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Introduction to Stochastic Computing

  • Vincent C. GaudetEmail author
  • Warren J. Gross
  • Kenneth C. Smith
Chapter

Abstract

In addition to opening the book, this chapter serves as a brief overview of the historical advances in stochastic computing. We highlight four distinct eras, including early work from the 1950s, fundamental work in the 1960s, an era of slower progress in the 1970s, 1980s, and 1990s, and a return to prominence in the 2000s.

References

  1. 1.
    J. von Neumann, Lectures on probabilistic logics and the synthesis of reliable organisms from unreliable components, California Institute of Technology, notes by R. S. Pierce, Jan. 1952.Google Scholar
  2. 2.
    J. von Neumann, “Probabilistic logics and the synthesis of reliable organisms from unreliable components,” Automata Studies, pp. 43-98, 1956.Google Scholar
  3. 3.
    P. Elias, “Computation in the Presence of Noise,” IBM Journal of Research and Development, vol. 2, no. 4, pp. 346-353, 1958.MathSciNetCrossRefGoogle Scholar
  4. 4.
    A.A. Mullin, “Reliable Stochastic Sequential Switching Circuits,” Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, vol. 77, no. 5, pp. 606-611, Nov. 1958.Google Scholar
  5. 5.
    J.D. Cowan, “Toward a Proper Logic for Parallel Computation in the Presence of Noise,” Bionics Symposium, Dayton, OH,Google Scholar
  6. 6.
    W.J. Poppelbaum, C. Afuso, and J. W. Esch, “Stochastic Computing Elements and Systems,” American Federation of Information Processing Societies, Fall Joint Computer Conference, vol. 31, pp. 635-644, Books, Inc., New York, 1967.Google Scholar
  7. 7.
    W.J. Poppelbaum and C. Afuso, Noise Computer, University of Illinois, Dept. Computer Science, Quarterly Technical Progress Reports, April 1965-January 1966.Google Scholar
  8. 8.
    J. Esch, Rascel – A Programmable Analog Computer Based on a Regular Array of Stochastic Computing Element Logic, doctoral thesis, University of Illinois, 1969.Google Scholar
  9. 9.
    C. Afuso, “Two Wire System Computer Circuits Using Transistor Difference Amplifier,” The Science Bulletin of the Division of Agriculture, Home Economics & Engineering, The University of the Ryukyus, no. 9, pp. 308-321, Dec. 1962. Abstract Available: http://ir.lib.u-ryukyu.ac.jp/handle/20.500.12000/23153. Accessed on Aug. 2, 2018.
  10. 10.
    C. Afuso, Analog Computing with Random Pulse Sequences, doctoral thesis, University of Illinois report #255, 1968.Google Scholar
  11. 11.
    Y. Nagata and C. Afuso, “A Method of Test Pattern Generation for Multiple-Valued PLAs,” International Symposium on Multiple-Valued Logic, pp. 87-91. 1993.Google Scholar
  12. 12.
    S.T. Ribeiro, Phase Plane Theory of Transistor Bistable Circuits, doctoral thesis, University of Illinois, 1963.Google Scholar
  13. 13.
    S. T. Ribeiro, “Comments on Pulsed-Data Hybrid Computers,” IEEE Transactions on Electronic Computers, vol. EC-13, no. 5, pp. 640-642, Oct. 1964.Google Scholar
  14. 14.
    S. T. Ribeiro, “Random-Pulse Machines,” IEEE Transactions on Electronic Computers, vol. EC-16, no. 3, pp. 261-276, June 1967.CrossRefGoogle Scholar
  15. 15.
    B. R. Gaines, “Stochastic Computing,” American Federation of Information Processing Societies, Spring Joint Computer Conference, vol. 30, pp. 149-156, Books, Inc., New York, 1967.Google Scholar
  16. 16.
    B. R. Gaines, “Techniques of Identification with the Stochastic Computer,” International Federation of Automatic Control Symposium on Identification, Prague, June 1967.Google Scholar
  17. 17.
    B. R. Gaines, “Stochastic Computer Thrives on Noise,” Electronics, vol. 40, no. 14, pp. 72-79, July 10, 1967.Google Scholar
  18. 18.
    B. R. Gaines, “Stochastic Computing,” Encyclopaedia of Information, Linguistics and Control, pp. 766-781, Pergamon Press, New York and London, 1968.Google Scholar
  19. 19.
    R.C. Lawlor, Computer Utilizing Random Pulse Trains, U.S. patent 3,612,845, priority date July 5, 1968, granted Oct. 12, 1971.Google Scholar
  20. 20.
    G. White, “The Generation of Random-Time Pulses at an Accurately Known Mean Rate and Having a Nearly Perfect Poisson Distribution,” Journal of Scientific Instruments, vol. 41, no. 6, p. 361, 1964.CrossRefGoogle Scholar
  21. 21.
    R.C. Lawlor, “What Computers can do: Analysis and Prediction of Judicial Decisions,” American Bar Association Journal, vol. 49, no. 4, pp. 337-344, April 1963.Google Scholar
  22. 22.
    W. Peakin, “Alexa, Guilty or Not Guilty?” posted Nov. 13, 2016. Available: <http://futurescot.com/alexa-guilty-not-guilty/>, Accessed: August 31, 2018.
  23. 23.
    W.J. Poppelbaum, “Statistical Processors,” Advances in Computers, vol. 14, pp. 187–230, 1976.Google Scholar
  24. 24.
    P. Mars and W. J. Poppelbaum, Stochastic and Deterministic Averaging Processors, Peter Peregrinus Press, 1981.Google Scholar
  25. 25.
    G.A. Black, Analog Computation Based on Random Pulse Density Modulation, doctoral thesis, University of Toronto, 1974.Google Scholar
  26. 26.
    ---, “Applications of Multiple-Valued Logic,” panel session at the International Symposium on Multiple-Valued Logic, chair: M.S. Michalski, panelists: B.R. Gaines, S. Haack, T. Kitahashi, W.J. Poppelbaum, D. Rine, and K.C. Smith, Logan, UT, May 1976.Google Scholar
  27. 27.
    ---, First International Symposium on Stochastic Computing and Its Applications, Toulouse, France, 420 pages, 1978.Google Scholar
  28. 28.
    R. Ananth, A Field Programmable Stochastic Computer for Signal Processing Applications, Master of Applied Science thesis, University of Toronto, 1992.Google Scholar
  29. 29.
    P. Jeavons, D.A. Cohen, J. and Shawe-Taylor, “Generating Binary Sequences for Stochastic Computing,” IEEE Transactions on Information Theory, vol. 40, pp. 716–720, 1994.MathSciNetCrossRefGoogle Scholar
  30. 30.
    A.F. Murray, S. Churcher, A. Hamilton, et al., “Pulse Stream VLSI Neural Networks,” IEEE Micro, vol. 13, no. 3, pp. 29-39.CrossRefGoogle Scholar
  31. 31.
    Y . Hirai, “PDM Digital Neural Network System,” in K. W. Przytula and V.K. Prasanna, Parallel Digital Implementations of Neural Networks, pp. 283-311, Englewood Cliffs: Prentice Hall, 1993.Google Scholar
  32. 32.
    J.E. Tomberg and K. Kaski, “Pulse Density Modulation Technique in VLSI Implementation of Neural Network Algorithms,” IEEE Journal of Solid-State Circuits, Vol. 25, no. 5, pp. 1277-1286, 1990.CrossRefGoogle Scholar
  33. 33.
    L. Zhao, Random Pulse Artificial Neural Network Architecture, Master of Applied Science Thesis, University of Ottawa, May 1998. Available: https://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/tape17/PQDD_0006/MQ36758.pdf. Accessed on August 2, 2018.
  34. 34.
    J.A. Dickson, R.D. McLeod, and H.C. Card, “Stochastic Arithmetic Implementations of Neural Networks with In Situ Learning,” International Conference on Neural Networks, pp. 711-716, 1993.Google Scholar
  35. 35.
    H. Card, “Limits to Neural Computations in Digital Arrays,” Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 1125-1129, 1997.Google Scholar
  36. 36.
    B.D. Brown and H.C. Card, “Stochastic Neural Computation. I. Computational Elements,” IEEE Transactions on Computers, vol. 50, no. 9, pp. 891-905, 2001.MathSciNetCrossRefGoogle Scholar
  37. 37.
    B.D. Brown and H.C. Card, “Stochastic Neural Computation. II. Soft Competitive Learning,” IEEE Transactions on Computers, vol. 50, no. 9, pp. 891-905, 2001.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vincent C. Gaudet
    • 1
    Email author
  • Warren J. Gross
    • 2
  • Kenneth C. Smith
    • 3
  1. 1.University of WaterlooWaterlooCanada
  2. 2.McGill UniversityMontréalCanada
  3. 3.University of TorontoTorontoCanada

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