IEEE Transactions on Electronic Computers

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»

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»

Phrase-structure grammars were first introduced and studied by Chomsky as devices for generating the sentences of a language. By means of increasingly heavy restrictions on the productions (rewriting rules), four types of grammars were singled out by Chomsky: type 0 (unrestricted), type 1 (context-dependent), type 2 (context-free), and type 3 (finite state). In this paper, a number of decision pro... 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»

A tabulation of the 2470 representative threshold functions of seven arguments has been prepared by the author. This paper discusses the methods used in, and the threshold logic implications of, the enumeration. The self-dual classification method of Goto-Takahasi was employed. A lattice was defined on the 8-cube in terms of which all 2-monotonic, canonical, self-dual functions of eight arguments ... 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»

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 elemen... View full abstract»

This paper discusses some optimum design problems which arise when paging and segmentation are used in a multiprogrammed computer system, and suggests approaches to their solution. It is argued that design optimization depends fundamentally on the statistics of the typical software load presented to the computer system, and also that the investigation requires the aid of a total system model. Stat... View full abstract»

Real numbers can be represented in a binary computer by the form i-B^e where i is the integer part, B the base, and e the exponent. The accuracy of the representation will depend upon the number of bits allocated to the integer part and exponent part as well as what base is chosen. If L(i) and L(e) are the number of bits allocated to the magnitudes of the integer and exponent... 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 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 new kind of machine is proposed, in which the continuous variable is represented as a probability of a pulse occurrence at a certain sampling time. It is shown that threshold gates can be used as simple and inexpensive processors such as adders and multipliers. In fact, for a random-pulse sequence, any Boolean operation among individual pulses will correspond to an algebraic expression among the... 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 ... View full abstract»

The methods for determining the carry skip distributions in the adders with the minimum carry propagation time and the minimum number of carry skip circuits for a given carry propagation time are presented on the assumption that every adder position is comprised either in one skip at most or in two skips at most. Two types of adders with carry skips and each of them without and with end-around-car... 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 review of content-addressable memory and associative computer systems represents an attempt to consolidate and report nontechnically the direction in which numerous independent research programs have progressed during the last ten years. The paper reflects the views of a myriad of researchers on subjects of organization (configuration concepts), hardware elements, logical operations, speed, c... View full abstract»

A method is illustrated for the selection of a minimal cost subset of prime implicants of a Boolean function. The selection problem is represented by a table (P-table), which is an extension of a prime implicant table. A technique for P-table reduction is presented, which allows tabular simplifications for cyclic prime implicant tables also. View full abstract»

A technique for solving a set of ordinary nonlinear differential equations of the form d Y<inf>i</inf>/d X = f<inf>i</inf>(Y<inf>i</inf>)g<inf>i</inf>(Y<inf>1</inf>, Y<inf>2</inf>, ..., Y<inf>n</inf>, X) is discussed. Sets of equations of this form describe such phenomena as heat transfer with variable specific hea... 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»

A synthesis technique is developed which forms an all NAND or all NOR structure from a combinational logical expression. The resultant structure has a maximum of three logic levels. It is shown that the structure can be obtained directly from the prime implicants describing the logical expression. Also, by grouping prime implicants into any one of three basic patterns, a reduction in the size of t... 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»