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Some remarks on Boolean sums

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Mathematical Foundations of Computer Science 1979 (MFCS 1979)

Part of the book series: Lecture Notes in Computer Science ((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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  • Pippenger, N.: On another boolean matrix, IBM Research Report 69/4, Dec. 1977.

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  • Wegener, I.: A new lower bound on the monotone network complexity of boolean sums, Preprint, Dept. of Mathematics, University of Bielefeld, 1978.

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Authors and Affiliations

  1. Fachbereich 10 — Angewandte Mathematik und Informatik, Universität des Saarlandes, 6600, Saarbrücken, BRD

    Kurt Mehlhorn

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  1. Kurt Mehlhorn
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Jiří Bečvář

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© 1979 Springer-Verlag Berlin Heidelberg

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Mehlhorn, K. (1979). Some remarks on Boolean sums. In: Bečvář, J. (eds) Mathematical Foundations of Computer Science 1979. MFCS 1979. Lecture Notes in Computer Science, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09526-8_36

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  • DOI: https://doi.org/10.1007/3-540-09526-8_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09526-2

  • Online ISBN: 978-3-540-35088-0

  • eBook Packages: Springer Book Archive

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