Languages with Bounded Multiparty Communication Complexity

0084614 - MÚ 2008 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Chattopadhyay, A. - Koucký, Michal - Krebs, A. - Szegedy, M. - Tesson, P. - Thérien, D.
Languages with Bounded Multiparty Communication Complexity.
[Jazyky s omezenou komunikační složitostí pro více hráčů.]
Proceeding of the 24th Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2007. Berlin: Springer-Verlag, 2007 - (Thomas, W.; Weil, P.), s. 500-511. Lecture Notes in Computer Science, 4393. ISBN 978-3-540-70917-6.
[Annual Symposium on Theoretical Aspects of Computer Science (STACS). Aachen (DE), 22.02.2007-24.02.2007]
Grant CEP: GA ČR GA201/05/0124
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: communication complexity * codes * Ramsey theory
Kód oboru RIV: BA - Obecná matematika

We study languages with bounded communication complexity in the multiparty "input on the forehead" model with worst-case partition. In the two party case,it is known that such languages are exactly those that are recognized by programs over commutative monoids.This can be used to show that these languages can be computed by shallow ACC^0 circuits. In contrast, we use coding techniques to show that there are languages of arbitrarily large circuit complexity than can be computed by k players using constant communication, if>=3. However, if the language has a neutral letter and constant communication complexity for k players for some fixed k, then the language is in fact regular. We give an algebraic characterization of regular languages with this property. We also prove than a symmetric language has bounded k-party communication complexity for some fixed k iff it has bounded 2-party communication complexity.

Zabýváme se výpočetní složitostí funkcí, jež mají omezenou komunikační složitost v komunikačních hrách více hráčů.
Trvalý link: http://hdl.handle.net/11104/0147333