Improved Separations between Nondeterministic and Randomized Multiparty Communication

  • Matei David
  • Toniann Pitassi
  • Emanuele Viola
Conference paper

DOI: 10.1007/978-3-540-85363-3_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5171)
Cite this paper as:
David M., Pitassi T., Viola E. (2008) Improved Separations between Nondeterministic and Randomized Multiparty Communication. In: Goel A., Jansen K., Rolim J.D.P., Rubinfeld R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg

Abstract

We exhibit an explicit function f : {0, 1}n →{0,1} that can be computed by a nondeterministic number-on-forehead protocol communicating O(logn) bits, but that requires nΩ(1) bits of communication for randomized number-on-forehead protocols with k = δ·logn players, for any fixed δ< 1. Recent breakthrough results for the Set-Disjointness function (Sherstov, STOC ’08; Lee Shraibman, CCC ’08; Chattopadhyay Ada, ECCC ’08) imply such a separation but only when the number of players is k < loglogn.

We also show that for any k = A loglogn the above function f is computable by a small circuit whose depth is constant whenever A is a (possibly large) constant. Recent results again give such functions but only when the number of players is k < loglogn.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Matei David
    • 1
  • Toniann Pitassi
    • 1
  • Emanuele Viola
    • 2
  1. 1.Department of Computer ScienceUniversity of Toronto 
  2. 2.Computer Science DepartmentColumbia University 

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