Showing papers in "Ibm Journal of Research and Development in 1959"

Some studies in machine learning using the game of checkers

Abstract: Two machine-learning procedures have been investigated in some detail using the game of checkers. Enough work has been done to verify the fact that a computer can be programmed so that it will lear...

Finite automata and their decision problems

Abstract: Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.

The reduction of two-way automata to one-way automata

Abstract: Rabin has proved 1,2 that two-way finite automata, which are allowed to move in both directions along their input tape, are equivalent to one-way automata as far as the classification of input tapes is concerned. Rabin's proof is rather complicated and consists in giving a method for the successive elimination of loops in the motion of the machine. The purposeo f this note is to give a short, direct proof of the result.

On the mathematical theory of error-correcting codes

Abstract: Hamming considered the problem of efficient, faultless transmission of binary data over a noisy channel. For a channel which corrupts no more than one binary digit in each sequence of length n, he constructed alphabets, the so-called Hamming codes, which permit error-free signalling. The authors study the analogous problem for channels which can corrupt a greater number of digits. Non-binary channels are also studied, and analogues of the Hamming codes are constructed. It is perhaps of interest that some of the techniques employed derive from algebraic and analytic number theory, mathematical disciplines not generally associated with the type of applied problems considered in this paper.

The thermal equivalent circuit of a transistor

Abstract: An exact electrical analogue is given for the thermal system between the collector junction and the constant-temperature environment of a transistor. For this circuit analogue, the voltage response to an applied current is equivalent to the temperature response of the collector junction to an applied-power dissipation. The objective of this paper is (1) to prove that this thermal equivalent circuit is entirely consistent with the rigorous, academic approach to the problem, which is to solve a boundary-value problem for heat flow in the transistor system; (2) to present an experimental method for obtaining the circuit parameters in the thermal equivalent circuit; and (3) to demonstrate the utility of the thermal equivalent circuit for the circuit designer and the transistor designer.

On codes for checking logical operations

Abstract: Two types of codes for checking logical operations digit by digit on two vectors of binary digits are studied. The first type attaches a check symbol to each vector of binary digits and requires that the check symbol for the logical function of two vectors can be determined from the check symbols of the two input vectors. The second type of coding is ordinary block coding into vectors of binary digits, with the added requirement that the coded vectors be processed digit by digit. The constraints on the codes resulting from the assumptions for the coding system are studied by typical algebraic arguments. It is shown that for both types of coding and for all nontrivial logical functions of two variables, except "exclusive or" and its complement, there is no system of checking simpler than duplication. For "exclusive or" and its complement, group alphabets can be used, and for the block coding these are the only codes which can be used.

A gas film lubrication study part I: some theoretical analyses of slider bearings

Abstract: The Reynolds differential equation describing flow in a compressible lubricating film is developed. Important characteristics of such films are determined directly from the Reynolds Equation. Pressure, load, velocity, and geometry characteristics are presented for many compressible slider bearing films based upon computer solutions of a Reynolds difference equation as derived in Part II. Part III cites experimental verification of computer solutions and describes experimental techniques.

Noise theory for hot electrons

Abstract: The subject of this note is the extension of the Nyquist theorem, which relates the electrical noise in a conductor in thermal equilibrium to the Ohmic conductivity, 1,2 to the “hot electron” situation in which there is a steady electric field E strong enough to disturb the distribution of electrons among Bloch states and for which the steady current density J will not in general be proportional to E. 3 For simplicity, we discuss the fluctuations of velocity, v, for a single electron. For a steady state the time average, equation, of a function ψ of the electron's state is the same as the ensemble average at any instant over all N electrons in the body: ψ = ifψ ψ (ψ).

A gas film lubrication study part III: experimental investigation of pivoted slider bearings

Abstract: The results of experimental measurements on pivoted slider bearings are presented, the experimental methods are described, and the experimental data are compared with data obtained from a numerical solution of the Reynolds differential equation for a compressible fluid.

A gas film lubrication study part II: numerical solution of the reynolds equation for finite slider bearings

Abstract: This paper presents a finite-difference technique for obtaining approximate numerical solutions to the Reynolds partial differential equation of gas film lubrication theory. A digital computer program is described, and discretization errors and stability of the difference equations are discussed.

Algebraic topological methods for the synthesis of switching systems, part III: minimization of nonsingular Boolean trees

Abstract: An algorithm is given for solving a general problem in combinational switching-circuit minimization theory. The circuits considered consist of a disjunction (OR-ing together) of trees of any set of logical elements, with the restriction that in any given tree no input appears more than once. To each logical element is attached a positive cost. A method is presented for designing a minimum-cost circuit of this variety for any given logical function. Two parallel treatments are given, one viewing it as an abstract mathematical problem, the other considering it as an engineering problem.

Two-parameter lifetime distributions for reliability studies of renewal processes

Abstract: Probability functions are defined for use in reliability studies of equipments which are maintained over a long period of time through replacement of components. These are: lifetime distribution function, lifetime density function, probability of survival, hazard, expected number of replacements, and renewal rate. Theoretical results of renewal theory are adapted to reliability studies of complex systems. The "exponential law" is equivalent to the assumption that survival probability for any given time interval is independent of the age oaf component at the beginning of the interval. It seems more realistic, however, to assume that this survival probability is a monotonically decreasing function of initial age, or, equivalently, that the hazard is a monotonically increasing function of the age of the component. Consequently, three two-parameter models of distribution functions, with the properties: (1) initial lifetime density greater than zero, and (2) monotonically increasing hazard, are proposed and discussed. The lifetime behavior associated with these models ranges from complete determinacy to complete randomness. An entropic measure of this randomness is introduced. The expected number of replacements is numerically calculated and plotted as a function of time for several different parameter values in each model.

On the reduction of continuous problems to discrete form

Abstract: A continuous problem, defined as one involving derivatives or integrals, is to be reduced to a discrete problem, involving only algebraic or evaluative operations. An approach involving cells instead of points is taken, and the unknown function is approximated by functional representations, each associated with one cell and an associated set of parameters. Suitable operations are then defined, each associated with a particular cell. These operations remove the configuration coordinates from the problem, leaving only the parameters. Similar operations are defined which link the approximations in adjacent cells, and which translate certain interface conditions to relations between parameters associated with cells. The entire set of relations is then the equivalent of the usual difference equations. A variational algorithm is introduced in order to circumvent certain difficulties associated with matching equations and unknowns. This also permits the convenient retention of certain "exact conditions" associated with the continuous problem. Some illustrative examples are given.

The multipurpose bias device, part II: the efficiency of logical elements

Abstract: The efficiency of a logical element can be equated with the set of subfunctions it realizes upon biasing or duplication of inputs. Various classes of elements are considered, and optimum or near-optimum examples are presented. Some related areas of study are suggested.

Indexing and control-word techniques

Abstract: In large-scale computers the details of data handling, such as indexing, transmission and ordering, may be performed either by programming or by built-in machine operations. An analysis of the most frequently performed functions justifies the expansion of single-valued index quantities to three-valued control words and the specification of built-in increment, count and refill operations to be used with these control words. STRETCH, the large-scale computer which is being developed by IBM for the Los Alamos Scientific laboratory, provides these control-word functions for data-handling operations.

Extension of Moore-Shannon model for relay circuits

Abstract: The Moore-Shannon model for switching circuits is extended to show how the number of redundant relays needed to improve reliability depends on the logical function of the entire circuit. The reliabilities of AND, OR, and EXCLUSIVE-OR relay circuits are studied as a function of the number of relays, the network topology, and the distribution of inputs. For the case of intermittent failures, a procedure is developed for calculating the reliability of combinational switching circuits, defined as the probability that the circuit will function as specified, averaged over all possible inputs, and subject to the idealizing assumptions of the Moore-Shannon model. The redundancies required to achieve a specified increase in reliability, although considerably smaller than for alternative methods, are still enormous. It is shown that a good way to improve an AND circuit, for example, is to use a series-parallel network in which the number of parallel lines varies with the logarithm of the number of basic AND circuits connected in series to form each line.

An experimental modulation-demodulation scheme for high-speed data transmission

Abstract: An experimental low-cost system was designed to determine speed and reliability limitations on transmitting binary data over private telephone lines. A brief review of alternative approaches is given, with a description of the laboratory model. Performance of the equipment is reported with the reliabilities experienced at 600, 1000, 1600, and 2400 bits per second.

Automatic failure recovery in a digital data processing system

Abstract: This paper describes a program which will enable a complex digital data processing system to give "first aid" to itself. Ordinarily, when an error occurs during system operations, the computer must be stopped for corrective maintenance. The FIX program, however, automatically compensates for computer malfunctions so that recovery from errors may be effected with a negligible loss of operational time. Some equipment features used by the FIX program are briefly outlined prior to a detailed discussion of the structure and function of the program itself. In its initial application in the SAGE system, FIX provided automatic recovery from more than 90% of all failures occurring during the period studied.

Doubling the efficiency of the load-sharing matrix switch

Abstract: Constantine* describes a novel load-sharing matrix switch in which the input winding pattern allows the selection of a single core, while ideally all other cores have zero net excitation These patterns realize 2 n−1 outputs with 2 n inputs, the inputs being grouped in 2 n−1 complementary pairs

Millimicrosecond magnetization reversal in thin magnetic films

Abstract: A special pulse equipment including a pulse sampling oscilloscope with an overall response time of 0.35 mμsec for the observation of the millimicrosecond flux reversal in thin permalloy films is described. Output signals as short as 1 mμsec have been obtained and are discussed with respect to the underlying reversal processes. Inverse switching times versus driving field curves have slopes of about 108/oe sec. Coherent rotation and oscillation of the magnetization have been clearly detected by picking up the flux change transverse to the driving field.

Some new aspects of color perception

Abstract: A mathematical analysis is made Land's recent experiments which showed that fully colored pictures can be produced by a two-color projection system. Although Land's results apparently had been at variance with the classical theories of color perception, it has now been found possible to explain the experiments within the framework of those theories and in conjunction with well-known phenomena in the field of experimental psychology. The results are interpreted in terms of a mechanism of color transformation.

Direct measurement of the angular dependence of the imaginary part of the atomic scattering factor of germanium

Abstract: In the dynamical theory of the anomalous transmission of x-rays through perfect thick crystals, the ratio of transmitted intensity to incident intensity depends upon [1- Kf″Ge(θhkl)/f″Ge(0°)] exponentially. Here K is the polarization factor and the f″Ge(θhkl) and f″Ge(0°) are the imaginary parts of the atomic scattering factors of germanium at the angle θhkl and 0°, respectively. This paper describes the measurement of the ratio f″Ge(θhkl)/f″Ge(0°) for several different sets of planes in nearly perfect germanium crystals.

On the transition from superconducting to normal phase,accounting for latent heat and eddy currents

Abstract: A rigorous solution is given for the superconducting transition of a semi-infinite slab held at a point below the critical temperature Tc, when a constant magnetic field above the critical value Hoc, is applied. The solution accounts for both the absorption of latent heat andth e dissipation of eddy-current heat during the transition. A numerical example is calculated for the case of constants close to those of tantalum.

Geometric effects in the superconducting transition of thin films

Abstract: A study is made of the effect of geometric factors and field orientation on the superconducting transition of bulk material whose dimensional ratios are comparable to those of thin evaporated films. An expression is derived for an effective demagnetizing coefficient in the direction of the applied field for an elliptic cylindrical superconductor, and it is shown that this deviates from 1 by quantities of the order of 10-2 or smaller for experimentally realizable conditions with typical films. These small coefficients give rise to surface fields sufficiently large for transition toth e intermediate state. The shape of the transition for various field orientations has been obtained experimentally, and these curves are analyzed qualitatively on the basis of Landau's and Andrew's theory of the intermediate state. For temperatures below the transition point, and in the absence of fields other than the earth's magnetic field, the possibility that these films are in the intermediate state is explored.

Computation of Sin N, Cos N and m √N using an electronic computer

Abstract: Rational Pade approximations to Sin N in the interval 0≤N≤41π/256 and to Cos N in 0≤N≤ 87π/256 allow the computation of both functions in 0≤N≤π/2 with the first ten correct significant digits in four multiplications and divisions only. If the infinite range 0≤N<∞ is considered, one more multiplication reduces it to the range 0≤N≤π/2 so that the total number of operations is five. The method is flexible and gives any desired accuracy. Thus if eighteen first correct significant digits are required, they are obtained in seven operations for any N in (0, ∞). The same method applied to √N and 3√N yields a very accurate first guess which then is improved by Newton's method. For the radicals m√N with m>4, Newton's method is too slow, and rational Pade approximations studied in this paper yield better subroutines.

Microwave resonance in gadolinium-iron garnet crystals

Abstract: Ferrimagnetic resonance has been observed in single crystals of gadolinium-iron garnet at 9479 and 23,725 mc. The resonance behavior is discussed in terms of a two-sublattice theory. The gadolinium g-factor is equal to 2.006 above -90°C and increases at lower temperatures. The gadolinium ions contribute to the anisotropy below -40°C. The assignment of separate damping constants to each sublattice explains the sharp variation in over-all damping with temperature near the compensation point.

Interatomic-force constants from a central-force law

Abstract: Interatomic-force constants may be predicted from standard central-force laws using thermodynamic data. For the three cases where diffraction data are available (aluminum, copper, and iron) the predicted values agree within an order of magnitude for aluminum and iron, but differ strongly in the case of copper. It is suggested that Jacobsen's α1, for copper, represents the strongest departure from a central-force model and should therefore be the most promising point for further theoretical work.

A cryogenic oscillator

Abstract: Two superconducting oscillators have been reported in the patent literature. F. E. Steele* of the Northrup Aircraft Corporation developed an oscillator based on a superconducting tank circuit. The device is characterized by high stability and low-energy outputs. Another oscillator was developed by E. A. Ericsson † of Sweden. This device also uses a tuned circuit but it is somewhat more complicated in design. The oscillator described in this communication, however, is much simpler in design than either of these and is based on a relaxation process in the transition between the superconducting and conducting phases of a Pb film.