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Super-logarithmic depth lower bounds via the direct sum in communication complexity

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Abstract

Is it easier to solve two communication problems together than separately? This question is related to the complexity of the composition of boolean functions. Based on this relationship, an approach to separatingNC 1 fromP is outlined. Furthermore, it is shown that the approach provides a new proof of the separation of monotoneNC 1 from monotoneP.

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Author notes

  1. Mauricio Karchmer

    Present address: ITG Inc., 44 Farnsworth St., 9th floor, 02210, Boston, MA

Authors and Affiliations

  1. Dept. of Mathematics, M.I.T., 02139, Cambridge, MA

    Mauricio Karchmer

  2. Dept. of App. Mathematics, Weizmann Institute, 76100, Rehovot, Israel

    Ran Raz

  3. Dept. of Computer Science, Hebrew University, Jerusalem, Israel

    Avi Wigderson

Authors
  1. Mauricio Karchmer
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  2. Ran Raz
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  3. Avi Wigderson
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Karchmer, M., Raz, R. & Wigderson, A. Super-logarithmic depth lower bounds via the direct sum in communication complexity. Comput Complexity 5, 191–204 (1995). https://doi.org/10.1007/BF01206317

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  • DOI: https://doi.org/10.1007/BF01206317

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