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A note on the simulation of exponential threshold weights

  • Thomas Hofmeister
Session 4
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1090)

Abstract

It is known (see [GHR],[GK]) that for F(x) = w0 + w1x1 + ...+ w n x n , a threshold gate G(x) = sgn(F(x)) which may have arbitrarily large integer weights w i can be computed (“simulated”) in threshold circuits of depth 2 with polynomial size. In this paper, we modify the method from [GK] to obtain an improvement in two respects: The approach described here is simpler and the size of the simulating circuit is smaller.

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References

  1. [GHR]
    M. Goldmann, J. Håstad, A. Razborov, Majority gates vs. general weighted threshold gates, Proceedings of 7th Annual Structure in Complexity Theory Conference (1992), pp. 2–13.Google Scholar
  2. [GK]
    M. Goldmann, M. Karpinski, Simulating Threshold Circuits by Majority Circuits, STOC 1993, p. 551–560.Google Scholar
  3. [H]
    T. Hofmeister, Depth-efficient threshold circuits for arithmetic functions, Chap. 2 in: Theoretical Advances in Neural Computation and Learning, V. Roychowdhury, K-Y. Siu, and A. Orlitsky (eds.), Kluwer Academic Publ.Google Scholar
  4. [M]
    S. Muroga, Threshold logic and its applications, John Wiley, New York, 1971.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Thomas Hofmeister
    • 1
  1. 1.Lehrstuhl Informatik IIUniversität DortmundDortmundGermany

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