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The Parity Function Again

  • Uwe Schöning
  • Randall Pruim

Abstract

The lower bound theory for circuits received an additional boost through algebraic techniques (in combination with probabilistic techniques) that go back to Razborov and Smolensky.

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References

  1. Valiant, Vazirani: NP is as easy as detecting unique solutions, Theoretical Computer Science 47 (1986), 85–93.MathSciNetzbMATHCrossRefGoogle Scholar
  2. A. Razborov: Lower bounds on the size of bounded depth networks over a complete basis with logical addition, Mathematical Notes of the Academy of Sciences of the USSR 41 (1987), 333–338.MathSciNetzbMATHCrossRefGoogle Scholar
  3. R. Smolensky: Algebraic methods in the theory of lower bounds for Boolean circuit complexity, Proceedings of the 19th Annual Symposium on Theory of Computing, ACM, 1979, 77-82.Google Scholar
  4. N. Alon, J.H. Spencer: The Probabilistic Method, Wiley, 1992, Chapter 11.Google Scholar
  5. R. Beigel: The polynomial method in circuit complexity, Structure in Complexity Theory Conference, IEEE, 1993.Google Scholar
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  7. J. Aspnes, R. Beigel, M. Furst, S. Rudich: The expressive power of voting polynomials, Combinatorica 14 (1994) 135–148MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Uwe Schöning
    • 1
  • Randall Pruim
    • 2
  1. 1.Abt. Theoretische InformatikUniversität UlmUlmGermany
  2. 2.Dept. of Mathematics and StatisticsCalvin CollegeGrand RapidsUSA

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