Advances in Information Systems Science pp 37-172 | Cite as
Stochastic Computing Systems
- 307 Citations
- 9 Mentions
- 152 Downloads
Abstract
The invention of the steam engine in the late eighteenth century made it possible to replace the muscle-power of men and animals by the motive power of machines. The invention of the stored-program digital computer during the second world war made it possible to replace the lower-level mental processes of man, such as arithmetic computation and information storage, by electronic data-processing in machines. We are now coming to the stage where it is reasonable to contemplate replacing some of the higher mental processes of man, such as the ability to recognize patterns and to learn, with similar capabilities in machines. However, we lack the “steam engine” or “digital computer” which will provide the necessary technology for learning and pattern recognition by machines.
Keywords
Logic Level Computing Element Clock Pulse Input Line Analog MultiplierPreview
Unable to display preview. Download preview PDF.
References
- 1.W. J. Poppelbaum and C. Afuso, Noise Computer, University of Illinois, Dept. Computer Science, Quarterly Technical Progress Reports (April 1965-January 1966).Google Scholar
- 2.W. J. Poppelbaum, C. Afuso, and J. W. Esch, Stochastic Computing Elements and Systems, in “Proc. American Federation of Information Processing Societies, Fall Joint Computer Conference,” Vol. 31, pp. 635–644, Books, Inc., New York (1967).Google Scholar
- 3.S. T. Ribeiro, Random Pulse Machines, IEEE Trans. Electronic Computers EC-16 261–276 (June 1967).Google Scholar
- 4.B. R. Gaines, Stochastic Computing, in “Proc. American Federation of Information Processing Societies, Spring Joint Computer Conference,” Vol. 30, pp. 149–156, Books, Inc., New York (1967).Google Scholar
- 5.B. R. Gaines, Techniques of Identification with the Stochastic Computer, in “Proc. International Federation of Automatic Control Symposium on Identification, Progue, June 1967.”Google Scholar
- 6.B. R. Gaines, Stochastic Computer Thrives on Noise, Electronics 40(14), 72–79 (July 10 1967).Google Scholar
- 7.B. R. Gaines, Stochastic Computing, in “Encyclopaedia of Information, Linguistics and Control,” pp. 766–781, Pergamon Press, New York and London (1968).Google Scholar
- 7a.J. T. Tou, Engineering Principles of Pattern Recognition, in “Advances in Information Systems Science,” Vol. 1, J. T. Tou, ed., Plenum Press, New York (1969).CrossRefGoogle Scholar
- 7b.K. S. Fu, Learning Control Systems, in “Advances in Information Systems Science,” Vol. 1, J. T. Tou, ed., Plenum Press, New York (1969).Google Scholar
- 8.J. H. Andreae, Learning Machines—A Unified View, in “Encyclopaedia of Information, Linguistics and Control,” Pergamon Press, New York and London (1968).Google Scholar
- 9.E. Feigenbaum and J. Feldman, “Computers and Thought,” McGraw-Hill Book Co., New York (1964).Google Scholar
- 10.L. Uhr, “Pattern Recognition,” John Wiley and Sons, New York (1966).Google Scholar
- 11.J. T. Tou and R. H. Wilcox, “Computer and Information Sciences,” Spartan Books, Washington, D.C. (1964).Google Scholar
- 12.W. J. Karplus and J. A. Howard, A Transfluxor Analog Memory Using Frequency Modulation, in “American Federation of Information Processing Societies,” Vol. 26, Part 1, pp. 673–683, Books, Inc., New York.Google Scholar
- 13.W. J. Karplus, A Hybrid Computer Technique for Treating Nonlinear Partial Differential Equations, IEEE Trans. Electronic Computers EC-13 (5) 597–605 (1964).Google Scholar
- 14.B. R. Gaines and J. H. Andreae, A Learning Machine in the Context of the General Control Problem, in “Proc. 3rd International Congress International Federation of Automatic Control, London, 1966,” Institution of Mechanical Engineers, London (1967).Google Scholar
- 15.W. J. Poppelbaum, Hybrid Graphical Processors, in “Computer Technology,” IEEE Conf. Publ., Vol. 32 (July 1967).Google Scholar
- 16.T. J. Williams, Process Dynamics, in “Proc. 2nd International Congress International Federation of Automatic Control, Basle, 1963.”Google Scholar
- 17.G. A. Korn and T. M. Korn, “Electronic Analog and Hybrid Computers,” McGraw-Hill Book Co., New York (1964).Google Scholar
- 18.J. R. Smith and C. O. Harbourt, An Adaptive Threshold Logic Gate Using Capacitive Analog Weights, IEEE Trans. Electronic Computers EC-17 (1), 78–81 (1968).CrossRefGoogle Scholar
- 19.H. Schmid, Sequential Analog-Digital Computer (SADC), in “American Federation of Information Processing Societies, Joint Computer Conference,” Vol. 27, Part 1, pp. 915–928, Books, Inc., New York (1965).Google Scholar
- 20.D. L. Greer, Characterization of the Magnetic Second-Harmonic Memory, IEEE Trans. Electronic Computers EC-17 (6), 551–558 (1968).CrossRefGoogle Scholar
- 21.B. Widrow, An Adaptive ADALINE Neuron Using Chemical Memistors, ERL Tech. Rep. No. 1553–2, Stanford University (1960).Google Scholar
- 22.G. Nagy, A Survey of Analog Memory Devices, IEEE Trans. Electronic Computers EC-12 388–393 (August 1963).CrossRefGoogle Scholar
- 23.S. Larach, “Photoelectronic Materials and Devices,” D. van Nostrand, Englewood Cliffs, New Jersey (1965).Google Scholar
- 24.D. R. Bosomworth and H. J. Gerritsen, Thick Holograms in Photocromic Materials, Appl. Optics 7(1), 95–98(1968).CrossRefGoogle Scholar
- 25.G. U. Kaiman, Holographic Graphical Storage in Thick Alkali-Halide Crystals, IEEE Int. Conv. Digest, p. 35(1968).Google Scholar
- 26.J. K. Hawkins and C. J. Munsey, Parallel Computer Organizations and Mechanizations, IEEE Trans. Electronic Computers EC-12 (3), 251–262 (1963).CrossRefGoogle Scholar
- 27.D. K. Pollock, C. J. Koester, and J. T. Tippett, “Optical Processing of Information,” Spartan Books, Washington, D.C. (1963).Google Scholar
- 28.S. J. Mathis, R. E. Wiley, and L. M. Spandorfer, “Microelectronics and Large Systems,” Spartan Books, Washington, D.C. (1965).Google Scholar
- 29.R. L. Petritz, Technological Foundations and Future Directions of Large-Scale Integrated Electronics, in “American Federation of Information Processing Societies, Fall Joint Computer Conference,” Vol. 29, pp. 65–87, Books, Inc., New York (1966).Google Scholar
- 30.D. L. Slotnick, W. C. Borck, and R. C. McReynolds, The Solomon Computer— A Preliminary Report, in “Computer Organization,” pp. 66–92, Spartan Books, Washington, DC, (1963).Google Scholar
- 31.W. A. Clark, S. M. Orstein, M. J. Stuki, A. S. Blum, T. J. Chaney, R. E. Olsen, R. A. Dammhoehler, W. E. Ball, C. E. Moinar, A. Antharvedi, Macromodular Computer Systems, in “American Federation of Information Processing Societies, Spring Joint Computer Conference,” Vol. 30, pp. 355–401, Books, Inc., New York (1967).Google Scholar
- 32.R. H. Fuller and R. M. Bird, An Associative Parallel Processor with Application to Picture Processing, in “American Federation of Information Processing Societies, Fall Joint Computer Conference,” Vol. 27, Part 1, pp. 105–116, Books, Inc., New York (1965).Google Scholar
- 33.J. C. Murtha, Highly Parallel Information Processing Systems, in “Advances in Computers,” Vol. 7, pp. 1–116 Academic Press, New York (1966).Google Scholar
- 34.E. L. Braun, “Digital Computer Design,” Chapter 8, Academic Press, New York (1963).Google Scholar
- 35.F. V. Mayorov and Y. Chu, “Digital Differential Analysers,” Iliffe Books (1964).Google Scholar
- 36.W. J. Karplus, Analog and Digital Techniques Combined, in “Computer Control Systems Technology,” pp. 148–155 McGraw-Hill Book Co., New York (1961).Google Scholar
- 37.Digital Operational Techniques, Computer Design 1963 (November), 12.Google Scholar
- 38.B. R. Gaines and P. L. Joyce, Phase Computers, in “Proc. 5th International Congress AICA, Lausanne, 1967.”Google Scholar
- 39.B. R. Gaines, A Modular Programmed DDA for Real-Time Computation, in “Proc. IFIP 68, Edinburgh, 1968.”Google Scholar
- 40.W. R. Schumann, Method and Apparatus for Averaging a Series of Transients, United States Patent 3, 182, 181 (May 5, 1965).Google Scholar
- 41.B. P. Th. Veltman and A. van den Bos, The Applicability of the Relay Correlator and Polarity Coincidence Correlator in Automatic Control, in “Proc. 2nd International Congress International Federation of Automatic Control,” Basle, 1963.Google Scholar
- 42.W. W. Peterson, “Error Correcting Codes,” John Wiley and Sons, New York (1961).Google Scholar
- 43.W. H. Kautz, “Linear Sequential Switching Circuits,” Holden-Day, San Francisco (1965).Google Scholar
- 44.S. W. Golomb, “Shift Register Sequences,” Holden-Day, San Francisco (1967).Google Scholar
- 45.A. Gill, “Finite-State Machines,” McGraw-Hill Book Co., New York (1962).Google Scholar
- 46.A. Gill, “Linear Sequential Circuits,” McGraw-Hill Book Co., New York (1967).Google Scholar
- 47.G. A. Korn, “Random-Process Simulation and Measurements,” McGraw-Hill Book Co., New York (1966).Google Scholar
- 48.P. A. N. Briggs, P. H. Hammond, M. T. G. Hughes, and G. O. Plumb, Correlation Analysis of Process Dynamics Using Pseudo-Random Binary Test Perturbations, in “Advances in Automatic Control,” pp. 37–51, Institution of Mechanical Engineers, London (1965).Google Scholar
- 49.R. P. Gilson, Some Results of Amplitude Distribution Experiments on Shift-Register Generated Pseudo-Random Noise, IEEE Trans. Electronic Computers EC-15 (6), 926–927 (1966).Google Scholar
- 50.R. C. White, Experiments with Digital Computer Simulations of Pseudo-Random Noise Generators, IEEE Trans. Electronic Computers EC-16 (3), 355–357 (1967).CrossRefGoogle Scholar
- 51.R. E. Kaiman, Nonlinear Aspects of Sampled-Data Control Systems, in “Proc. Symp. Nonlinear Circuit Analysis,” pp. 273–313, Polytechnic Institute of Brooklyn, New York (1957).Google Scholar
- 52.M. Arbib, Tolerance Automata, in “Kybernetika Cislo 3,” pp. 223–233 (1967).Google Scholar
- 53.W. De Backer and L. Verbeek, Study of Analog, Digital, and Hybrid Computers Using Automata Theory, ICC Bulletin 5, 215–244 (1966).Google Scholar
- 54.M. Arbib, “Algebraic Theory of Machines, Languages and Semigroups,” Academic Press, New York (1968).Google Scholar
- 55.K. H. Hofman and P. S. Mostert, “Elements of Compact Semigroups,” Merrill Books, Columbus, Ohio (1966).Google Scholar
- 55a.J. T. Tou, ed., “Applied Automata Theory,” Academic Press, New York (1968).Google Scholar
- 56.M. O. Rabin, Probabilistic Automata, Information and Control 6, 230–245 (1963).CrossRefGoogle Scholar
- 57.A. Paz, Some Aspects of Probabilistic Automata, Information and Control 9, 26–60 (1966).CrossRefGoogle Scholar
- 58.W. Feller, “An Introduction to Probability Theory and Its Applications,” John Wiley and Sons, New York (1957).Google Scholar
- 59.L. Takacs, “Stochastic Processes,” Methuen, London (1960).Google Scholar
- 60.R. McNaughton, The Theory of Automata—A Survey, in “Advances in Computers,” Vol. 2, pp. 379–421, Academic Press, New York (1961).Google Scholar
- 61.J. Fox, “Mathematical Theory of Automata,” Polytechnic Institute of Brooklyn Press, New York (1963).Google Scholar
- 62.T. L. Booth, “Sequential Machines and Automata Theory and Sons, New York” John Wiley (1967).Google Scholar
- 63.G. C. Bacon, Minimal-State Stochastic Finite State Systems, IEEE Trans. CT-11, 307–308 (1964).Google Scholar
- 64.G. H. Ott, Reconsider the Minimization Problem for Stochastic Finite State Systems, in “Proc. IEEE 7th Symp. Switching and Automata Theory,” pp. 251–261 (1966).Google Scholar
- 65.G. C. Bacon, The Decomposition of Stochastic Automata, Information and Control 7, 320–339 (1964).CrossRefGoogle Scholar
- 66.C. V. Page, Equivalences between Probabilistic Machines, Tech. Rep. 03105–41-T, University of Michigan (1965).Google Scholar
- 67.J. W. Carlyle, State-Calculable Stochastic Sequential Machines, Equivalences and Events, in “Proc. IEEE Symp. Switching Circuit Theory and Logical Design,” pp. 258–263 (1965).Google Scholar
- 68.J. von Neumann, Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components, in “Automata Studies,” Princeton University Press, Princeton, New Jersey (1956).Google Scholar
- 69.S. Winograd and J. D. Cowan, “Reliable Computation in the Presence of Noise,” MIT Press, Cambridge, Mass. (1963).Google Scholar
- 70.J. D. Cowan, The Problem of Organismic Reliability, in “Cybernetics of the Nervous System,” Elsevier Amsterdam (1965).Google Scholar
- 71.F. Rosenblatt, A Model for Experiental Storage in Neural Networks, in “Computer and Information Sciences,” (J. T. Tou and R. H. Wilcox, eds.), pp. 16–66, Spartan Books Washington, D.C. (1964).Google Scholar
- 72.B. Widrow and F. W. Smith, Pattern-Recognizing Control Systems, in “Computer and Information Sciences,” (J. T. Tou and R. H. Wilcox, eds.), pp. 288–317, Spartan Books Washington, D.C. (1964).Google Scholar
- 73.K. Steinbuch and U. A. W. Piske, Learning Matrices and Their Applications, IEEE Trans. Electronic Computers EC-12 (5), 846–862 (1963).CrossRefGoogle Scholar
- 74.N. J. Nilsson, “Learning Machines,” McGraw-Hill Book Co., New York (1965).Google Scholar
- 75.A. Novikoff, On Convergence Proofs for Perceptrons, in “Automata Theory,” pp. 615–622, Polytechnic Institute of Brooklyn Press, New York (1963).Google Scholar
- 76.G. L. Clapper, Machine Looks, Listens, Learns, Electronics 1967 (October 30), 91–102.Google Scholar
- 77.W. C. Ridgeway, An Adaptive Logic System with Generalizing Properties, Report SEL-62–040, Stanford Electronics Laboratories (April 1962).Google Scholar
- 78.I. Aleksander and R. C. Albrow, Adaptive Logic Circuits, Computer J. 11 (1), 65–71 (1968).CrossRefGoogle Scholar
- 79.S. Muroga, Lower Bounds on the Number of Threshold Functions and a Maximum Weight, IEEE Trans. Electronic Computers EC-14 136–148 (1965).CrossRefGoogle Scholar
- 80.Sze-Tsen Hu, “Threshold Logic,” University of California Press, Berkeley, Calif. (1965).Google Scholar
- 81.M. Cuenod and A. P. Sage, Comparison of Some Methods Used for Process Identification, in “Proc. International Federation of Automatic Control Symposium on Identification in Automatic Control Systems, Prague, June 1967.”Google Scholar
- 82.P. Eykhoff, Process Parameter and State Estimation, in “Proc. International Federation of Automatic Control Symposium on Identification in Automatic Control Systems, Prague, June 1967.”Google Scholar
- 83.M. J. Levin, Optimum Estimation of Impulse Response in the Presence of Noise, IRE Natl. Com. Record 4, 147–182 (1959).Google Scholar
- 84.W. W. Lichtenberger, A Technique of Linear System Identification Using Correlating Filters, IRE Trans. Automatic Control AC-6 (2), 183–199 (1961).CrossRefGoogle Scholar
- 85.Y. Kaya and S. Yamamura, A Self-Adaptive System with a Variable Parameter PID Control, AIEE Trans. Appln. Ind. 58, 378–386 (1962).Google Scholar
- 86.M. Margolis and C. T. Leondes, A Model-Referenced Parameter Tracking Technique for Adaptive Control Systems, IEEE Trans. Appln. Ind. 68, 241–261 (1963).Google Scholar
- 87.B. G. Madden, Simultaneous Determination of System Parameters from Transient Response, IEEE Trans. Appln. Ind. 69, 327–331 (1963).CrossRefGoogle Scholar
- 88.P. C. Young, The Determination of the Parameters of a Dynamic Process, Radio and Electronic Engineer 29 (6), 345–361 (1965).CrossRefGoogle Scholar
- 89.D. D. Donalson and F. H. Kishi, Review of Adaptive Control System Theories and Techniques, in “Modern Control Systems Theory,” McGraw-Hill Book Co., New York (1965).Google Scholar
- 90.P. E. K. Donaldson, Error Decorrelation Studies on a Human Operator Performing a Balancing Task, Med. Electron. Biol. Eng. 2, 393–410 (1964).CrossRefGoogle Scholar
- 91.T. F. Potts, G. N. Ornstein, and A. B. Clymer, The Automatic Determination of Human and Other System Parameters, in “Proc. Western Joint Computer Conference, Los Angeles, pp. 645–660 (1961).Google Scholar
- 92.C. L. Becker and J. V. Wait, Two-Level Correlation on an Analog Computer, IRE Trans. Electronic Computers EC-10 (4), 752–758 (1961).CrossRefGoogle Scholar
- 93.Y. Lundh, A Digital Integrator for On-line Signal Processing, IEEE Trans. Electronic Computers EC-12 (1), 26–28 (1963).CrossRefGoogle Scholar
- 94.P. Jespers, P. T. Chu, and A. Fettweis, A New Method to Compute Correlation Functions, in “International Symp. Information Theory, Brussels, 1962.”Google Scholar
- 95.B. Widrow, Statistical Analysis of Amplitude-Quantized Sampled Data Systems, IRE Trans. CT-3 (1956).Google Scholar
- 96.D. G. Watts, “A General Theory of Amplitude Quantization with Applications to Correlation Determination,” IEE Monograph No. 481 M (November 1961).Google Scholar
- 97.A. K. Nath and A. K. Mathalanabis, Method of Statistical Linearization, Proc. IEE 113 (12), 2081–2086 (1966).Google Scholar
- 98.A. A. Pervozanskii, “Random Processes in Nonlinear Control,” Academic Press, New York (1965).Google Scholar
- 99.O. I. Elgard, High-Frequency Signal Injection : A Means of Changing the Transfer Characteristics of Nonlinear Elements, WESCON (1962).Google Scholar
- 100.G. R. Cooper, R. L. Gassner, and C. D. McGillem, in “Proc. 21st National Electronics Conference,” pp. 656–661, National Electronics Conference, Chicago, Illinois (1965).Google Scholar
- 101.L. J. Savage, “The Foundations of Statistical Inference,” Methuen, London (1962).Google Scholar
- 102.S. Watanabe, Information-Theoretical Aspects of Inductive and Deductive Inference, IBM J. Res. Dev. 14 (2), 208–231 (1960).CrossRefGoogle Scholar
- 103.D. Middleton, “Topics in Communication Theory,” McGraw-Hill Book Co., New York (1965).Google Scholar
- 104.M. E. Maron, Design Principles for an Intelligent Machine, IRE Trans. Information Theory IT-8 (5), 179–185 (1962).CrossRefGoogle Scholar
- 105.M. Minsky and O. G. Selfridge, Learning in Random Nets, in “Information Theory,” pp. 335–347, Butterworths, London (1961).Google Scholar
- 106.K. S. Fu, A Learning Control System Using Statistical Decision Processes, in “Proc. International Federation of Automatic Control Symp. Self-Adaptive Control Systems, Teddington, England, 1965,” Plenum Press, New York (1965).Google Scholar
- 107.D. R. Hill, An ESOTerIC Approach to Automatic Speech Recognition, Int. J. Man-Machine Studies 1(1) (January 1969).Google Scholar
- 108.S. Kullback, “Information Theory and Statistics,” John Wiley and Sons, New York (1959).Google Scholar
- 109.B. G. Farley and W. A. Clark, Simulation of Self-Organizing Systems by Digital Computer, IRE Trans. Information Theory IT-4, 76–84 (September 1954).Google Scholar
- 110.R. L. Beurle, Properties of a Mass of Cells Capable of Regenerating Pulses, Trans. Roy. Soc. (London) B240, 55–94 (August 1956).CrossRefGoogle Scholar
- 111.L. D. Harmon, W. A. Bergeijk, and J. Levinson, Studies with Artificial Neurons, Kybernetik 1, 89–117 (December 1961).CrossRefGoogle Scholar