William A. Martin

Computer input/output of mathematical expressions

Studying mathematics is, in part, a language problem. Naturally, mathematicians are more likely to resist using a computer as a tool in their work if the tedious task of learning a new language for mathematics is part of the bargain. Furthermore, until a new language is thoroughly learned, difficulty in communication will make it less likely that their new experience will be a successful one. Beyond that, if a new computer language does not provide the same visual clues as standard mathematical notation, it may never adequately serve the mathematician. It therefore seems fair to assume that the computer input/output of mathematical expressions in a form resembling standard notation is an important goal. This form of expression is considerably more complex and expensive to handle than those used in, for example, the programming language FORTRAN. But the alternative (e.g., correctly manipulating a one page FORTRAN expression) is often quite painful.

Optimizing binary trees grown with a sorting algorithm

Items can be retrieved from binary trees grown with a form of the Algorithm Quicksort in an average time proportional to log n, where n is the number of items in the tree. The binary trees grown by this algorithm sometimes have some branches longer than others; therefore, it is possible to reduce the average retrieval time by restructuring the tree to make the branches as uniform in length as possible. An algorithm to do this is presented. The use of this algorithm is discussed, and it is compared with another which restructures the tree after each new item is added.

Applications of artificial intelligence

One of the aims of artificial intelligence has been to make machines behave intelligently as humans do. Thus the study of artificial intelligence includes the study of how humans acquire and apply knowledge, reason under uncertainty and in complex environments, and how they do planning and solve problems. Knowledge-based automation deals with the application of artificial intelligence to a production environment in order to reduce the involvement of human beings to a minimum.

Automatic generation of customized, model based information systems for operations management

Abstract : The paper discusses the need for developing a customized, model based system to support management decision making in the field of operations management. It provides a critique of the current approaches available, formulates a framework to classify logistics decisions, and suggests an approach for the automatic development of logistics systems. (Author)

Determining the equivalence of algebraic expressions by hash coding

In algebraic manipulation one often wants to know if two expressions are equivalent under the algebraic and trigonometric identities. One way to check this is to substitute a random value for each variable in the expressions and then see if both expressions evaluate to the same result. Round-off and overflow errors can be avoided if the evaluation is done modulo a large prime number. Of course, there is still a small probability of a random match. If arithmetic expressions in exponents are evaluated, using the same prime number then identities such as xl/2 ï¾ xl/2 &equil; x will not necessarily hold. However, by proper choice of the prime number and the use of special case checks these identities as well as many trigonometric identities can often be preserved.

Computer education in a graduate school of management

Several years of experience have led to the belief that the creative design and evaluation of management information systems requires a thorough understanding of the related computer technology. Concepts such as paging and priority interrupt systems can best be explained at the machine language level. Any machine used for exposition should fulfill several criteria. It should: (1) raise as few spurious issues as possible; (2) allow, without undue effort, the solution of interesting problems; (3) be capable of exposing all outstanding issues of significance, within the chosen machine; (4) be useful for pursuing issues in great depth when appropriate; (5) not be committed to the equipment provided by any manufacturer; (6) be able to provide the student with diagnostic aids to a great depth; (7) allow the student ready access to the machine; (8) be capable of extension to expose new issues as they come along. We have constructed a simulated machine and its associated software which meets these criteria. This system, called the PRISM system, is documented by a primer and a reference manual.

A Logical Form Based on the Structural Descriptions of Events

Facilitating the precise interpretation of statements first made in natural language — this has been the role of mathematical notations like predicate calculus and lambda calculus. Their use has been for the clarification of argument. They were faulted for inadequate precision or the introduction of paradox, never for forcing too much precision. Formal languages are precise, but selective in what can be easily expressed. It has always been understood that quantifiers like ∀ and ∃ only modeled some aspects of a system of natural language quantifiers. However, they captured the most useful properties very neatly.

Natural language interfaces

The panel will focus on the different approaches to creating natural language interfaces to DBMS. Of particular interest is the manner in which database definition information, user feedback dialogues, storage of the lexicon and database path selection are handled. The panelists have all been involved in implementing such interfaces.