The multiplicative complexity of boolean functions

  • C. P. Schnorr
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 357)


Let the multiplicative complexity L(f) of a boolean function f be the minimal number of Λ-gates (with two entries) that are sufficient to evaluate f by circuits over the basis Λ,⊕,1. We relate L(f) with the dimension of the dual domain D(f); D(f) is the minimal linear space of linear boolean forms such that f modulo linear functions can be written as a function which takes for input linear forms in D(f).


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  1. J. Ja' Ja' (1979): Optimal evaluation of pairs of bilinear forms. Siam J. Computing 8 (1979), 443–462.Google Scholar
  2. J. Ja' Ja' (1980): On the complexity of bilinear forms. Siam J. Computing 9 (1980), 713–728.Google Scholar
  3. R. Mirwald and C.P. Schnorr (1987): The multiplicative complexity of quadratic boolean forms. Symposium on 28th annual Symposium on Foundations of Computer Science, Los Angeles, pp. 141–149.Google Scholar
  4. C.P. Schnorr (1986): A Gödel theorem on network complexity lower bounds. Zeitschrift für math. Logik und Grundlagen der Mathematik 32 (1986), 377–384.Google Scholar
  5. C.P. Schnorr (1980): A 3n-lower bound on the network complexity of Boolean functions. Theor. Comp. Science 10 (1986), 83–92.Google Scholar
  6. V. Strassen (1973): Vermeidung von Divisionen. Crelles Journal für die reine und angew. Mathematik 264 (1973), 184–202.Google Scholar
  7. V. Strassen (1984): Algebraische Berechnungskomplexität. In Perspectives in Mathematics, Birkhäuser Verlag, Basel.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • C. P. Schnorr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität FrankfurtGermany

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