IEEE Transactions on Electronic Computers

A set of conditions are described which determine whether or not two successive portions of a given program can be performed in parallel and still produce the same results. The conditions are general and can be applied to sections of the program of arbitrary size. The conditions are interesting because of the light they shed on the structure of programs amenable to parallel processing and the memo... View full abstract»

It is suggested that the economics of present large-scale scientific computers could benefit from a greater investment in hardware to mechanize multiplication and division than is now common. As a move in this direction, a design is developed for a multiplier which generates the product of two numbers using purely combinational logic, i.e., in one gating step. Using straightforward diode-transisto... View full abstract»

This paper develops the separating capacities of families of nonlinear decision surfaces by a direct application of a theorem in classical combinatorial geometry. It is shown that a family of surfaces having d degrees of freedom has a natural separating capacity of 2d pattern vectors, thus extending and unifying results of Winder and others on the pattern-separating capacity of hyperplanes. Applyi... View full abstract»

This paper describes error-correction adjustment procedures for determining the weight vector of linear pattern classifiers under general pattern distribution. It is mainly aimed at clarifying theoretically the performance of adaptive pattern classifiers. In the case where the loss depends on the distance between a pattern vector and a decision boundary and where the average risk function is unimo... View full abstract»

Equations are developed which accurately describe the characteristic impedance and signal propagation delay for narrow microstrip transmission lines. Differences in signal propagation delay for microstrip, strip line, and coaxial cables are compared as a function of dielectric constant. The characteristic impedance equation is verified through comparison with experimental results for impedance val... View full abstract»

As digital system speeds increase and their sizes diminish, it becomes increasingly important to understand the mechanism of signal crosstalk (noise) in interconnections between logic elements. The worst case is when two wires run parallel for a long distance. Past literature has been unsuccessful in explaining crosstalk between parallel wires above a ground plane, because it was assumed that only... View full abstract»

The use is discussed of a fast core memory of, say, 32000 words as a slave to a slower core memory of, say, one million words in such a way that in practical cases the effective access time is nearer that of the fast memory than that of the slow memory. View full abstract»

It is shown that a set of diagnostic tests designed for a redundant circuit under the single-fault assumption is not necessarily a valid test set if a fault occurrence is preceded by the occurrence of some (undetectable) redundant faults. This is an additional reason (besides economy) for trying to eliminate certain kinds of redundancy from the circuit. However, single-fault analysis may remain va... View full abstract»

A procedure is described for finding, by shortcut methods, a near-minimal set of tests for detecting all single faults in a combinational logic net. The procedure should prove useful for nets which are too large to be treated by more exact methods [2]. The set of tests so found also appears useful for diagnosing (i.e., locating) faults. The class of faults considered is that which causes connectio... View full abstract»

This paper describes the logical design of an accumulator register for a general purpose digital computer. The only logic gates used are NOR gates and inverter gates and the sole storage device is a gated clocked flip-flop which takes the value on a single input line when the gate line is high. The accumulator register operates in conjunction with another register called the memory exchange regist... View full abstract»

A Boolean function has an inverse when every output is the result of one and only one input. There are 2ⁿ! Boolean functions of n variables which have an inverse. Equivalence classes of these functions are sets of equivalent functions in the sense that they are identical under a group operation on the input and output variables. This paper counts through five variables the n... View full abstract»

This paper treats the problem of automatic fault diagnosis for systems with multiple faults. The system is decomposed into n units u<inf>1</inf>, u<inf>2</inf>, . . . , u<inf>n</inf>, where a unit is a well-identifiable portion of the system which cannot be further decomposed for the purpose of diagnosis. By means of a given arrangement of testing links (connect... View full abstract»

Given two implicants of a Boolean function, we can, by performing their consensus, find a third implicant. This operation has been used for finding the prime implicants of a Boolean function. In this paper, the consensus is extended from two to any number of terms. A property of these generalized consensus relations leads to a systematic way of finding them. It is shown that any prime implicant of... View full abstract»

Many medium-scale electronic computers currently are being designed to cater to scientific and business data-processing problems. Efficiency of floating point computation for scientific problems usually favors a fixed-word format and a word-oriented memory, so that a complete floating-point operand may be read out of or stored in memory in parallel. The logical processing of strings of characters ... View full abstract»

This paper describes the development of a procedure that enables a digital computer to solve ``apictorial'' jigsaw puzzles, i.e., puzzles in which all pieces are uniformly gray and the only available information is the shape of the pieces. The problem was selected because it provided an excellent vehicle to develop computer techniques for manipulation of arbitrary geometric patterns, for pattern i... View full abstract»

The complete set of orthogonal functions of binary variables called Walsh functions can be obtained as direct products of the subclass of these functions known as Rademacher functions. The complete set of Walsh functions can be conveniently represented by a square matrix of l's and -1's, which, when normalized, is an orthogonal matrix. The correct Rademacher functions to multiply together to obtai... View full abstract»

Solving prime implicant tables is greatly facilitated by reduction techniques such as row dominance, column dominance, and essential row selection. This paper presents a new reduction technique which is operable on any otherwise irreducible table having a column covered by exactly two rows. View full abstract»

Two identical low-pass electrical filters, having any realizable low-pass frequency-response characteristic and synthesized from linear analog computer components by any convenient method, may be interconnected in a simple manner to form a band-pass filter whose frequency-response characteristic represents a translation along the frequency axis of the frequency response characteristic of the origi... View full abstract»

This paper describes iterative procedures for determining linear and piecewise linear discriminant functions for multicategory pattern classifiers. While classifiers with the same structure have often been proposed, it is less well known that their parameters can be efficiently determined by simple adjustment procedures. For linear discriminant functions, convergence proofs are given for procedure... View full abstract»

A new method for obtaining pure delay of voltage waveforms on the analog computer is discussed. This method, which is based upon frequency-domain sampling in combination with a feedforward-feedback technique, is capable of producing relatively long delays. The theory underlying the method has been previously presented. In this paper experimental aspects are described in detail. Particular emphasis... View full abstract»

A new group of time-delay polynomial approximations are obtained by trial and error methods. The results of the trial and error procedure suggest an analytic method for finding the new approsimations. The new approximations and their usable bandwidths are tabulated for second-through sixth-order polynomials. Delay vs. frequency graphs of the fourth-and fifth-order polynomials are compared with sev... View full abstract»

A method of decomposing logical functions using three input majority gates is given. This method requires that at least one of the inputs to the gate be specified, and from this the other inputs may be found. For unate functions one of the variables may be completely separated at each level. A method using a Karnaugh map is proposed for finding the best function to use as the specified input, whic... View full abstract»

The problem of recognizing a large alphabet (1000 different characters) is approached using a two stage process. In the first stage of design, the data is partitioned into groups of similar characters by means of heuristic and iterative algorithms. In the second stage, peephole templates are generated for each character in such a way as to guarantee discrimination against other characters in the s... View full abstract»

This report gives a complete catalog of minimal NOR circuits and minimal NAND circuits, assuming complements not available, for all logic functions of three variables. Minimal circuits for a function are those that satisfy these conditions: 1) The number of logic blocks of the circuit is least possible for performing the function; 2) The number of connections in the circuit (total number of inputs... View full abstract»

This paper considers a class of information sources consisting of text and pictures. The text is English language text appearing in scientific and technical documents. The picture sources are the largely schematic pictures that occur in the same class of documents. However, the discussion is broadened slightly to include other picture sources. For a tiny fragment of English, the paper shows how th... View full abstract»

Supplementing earlier papers, this note treats two topics: nonsupervised adaptation to the optimum hypersphere for normal distributions, and supervised estimation of the shape parameter m for Pearson probability distributions. View full abstract»

This paper presents methods for realizing simple threshold functions of n arguments by networks of k-input majority gates, where k≪n. An optimal network realization of the 5-argument majority function using 3-input majority gates is given, and it is then generalized by steps with realizations for the (2n-l)-argument majority function (where n = 3, 4, ...) using (2n-3)-input majority gates, and the... View full abstract»

The paper gives a survey of the learning circuits which became known as learning matrices and some of their possible technological applications. The first section describes the principle of learning matrices. So-called conditioned connections between the characteristics of an object and the meaning of an object are formed in the learning phase. During the operation of connecting the characteristic... View full abstract»

A mathematical model for multiple reflections on lossless, distortionless signal transmission lines is developed for step changes in voltage or current at the source. The model is quite general and is valid for a source driving either one or two lines each loaded with an arbitrary number of discontinuities at arbitrary distances. It will give an exact solution for discontinuities and terminations ... View full abstract»

When diode selection circuits are fed with signals that vary linearly with an input variable, they produce as output a convex or concave function consisting of one linear section per diode. In the present circuits, by combining each diode with a suitable series ``interpolating'' resistor, and feeding the output connection with constant current, it is possible to produce 2n-1 linear sections with n... View full abstract»

A practical method of determining weights for crossproduct and power terms in the variable inputs to an adaptive threshold element used for statistical pattern classification is derived. The objective is to make it possible to realize general nonlinear decision surfaces, in contrast with the linear (hyperplanar) decision surfaces that can be realized by a threshold element using only first-order t... View full abstract»

The purpose of this paper is to derive the optimum word length for the simultaneous digital transmission of a number of continuous signals in real time, through a single communication channel. The transmission introduces sampling and quantization errors; the relation between the fineness of the quantization and the sampling rate, as a function of word length, for a given capacity of the channel, i... View full abstract»

In the most direct method for measuring correlation functions with an analog computer a delay must be simulated. Since a lumped parameter system is used, we can only hope to approximate this delay. We intentionally exclude such storage systems as magnetic tapes because of their cost, and confine ourselves to the use of commonly available analog computer components. Extensive work has been carried ... View full abstract»

An exponentially convergent and finite algorithm is presented for the determination of the solution α of the linear inequalities Aα>0 for a given matrix A, or for determining the non-existence of solution for Aα>0. This result is useful in threshold-switching theory and in pattern classification problems. Experiments indicate extremely rapid convergence of the method. View full abstract»

The functional states of a neural (combinational) net of prescribed interconnection geometry and over-all net function are characterized and enumerated. The problem is formalized for a class of nets having an arbitrary number of inputs and outputs by introducing the notion of a Boolean matrix. The concept of stability of neural nets (which is closely related to the set of functional states over wh... View full abstract»

A method is developed for the synthesis of arbitrary combinational logical functions using three-input majority elements. The networks that result are in the form of modified trees. It is shown that an average saving of 30 per cent in majority elements is made on trees of majority elements which individually produce ``AND'' and ``OR'' functions. Several variations of the basic method are developed... View full abstract»

A new logical algebra, ternary threshold logic, is defined and developed. The system is shown to be capable of representing all three-valued functions, and two methods of synthesizing these functions from their truth tables are given. One of the methods produces a normal form that is analogous to the disjunctive normal form of Boolean algebra. A list of single-threshold-operator equivalents of cer... View full abstract»

A definite automaton is, roughly speaking, an automaton (sequential circuit) with the property that for some fixed integer k its action depends only on the last k inputs. The notion of a definite event introduced by Kleene, as well as the related concepts of definite automata and tables, are studied here in detail. Basic results relating to the minimum number of states required for synthesizing an... View full abstract»

THE TUNNEL DIODE may be advantageously used as a threshold device in a magnetic memory sense amplifier. A signal voltage is induced in a small segment of a sense line. This induced voltage is propagated through the sense line and amplified. Finally, a current proportional to the signal voltage is compared to a threshold current to determine if the information is binary 1 or binary 0. This threshol... View full abstract»

A thermal plant usually consists of various pieces of heat transfer apparatus connected together by pipes. Simulation of the transport delay introduced by these pipes is frequently required. When the fluid velocity through the pipes is constant, the transfer function of the piping lag is easily derived. When the velocity of the fluid is a function of time, however, the transport delay also becomes... View full abstract»

By way of worked examples in typical but somewhat idealized cases the effect on circuit speed of circuit interconnections is studied. The source, calculation and minimization of interconnection crosstalk is also discussed. It is shown that high-speed circuitry must be miniaturized and the implications are discussed. View full abstract»

This paper describes a high-speed arithmetic unit which utilizes a ``sub-multiple algorithm'' in both multiplication and division. The organization and circuits, which make the algorithm practical and economical, are presented. High performance in the unit is achieved by the use of tunnel diodes in four key areas, namely, in a tunnel diode memory using nondestructive readout, in the memory selecti... View full abstract»

The system design of a general-purpose digital computer, CIRRUS, is described. An extensive order code with reasonable order execution times has been achieved at relatively low cost. Comprehensive multiprogram operation is provided. These facilities have been produced largely with microprogramming. The basic hardware is comprised of general purpose registers, a half-word arithmetic unit and two st... View full abstract»

In this paper the system design of a 250 Mc tunnel-diode computer is presented. To resolve the disparity between the obtainable arithmetic and main memory speeds, a sophisticated advanced control is used. The advanced control fetches instructions and operands from the main memory before they are actually needed by the arithmetic unit. These instructions and operands are stored in two small, high-s... View full abstract»