each move the conditions necessary for this move to occur. It must find how to avoid a dangerous move. We describe the part of the program playing the combinatorial game in order to win: how it can find the moves which lead to victory and what are the only opponent's moves with which he does not lose. This program has been tried with various games: chess, tictac-too, etc. 1. INTRODUCTION My aim was to realize a program playing several games. The rules of the particular game which it must play are given as data. If we want to have a performing program, it must be capable of studying these rules.

"A computer program has been written which can formulate hypotheses from a given set of scientific data. The data consist of the mass spectrum and the empirical formula of an organic chemical compound. The hypotheses which are produced describe molecular structures which are plausible explanations of the data. The hypotheses are generated systematically within the program's theory of chemical stability and within limiting constraints which are inferred from the data by heuristic rules. The program excludes hypotheses inconsistent with the data and lists its candidate explanatory hypotheses in order of decreasing plausibility. The computer program is heuristic in that it searches for plausible hypotheses in a small subset of the total hypothesis space according to heuristic rules learned from chemists."In Meltzer, B., Michie, D., and Swann, M. (Eds.), Machine Intelligence 4, pp. 209-254. Edinburgh University Press

COMPUTER SOLUTION OF CALCULUS WORD PROBLEMS* Eugene Charniak Massachusetts Ins:itute of Technology Cambridge, Massachusetts SUMMARY A program was written to solve calculus word problems. The program, CARPS (CAlculus Rate Problem Solver), is restricted to rate problems. The overall plan of the program is similar to Bobrow's STUDENT, the primary difference being the introduction of "structures" as the internal model in CARPS. Structures are stored internally as trees, each structure holding the information gathered about one object. It was found that the use of structures made CARPS more powerful than STUDENT in several respects. In calculus word problems it is not uncommon to have two or three sentences providing information for one equation. For example, in a problem about a filter, ALTITUDE was interpreted as ALTITUDE OF THE FILTER because CARPS knew that since the filter was a cone and cones have altitudes the filter had an altitude. The program has solved 14 calculus problems, most taken (sometimes with slight modifications) from standard calculus texts. CARPS is written in two languages. The bulk of the coding is in LISP.

See also: Education Resources Information CenterSupplement to Proceedings of the IFIP 68 International Congress, Edinburgh, August 1968. Published in A. J. H. Morrell (ed.), Information Processing 68, Vol. II, pp. 1008-1022, Amsterdam: North-Holland, 1969.