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A note on multiplying boolean matrices II

In a note by Baker [1], a method is given for getting the limiting connectivity matrix, B, of a matrix whose entries are Boolean 0's and 1's. Harary [2] suggests determining An-1 since An-1 = An = ··· , where n is the order of the matrix. The purpose of this note is to give a method for determining An-1. The method is also applicable to finding the output matrix of a switching network as described in [3] and [4] where again An-1 = An = ··· , but A now has Boolean switching functions as entries instead of 0's and 1's.

An efficient composite formula for multidimensional quadrature

A (2s+1)-point, second-degree quadrature formula for integration over an s-dimensional hyper-rectangle is presented. All but one of the points lie on the surface with weights of opposite sign attached to points on opposite faces. When a large volume is subdivided into congruent rectangular subdivisions, only one point is required in each interior subdivision to achieve second-degree accuracy.

On the numerical solution of boundary value problems for linear ordinary differential equations

A numerical method is presented for the solution of boundary value problems involving linear ordinary differential equations. The method described is noniterative and makes use of any one-step numerical integration scheme to reduce the problem from one of boundary values to one of initial values. Comments are made concerning some numerical results of applying the method to a specific problem. In addition an extension of the algorithm described to more general problems is discussed.

Telefile: a case study of an online savings bank application

The development of an on-line computer system for a savings bank institution is traced from the early conceptual needs of the bank to the consummation of design by The Teleregister Corporation. Both bank and equipment criteria are specified which led to the development of the Telefile System of The Teleregister Corporation.Operation of the on-line and off-line programs are described and statistics are cited for reliability and performance of the system. Benefits to the bank are discussed from the banker's point of view; an indication of future trends in the on-line savings bank field is also discussed.

Some legal implications of the use of computers in the banking business

The introduction of computers into the banking business has a wide variety of legal implications that merit careful attention at this very early stage. The industry is highly regulated by government and, hence, is subject to many statutes and regulations. It also is affected by important common law rules established by courts. The legal ramifications involve not only the mechanization itself, but also the very significant, economically attractive phenomenon of off premises processing. It is essential to identify and provide for many legal aspects right now, before systems and practices crystallize, in order to avoid the later impact of unanticipated physical complications and expense.The legal aspects of computerization in the banking business are especially diverse. In some states, there might be the basic question whether banks are authorized by law to invest in the new facilities, either directly or through cooperatives. More challenging are questions relating to off-premises processors, particularly with respect to the obligation not to disclose information concerning a bank's customers, the adequacy of fidelity bond coverage, the extent of liability for improper refusal to pay a check, and susceptibility to regulation by government agencies. Also pertinent is the propriety of data processing by banks for nonbank entities and particularly of the rendering of that service without charge for bank depositors.

A serial technique to determine minimum paths

The need to determine minimum paths through a maze very often arises in such fields as traffic, transportation, communication and network studies. Computer analysis of these maze problems has been hampered in many cases due to the excessive size of the network under consideration. A technique has been developed to handle networks of very large magnitude by serially processing the network repetitively until only minimum paths remain.

Report of a visit to discuss common programming languages in Czechoslavakia and Poland, 1963

Early in June 1963 there was a meeting in Berlin [1] of the Subcommittee for Programming Languages, SC5 of TC97, the Technical Committee for Standardization of Computers and Information Processing [2]. Taking advantage of the proximity of Poland and Czechoslovakia, who are interested in the subject but have not actively participated in SC5, a small group representing the Secretariat of SC5 visited those countries. The major purpose of the visit was to discuss such topics as the state of the art of programming languages in each country—both development and use, any national standardization activity, participation in international standardization, and the present state and future prospects of international standardization. A formal report was made to SC5 in Berlin after the visit. The present report is not an official report of the visit. It is a private report of the group, intended for public dissemination. It includes some material not directly relevant to the official purpose of the visit and omits some of the material pertinent only to the official ISO activity, or parts of the discussions which it would be premature or discourteous to publish at this time.

Recent improvements in MADCAP

MADCAP is a programming language admitting subscripts, superscripts and certain forms of displayed formulas. The basic implementation of this language was described in a previous paper [MADCAP: A scientific compiler for a displayed formula textbook language, Comm. ACM 4 (Jan. 61), 31-36]. This paper discusses recent improvements in the language in three areas: complex display, logical control, and subprogramming. In the area of complex display, the most prominent improvements are a notation for integration and for the binomial coefficients. In the area of logical control the chief new feature is a notation for variably nested looping. The discussion of subprogramming is focused on MADCAP's notation for and use of “procedures.”

Flexible abbreviation of words in a computer language

An increasing number of computer programs are designed to accept and translate a symbolic, English-like language which facilitates communication between the user and the computer. A common feature of such programs is a pre-determined vocabulary of expressions for specifying the input to the program. This note describes a generalized technique for permitting flexible abbreviation of such expressions in order to further simplify the task of writing source programs.

Optimizing bit-time computer simulation

A major component of a bit-time computer simulation program is the Boolean compiler. The compiler accepts the Boolean functions representing the simulated computer's digital circuits, and generates corresponding sets of machine instructions which are subsequently executed on the “host” computer. Techniques are discussed for increasing the sophistication of the Boolean compiler so as to optimize bit-time computer simulation. The techniques are applicable to any general-purpose computer.

Length of strings for a merge sort

Detailed statistics are given on the length of maximal sorted strings which result from the first (internal sort) phase of a merge sort onto tapes. It is shown that the strings produced by an alternating method (i.e. one which produces ascending and descending strings alternately) tend to be only three-fourths as long as those in a method which produces only ascending strings, contrary to statements which have appeared previously in the literature. A slight modification of the read-backward polyphase merge algorithm is therefore suggested.

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