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  Harmonic analysis, real approximation, and the communication complexity of Boolean functions

Grolmusz, V.(1993). Harmonic analysis, real approximation, and the communication complexity of Boolean functions (MPI-I-93-161). Saarbrücken: Max-Planck-Institut für Informatik.

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Grolmusz, Vince1, Author
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: In this paper we prove several fundamental theorems, concerning the multi--party communication complexity of Boolean functions. Let $g$ be a real function which approximates Boolean function $f$ of $n$ variables with error less than $1/5$. Then --- from our Theorem 1 --- there exists a $k=O(\log (n\L_1(g)))$--party protocol which computes $f$ with a communication of $O(\log^3(n\L_1(g)))$ bits, where $\L_1(g)$ denotes the $\L_1$ spectral norm of $g$. We show an upper bound to the symmetric $k$--party communication complexity of Boolean functions in terms of their $\L_1$ norms in our Theorem 3. For $k=2$ it was known that the communication complexity of Boolean functions are closely related with the {\it rank} of their communication matrix [Ya1]. No analogous upper bound was known for the k--party communication complexity of {\it arbitrary} Boolean functions, where $k>2$.

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Language(s): eng - English
 Dates: 1993
 Publication Status: Issued
 Pages: 15 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/93-161
Report Nr.: MPI-I-93-161
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Title: Research Report / Max-Planck-Institut für Informatik
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