# One-way communication complexity of symmetric Boolean functions

Jan Arpe; Andreas Jakoby; Maciej Liśkiewicz

RAIRO - Theoretical Informatics and Applications (2010)

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

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topArpe, Jan, Jakoby, Andreas, and Liśkiewicz, Maciej. "One-way communication complexity of symmetric Boolean functions." RAIRO - Theoretical Informatics and Applications 39.4 (2010): 687-706. <http://eudml.org/doc/92785>.

@article{Arpe2010,

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},

keywords = {Communication complexity; Boolean functions; Hankel matrices.},

language = {eng},

month = {3},

number = {4},

pages = {687-706},

publisher = {EDP Sciences},

title = {One-way communication complexity of symmetric Boolean functions},

url = {http://eudml.org/doc/92785},

volume = {39},

year = {2010},

}

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

DA - 2010/3//

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/92785

ER -

## References

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