One-way communication complexity of symmetric boolean functions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 4, pp. 687-706.

We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are established and 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 that neither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient to consider only the communication direction from 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.

DOI: 10.1051/ita:2005037
Classification: 68Q99,  06E30,  94A05,  68R15
Keywords: communication complexity, boolean functions, Hankel matrices
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Arpe, Jan; Jakoby, Andreas; Liśkiewicz, Maciej. One-way communication complexity of symmetric boolean functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 4, pp. 687-706. doi : 10.1051/ita:2005037. http://www.numdam.org/articles/10.1051/ita:2005037/

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