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computational complexity

, Volume 15, Issue 4, pp 391–432 | Cite as

A Strong Direct Product Theorem for Corruption and the Multiparty Communication Complexity of Disjointness

  • Paul Beame
  • Toniann Pitassi
  • Nathan Segerlind
  • Avi Wigderson
Open Access
Article

Abstract.

We prove that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a “corruption” or “one-sided discrepancy” method over a rectangular distribution. We use this to prove new n Ω(1) lower bounds for 3-player number-on-the-forehead protocols in which the first player speaks once and then the other two players proceed arbitrarily. Using other techniques, we also establish an Ω(n 1/(k−1)/(k − 1)) lower bound for k-player randomized number-on-the-forehead protocols for the disjointness function in which all messages are broadcast simultaneously. A simple corollary of this is that general randomized number-on-the-forehead protocols require Ω(log n/(k − 1)) bits of communication to compute the disjointness function.

Keywords.

Communication complexity direct product direct sum multiparty protocols lower bounds 

Subject classification.

68Q10 68Q15 68Q17 06D15 06E30 

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  • Paul Beame
    • 1
  • Toniann Pitassi
    • 2
  • Nathan Segerlind
    • 3
  • Avi Wigderson
    • 4
  1. 1.Computer Science & EngineeringUniversity of WashingtonSeattleUSA
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada
  3. 3.Department of Computer SciencePortland State UniversityPortlandUSA
  4. 4.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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