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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.
@article{ITA_2005__39_4_687_0,
author = {Arpe, Jan and Jakoby, Andreas and Li\'skiewicz, Maciej},
title = {One-way communication complexity of symmetric boolean functions},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {687--706},
publisher = {EDP-Sciences},
volume = {39},
number = {4},
year = {2005},
doi = {10.1051/ita:2005037},
mrnumber = {2172147},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2005037/}
}
TY - JOUR AU - Arpe, Jan AU - Jakoby, Andreas AU - Liśkiewicz, Maciej TI - One-way communication complexity of symmetric boolean functions JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 687 EP - 706 VL - 39 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2005037/ DO - 10.1051/ita:2005037 LA - en ID - ITA_2005__39_4_687_0 ER -
%0 Journal Article %A Arpe, Jan %A Jakoby, Andreas %A Liśkiewicz, Maciej %T One-way communication complexity of symmetric boolean functions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 687-706 %V 39 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2005037/ %R 10.1051/ita:2005037 %G en %F ITA_2005__39_4_687_0
Arpe, Jan; Jakoby, Andreas; Liśkiewicz, Maciej. One-way communication complexity of symmetric boolean functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 4, pp. 687-706. doi: 10.1051/ita:2005037
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