One-way communication complexity of symmetric boolean functions

Jan Arpe; Andreas Jakoby; Maciej Liśkiewicz

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

  • Volume: 39, Issue: 4, page 687-706
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Arpe, Jan, Jakoby, Andreas, and Liśkiewicz, Maciej. "One-way communication complexity of symmetric boolean functions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.4 (2005): 687-706. <http://eudml.org/doc/246030>.

@article{Arpe2005,
abstract = {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.},
author = {Arpe, Jan, Jakoby, Andreas, Liśkiewicz, Maciej},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {communication complexity; boolean functions; Hankel matrices},
language = {eng},
number = {4},
pages = {687-706},
publisher = {EDP-Sciences},
title = {One-way communication complexity of symmetric boolean functions},
url = {http://eudml.org/doc/246030},
volume = {39},
year = {2005},
}

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
PB - EDP-Sciences
VL - 39
IS - 4
SP - 687
EP - 706
AB - 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.
LA - eng
KW - communication complexity; boolean functions; Hankel matrices
UR - http://eudml.org/doc/246030
ER -

References

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