Donald R. Haring

Multi-threshold threshold elements

A multi-threshold element is one in which several thresholds are used to separate the true inputs from the false inputs. Many circuit elements and configurations can be described by this model. An approach, based on conventional single-threshold threshold elements, is developed for the analysis and synthesis of multithreshold threshold elements. It is shown that the basic properties of such elements are similar to conventional threshold elements, and that k-threshold threshold-element realizability of an arbitrary n-variable Boolean function can be related to conventional threshold-element realizability of a related (n+k-1)-variable Boolean function. Foundations for two basically different methods for the synthesis of a single-element realization of an arbitrary Boolean function are developed, as are procedures for transforming such a realization into both two-level and multilevel loop-free networks of k-threshold threshold elements k?1. Every element in the networks has the identical weight vector for the independent variables, which is some-times desirable. The transformation technique is a useful approach to the synthesis of functions by networks of conventional threshold elements. It is proved that if the given function requires a k-threshold threshold element, then at least [k/2+I] conventional threshold elements in a two-level network or [1+log 2 k] such elements in a multilevel network are required. Transformations are given for corresponding minimum-gate networks. Electronic-circuit realizations of multi-threshold elements and some logical-design applications of the multi-threshold approach to network design are discussed. The latter indicate that this approach can be easy to use and can result in economical realizations.

A Tabular Method for the Synthesis of Multithreshold Threshold Elements

This paper presents a tabular method for synthesizing Boolean functions having four or less variables with multithreshold threshold elements. The method is similar to that used for conventional single-threshold threshold elements. All 224 functions of four variables are divided into 221 equivalence classes by variable complementations and/or permutations and/or function complementation. Each equivalence class is characterized by a subset of its corresponding Rademacher-Walsh coefficients, the size of the subset being determined by the number of thresholds required to realize that equivalence class. An arbitrary Boolean function of four or less variables is synthesized by systematically calculating subsets of its Rademacher-Walsh coefficients until, through simple equivalence operations, the equivalence class of the function is found in a table of the 221 equivalence classes. The table indicates a multithreshold realization of the given function. The table shows that any 4-variable function can be realized with at most five thresholds, or by a network of conventional, or single-threshold, threshold elements with at most three gates in which each gate has the identical weight vector for the four input variables.

A combined display for computer venerated data and scanned photographic images

Project Intrex (INformation TRansfer EXperiments) is a program of research and experiments intended to provide a foundation for the design of future information-transfer systems. The library of the future is conceived as a computer-based communications network, but at this time we do not know enough details about such a network to design it. Lacking are the necessary experimental facts, especially in the area of users interaction with such a system. To discover these facts, we want to conduct experiments not only in the laboratory, but above all, in the real-life environment of a useful operating library.

Computer-driven display facilities for an experimental computer-based library

Project Intrex (information transfer experiments) is a program of research and experiments intended to provide a foundation for the design of future information-transfer systems. The library of the future is conceived as a computer-based communications network, but at this time we do not know enough details about such a network to design it. Lacking are the necessary experimental facts, especially in the area of users interaction with such a system. To discover these facts, we want to conduct experiments not only in the laboratory, but above all, in the real-life environment of a useful operating library.