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Some remarks on Boolean sums

  • Kurt Mehlhorn
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 74)

Abstract

Neciporuk, Lamagna/Savage and Tarjan determined the monotone network complexity of a set of Boolean sums if any two sums have at most one variable in common. Wegener then solved the case that any two sums have at most k variables in common. We extend his methods and results and consider the case that any set of h+1 distinct sums have at most k variables in common. We use our general results to explicitly construct a set of n Boolean sums over n variables whose monotone complexity is of order n5/3. The best previously known bound was of order n3/2. Related results were obtained independently by Pippenger.

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Bibliography

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.Fachbereich 10 — Angewandte Mathematik und InformatikUniversität des SaarlandesSaarbrückenBRD

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