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1 results

  • One-way communication complexity of symmetric Boolean functions

  • Jan Arpe, Andreas Jakoby, Maciej Liśkiewicz
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 39 / Issue 4 / October 2005
    Published online by Cambridge University Press:
    15 October 2005, pp. 687-706
    Print publication:
    October 2005

  • We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are establishedand applied to the one-way two-party communication complexity of symmetric Boolean functions.It is shown that the number of required communication bits does not depend on the communication direction, provided thatneither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient to consider only the communication directionfrom the party with the shorter input to the other party. These facts do not hold for arbitrary Boolean functions in general. Next, gaps between one-way and two-way communication complexity for symmetric Boolean functions are discussed.Finally, we give some generalizations to the case of multiple parties.