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Showing papers in "IEEE Transactions on Computers in 1973"


Journal ArticleDOI
TL;DR: The primary problem dealt with in this paper is the specification of a descriptive scheme, and a metric on which to base the decision of "goodness" of matching or detection.
Abstract: The primary problem dealt with in this paper is the following. Given some description of a visual object, find that object in an actual photograph. Part of the solution to this problem is the specification of a descriptive scheme, and a metric on which to base the decision of "goodness" of matching or detection.

1,536 citations


Journal ArticleDOI
TL;DR: This paper uses a technique called recursive doubling in an algorithm for solving a large class of recurrence problems on parallel computers such as the Iliac IV.
Abstract: An mth-order recurrence problem is defined as the computation of the series x 1 , x 2 , ..., X N , where x i = f i (x i-1 , ..., x i-m ) for some function f i . This paper uses a technique called recursive doubling in an algorithm for solving a large class of recurrence problems on parallel computers such as the Iliac IV. Recursive doubling involves the splitting of the computation of a function into two equally complex subfunctions whose evaluation can be performed simultaneously in two separate processors. Successive splitting of each of these subfunctions spreads the computation over more processors. This algorithm can be applied to any recurrence equation of the form x i = f(b i , g(a i , x i-1 )) where f and g are functions that satisfy certain distributive and associative-like properties. Although this recurrence is first order, all linear mth-order recurrence equations can be cast into this form. Suitable applications include linear recurrence equations, polynomial evaluation, several nonlinear problems, the determination of the maximum or minimum of N numbers, and the solution of tridiagonal linear equations. The resulting algorithm computes the entire series x 1 , ..., x N in time proportional to [log 2 N] on a computer with N-fold parallelism. On a serial computer, computation time is proportional to N.

1,264 citations


Journal ArticleDOI
TL;DR: A nonparametric clustering technique incorporating the concept of similarity based on the sharing of near neighbors is presented, which is an essentially paraliel approach and is applicable to a wide class of practical problems involving large sample size and high dimensionality.
Abstract: A nonparametric clustering technique incorporating the concept of similarity based on the sharing of near neighbors is presented. In addition to being an essentially paraliel approach, the computational elegance of the method is such that the scheme is applicable to a wide class of practical problems involving large sample size and high dimensionality. No attempt is made to show how a priori problem knowledge can be introduced into the procedure.

956 citations


Journal ArticleDOI
C.R. Baugh1, Bruce A. Wooley
TL;DR: An algorithm for high-speed, two's complement, m-bit by n-bit parallel array multiplication is described, which is converted to an equivalent parallel array addition problem in which each partial product bit is the AND of a multiplier bit and a multiplicand bit.
Abstract: An algorithm for high-speed, two's complement, m-bit by n-bit parallel array multiplication is described. The two's complement multiplication is converted to an equivalent parallel array addition problem in which each partial product bit is the AND of a multiplier bit and a multiplicand bit, and the signs of all the partial product bits are positive.

663 citations


Journal ArticleDOI
TL;DR: It is demonstrated that, for convolution-type models of image restoration, special properties of the linear system of equations can be used to reduce the computational requirements.
Abstract: Constrained least squares estimation is a technique for solution of integral equations of the first kind The problem of image restoration requires the solution of an integral equation of the first kind However, application of constrained least squares estimation to image restoration requires the solution of extremely large linear systems of equations In this paper we demonstrate that, for convolution-type models of image restoration, special properties of the linear system of equations can be used to reduce the computational requirements The necessary computations can be carried out by the fast Fourier transform, and the constrained least squares estimate can be constructed in the discrete frequency domain A practical procedure for constrained least squares estimation is presented, and two examples are shown as output from a program for the CDC 7600 computer which performs the constrained least squares restoration of digital images

590 citations


Journal ArticleDOI
TL;DR: A simple parallel procedure for selecting significant curvature maxima and minima on a digital curve is described.
Abstract: A simple parallel procedure for selecting significant curvature maxima and minima on a digital curve is described.

524 citations


Journal ArticleDOI
TL;DR: The design of totally self-checking check circuits for m-out-of-n codes is described and various gate level implementations for the majority detection circuits are presented, although the self- checking capability of the checker does not depend on their particular implementation since they are exhaustively tested by code inputs.
Abstract: The design of totally self-checking check circuits for m-out-of-n codes is described. Totally self-checking m-out-of-n checkers provide an error indication whenever the input is not an m-out-of-n code or whenever a fault occurs within the checker itself. Since the checker checks itself, there is no need for additional maintenance access or periodic exercise of the checker to verify its ability to detect errors. The basic structure of the checker relies on the use of majority detection circuits. Various gate level implementations for the majority detection circuits are also presented, although the self-checking capability of the checker does not depend on their particular implementation since they are exhaustively tested by code inputs. The self-testing checkers for k-out-of-2k codes are discussed in the most detail since the totally self-checking checkers for 1-out-of-n and arbitrary m-out-of-n codes are constructed by first translating the code to a k-out-of-2k code via a totally self-checking translator.

382 citations


Journal ArticleDOI
TL;DR: Observations are shown of oscillatory and metastable behavior of flip-flops in response to logically undefined input conditions such as those that occur in synchronizers and arbiters.
Abstract: Observations are shown of oscillatory and metastable behavior of flip-flops in response to logically undefined input conditions such as those that occur in synchronizers and arbiters. Significant systems failures have resulted from this fundamentally inescapable problem that is generally not appreciated by system designers and users.

331 citations


Journal ArticleDOI
TL;DR: With the increasing complexity of logic that can be fabricated on a single large-scale integrated (LSI) circuit chip, there is a growing problem of checking the logical behavior of the chips at manufacture.
Abstract: With the increasing complexity of logic that can be fabricated on a single large-scale integrated (LSI) circuit chip, there is a growing problem of checking the logical behavior of the chips at manufacture. The problem is particularly acute for sequential circuits, where there are difficulties in setting and checking the state of the system.

310 citations


Journal ArticleDOI
TL;DR: The problem of assigning a probability to each word of a language is considered and two methods are discussed.
Abstract: The problem of assigning a probability to each word of a language is considered. Two methods are discussed. One method assigns a probability to a word on the basis of particular measurable features of the language. The second method is applied to languages L(G) generated by a grammar G. A probability is associated with each production of G. These in turn define the word probabilities of each word in the language. The conditions for this assignment to be a probabilistic measure are derived.

262 citations


Journal ArticleDOI
TL;DR: Property of systems that enable them to be tested with a fixed constant number of tests independent of p, the number of cells in the system are considered, referred to as C-testable.
Abstract: It has been shown that the number of tests required to detect all faults in a one-dimensional unilateral combinational iterative array consisting of p cells will, in general, be proportional to p. In this paper we consider properties of such systems that enable them to be tested with a fixed constant number of tests independent of p, the number of cells in the system. Such systems are referred to as C-testable. Necessary and sufficient conditions on the basic cell state table are derived for an iterative system to be C-testable. It is shown that an arbitrary N-state cell table can be augmented by the addition of, at most, one row and less than [log2 N]2 columns (for N ≥ 2) so as to be C-testable.

Journal ArticleDOI
Thomas F. Arnold1
TL;DR: It is shown that even a small number of such faults may severely degrade the mean time to system failure and the expected downtime for an otherwise highly reliable system.
Abstract: Duplication is a technique frequently employed to achieve high reliability for a repairable system. Although the philosophy of duplication is that it takes two faults to place a system out of service, there are generally some critical single faults that cause a system failure. This paper considers the effect of such a set of faults on a repairable system's reliability. It is shown that even a small number of such faults may severely degrade the mean time to system failure and the expected downtime for an otherwise highly reliable system.

Journal ArticleDOI
TL;DR: A unified formulation for lower bounds on the minimum number of processors and on time is presented and these lower bounds are sharper than previously known values and provide a general framework that gives insight for deriving simplified expressions.
Abstract: Two problems of importance for the scheduling of multiprocessing systems composed of identical units are discussed in this paper. 1) Given a partially ordered set of computations represented by the vertices of an acyclic directed graph with their associated execution times, find the minimum number of processors in order to execute them in a time not exceeding the length of the critical path of this graph. 2) Determine the minimum time to process this set of computations when a fixed number of processors is available. A unified formulation for lower bounds on the minimum number of processors and on time is presented. These lower bounds are sharper than previously known values and provide a general framework that gives insight for deriving simplified expressions. A new upper bound on the minimum number of processors is presented, which is sharper than the known bounds. The computational aspects of these bounds are also discussed.

Journal ArticleDOI
TL;DR: Three separate types of counters are described, analyzed, and compared: the first counter consists of a network of full adders, the second uses a combination of fullAdders and fastAdders, and the third uses quasi-digital techniques to generate an analog signal proportional to the count which is then digitized.
Abstract: Multiple-input circuits that count the number of their inputs that are in a given state (normally logic ONE) are called parallel counters. In this paper three separate types of counters are described, analyzed, and compared. The first counter consists of a network of full adders. The second counter uses a combination of full adders and fast adders (that may be realized with READ-ONLY memories), while the third type of counter uses quasi-digital (i.e., analog current summing) techniques to generate an analog signal proportional to the count which is then digitized.

Journal ArticleDOI
TL;DR: In this article, the error correcting properties of the redundant residue number systems (RNS) were investigated through a more natural a approach than was previously known, and the necessary and sufficient condition for the correction of a given error affecting a single residue digit of any legitimate number in an RRNS was determined.
Abstract: The error correcting properties of the redundant residue number systems (RNS) are investigated through a more natural a approach than was previously known. The necessary and sufficient condition for the correction of a given error affecting a single residue digit of any legitimate number in an RRNS is determined. The minimal redundancy allowing the correction of the whole class of the single residue digit errors is derived and an efficienit procedure for error correction is given. Moreover, it is shown that a smaller redundancy and a single redundant modulus may allow the correction of certain important subclasses of single residue digit errors, e.g., the set of errors affecting a single bit in the code. Examples are given.

Journal ArticleDOI
TL;DR: An automaton theoretic model of replacement algorithms is introduced for the class of ``random partially preloaded'' replacement algorithms, which contain certain algorithms of practical and theoretical interest and it is shown that the well-known page replacement algorithms FIFO and RAND yield the same long-run page-fault rates.
Abstract: The replacement problem arises in computer system management whenever the executable memory space available is insufficient to contain all data and code that may be accessed during the execution of an ensemble of programs. An example of this is the page replacement problem in virtual memory computers. The problem is solved by using a replacement algorithm that selects code or data items that are to be removed from executable memory whenever new items must be brought in and no more free storage space remains. An automaton theoretic model of replacement algorithms is introduced for the class of ``random partially preloaded'' replacement algorithms, which contain certain algorithms of practical and theoretical interest. An analysis of this class is provided in order to evaluate their performance, using the assumption that the references to the items to be stored are identically distributed independent random variables. With this model, it is shown that the well-known page replacement algorithms FIFO and RAND yield the same long-run page-fault rates.

Journal ArticleDOI
E. A. Feustel1
TL;DR: The paper shows that the advantages of the change from the traditional von Neumann machine to tagged architecture are seen in all software areas including programming systems, operating systems, debugging systems, and systems of software instrumentation.
Abstract: This paper proposes that all data elements in a computer memory be made to be self-identifying by means of a tag. The paper shows that the advantages of the change from the traditional von Neumann machine to tagged architecture are seen in all software areas including programming systems, operating systems, debugging systems, and systems of software instrumentation. It discusses the advantages that accrue to the hardware designer in the implementation and gives examples for large- and small-scale systems. The economic costs of such an implementation for a minicomputer system are examined. The paper concludes that such a machine architecture may well be a suitable replacement for the traditional von Neumann architecture.

Journal ArticleDOI
TL;DR: Waveform segmentation is treated as a problem of piecewise linear uniform (minmax) approximation and can be used for pattern recognition, data compression, and nonlinear filtering not only for waveforms but also for pictures and maps.
Abstract: Waveform segmentation is treated as a problem of piecewise linear uniform (minmax) approximation. Various algorithms are reviewed and a new one is proposed based on discrete optimization. Examples of its applications are shown on terrain profiles, scanning electron microscope data, and electrocardiograms. The processing is sufficiently fast to allow its use on-line. The results of the segmentation can be used for pattern recognition, data compression, and nonlinear filtering not only for waveforms but also for pictures and maps. In the latter case some additional preprocessing is required and it is described in [19].

Journal ArticleDOI
TL;DR: An approach of representing patterns by trees rather than by strings is described, and the tree system is applied to the problem of syntactic pattern recognition.
Abstract: An approach of representing patterns by trees rather than by strings is described. A review of tree systems that include tree grammars, transformations, and mappings on trees and tree automata is briefly presented. The tree system is then applied to the problem of syntactic pattern recognition. Tree grammars are used for pattern description, and tree automata are used for classification. Illustrative examples include the application of the tree system to the classification of bubble chamber events and some English characters.

Journal ArticleDOI
TL;DR: It is proved that a matrix satisfies its two-dimensional characteristic function, and this property is used to form a diagnostic matrix, which is used in a minimization technique.
Abstract: A model for two-dimensional linear iterative circuits is defined in the form of matrix equations. From the matrix equations, a two-dimensional characteristic function is defined. It is then proved that a matrix satisfies its two-dimensional characteristic function. This property is used to form a diagnostic matrix. Finally, the diagnostic matrix is used in a minimization technique.

Journal ArticleDOI
TL;DR: Previous work on evaluation nets is extended through the use of macro nets that represent structures made up of the primitives, allowing compression of the net for easier understanding.
Abstract: An extension of Petri nets called evaluation nets (E-nets) has been developed for use in representation of computer systems. These lead to interpreted graphs for use in human communication and to machine-interpretable descriptions. They may be used as aids in development of simulations and planning of measurements for examining characteristics such as throughput, turnaround time, and utilization of resources. This paper reviews the five primitives used to form nets expressing logical interactions among tokens (or tasks) flowing through the net and system resources represented by the net. Inherent in the use of the primitives is the ability to express time delays associated with the flow of tokens through the network and the modification of attributes of these tokens. This paper extends previous work on evaluation nets through the use of macro nets that represent structures made up of the primitives, allowing compression of the net for easier understanding. The macro nets are ``open-ended'' in the sense that the user can develop new macros to suit the needs of a particular study. Evaluation nets can be used informally like flow charts or block diagrams, although they provide greater power of expression than either. They can also be used more formally to develop machine aids, e.g., for on-line editing of evaluation nets or for development of simulation programs. Some examples of evaluation nets are provided that model a CDC 6400 and the cooperation of n independent sequential processes.

Journal ArticleDOI
TL;DR: It is shown that associated pairs of vectoral items can be recorded by transforming them into a matrix operator M so that a particular stored vector X(r) can be reproduced by multiplying an associated cue vector Q( r) by M.
Abstract: It is shown that associated pairs of vectoral items (Q(r), X(r)) can be recorded by transforming them into a matrix operator M so that a particular stored vector X(r) can be reproduced by multiplying an associated cue vector Q(r) by M. If the number of pairs does not exceed the dimension of the cue and all cue vectors are linearly independent, then the recollections are perfect replicas of the recorded items and there will be no crosstalk from the other recorded items. If these conditions are not valid, the recollections are still linear least square approximations of the X(r). The relationship of these mappings to linear estimators is discussed. These transforms can be readily implemented by linear analog systems.

Journal ArticleDOI
B. Kruse1
TL;DR: A parallel picture processing machine (PPM) is presented that can perform local operations of both logical and arithmetical character on three by three neighborhoods of digitized pictures.
Abstract: A parallel picture processing machine (PPM) is presented. The proposed machine can perform local operations of both logical and arithmetical character on three by three neighborhoods of digitized pictures. It is essentially a two-dimensional machine but in a restricted sense it can be regarded as three-dimensional. The instruction repertoire is thoroughly discussed and several program examples are presented. In thelast section the implementation of the machine is described and v various tradeoffs between speed and economy are discussed. A dynamically programmable microprogram store is shown to give great freedom in program design.

Journal ArticleDOI
TL;DR: In designing a self-checking processor, it is essential to recognize the types of failures that are most probable and match the checking techniques with the type of faults that are expected to occur to yield the best result with the least amount of hardware.
Abstract: In designing a self-checking processor, it is essential to recognize the types of failures that are most probable. Matching the checking techniques with the type of faults that are expected to occur should yield the best result with the least amount of hardware. The microprogram control will consist of integrated circuits: large-scale integration (LSI) for the memory and small-scale integration (SSI) for the associated control logic. Because of the density of chips on a plug-in package and the physical proximity of the devices on an integrated circuit, multiple faults within a single circuit are highly probable. The types of faults within a circuit have been analyzed and found to be of the type which would tend to affect the bits in a unidirectional manner. Also the failed bits would probably be adjacent rather than randomly dispersed throughout-the microprogram store word.

Journal ArticleDOI
Raymond E. Miller1
TL;DR: This paper describes and compares a number of theoretical models for parallel computation; namely, Petri nets, computation graphs, and parallel program schemata, and shows how marked graphs, a particular type of Petri net, are a restricted type of computation graph.
Abstract: In this paper we briefly describe and compare a number of theoretical models for parallel computation; namely, Petri nets, computation graphs, and parallel program schemata. We discuss various problems and properties of parallel computation that can be studied within these formulations and indicate the ties between these properties and the more practical aspects of parallel computation. We show how marked graphs, a particular type of Petri net, are a restricted type of computation graph and indicate how some results of marked graphs can be obtained from known results of computation graphs. Also, for schemata we discuss the decidability versus undecidability of various properties and several techniques of schemata composition.

Journal ArticleDOI
TL;DR: Fundamental results related to the problems of characterization and detection of intermittent faults in digital circuits, which, up to now, have been almost totally ignored, are presented.
Abstract: In this paper we present a few fundamental results related to the problems of characterization and detection of intermittent faults in digital circuits, which, up to now, have been almost totally ignored. This problem is important since in many technologies intermittency is a predominant mode of failure.

Journal ArticleDOI
TL;DR: This paper develops a direct implementation of a nonparametric representation of a curve, f(x, y) = 0, that allows steps to be taken to any point adjacent to the current one, and uses decision variables closely related to an error criterion.
Abstract: Generation of curves using incremental steps along fixed coordinate axes is important in such diverse areas as computer displays, digital plotters, and numerical control. Direct implementation of a nonparametric representation of a curve, f(x, y) = 0, has been shown to be attractive for digital generation. The algorithm in this paper is developed directly from the nonparametric representation of the curve, allows steps to be taken to any point adjacent to the current one, and uses decision variables closely related to an error criterion. Consequently, the algorithm is more general and produces curves closer to the actual curve than do previously reported algorithms.

Journal ArticleDOI
TL;DR: A method is developed for the reconstruction of a two-dimensional convex symmetric object from two orthogonal projections and application of this technique to cardiac cineangiography is discussed.
Abstract: A method is developed for the reconstruction of a two-dimensional convex symmetric object from two orthogonal projections. To reconstruct a three-dimensional object, the object is divided into thin slices and the slices are individually reconstructed. An experimental result of the reconstruction of a clay model from its X-ray pictures is described. Applicability of this technique to cardiac cineangiography is discussed.

Journal ArticleDOI
TL;DR: A novel technique for digital multiplication is presented that represents a considerable departure from conventional (i.e., add and shift or fully parallel) multiplication algorithms, and generates the bits of the product sequentially from least significant to most significant.
Abstract: A novel technique for digital multiplication is presented that represents a considerable departure from conventional (i.e., add and shift or fully parallel) multiplication algorithms. The quasi-serial multiplier generates the bits of the product sequentially from least significant to most significant. Each bit is computed by "counting" the number of ones in the corresponding column of the bit-product matrix and adding the previous carrys. This single operation yields both the product bit and the carrys for the next column. The quasi-serial multiplier requires 2n of these count and add operations to determine the product of two n-bit numbers.

Journal ArticleDOI
TL;DR: Two reduction techniques–state assignment to the DON'T CARE entries, and so-called "state splitting"–are investigated, and the question, "Can I achieve an equivalent k state machine?" is shown to bePolynomial complete, with the resulting conjecture that neither is solvable in time bounded by a polynomial function of the size of the machine.
Abstract: The problem of reducing the number of states in an arbitrary incompletely specified deterministic finite-state machine to k states (for a given k) has proven intractible to solution within "reasonable" time; most techniques seem to require exponential time. Two reduction techniques–state assignment to the DON'T CARE entries, and so-called "state splitting"–are investigated. For both of the techniques, the question, "Can I achieve an equivalent k state machine?" is shown to be polynomial complete, with the resulting conjecture that neither is solvable in time bounded by a polynomial function of the size of the machine.