Private vs. common random bits in communication complexity
Information Processing Letters
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Rounds in communication complexity revisited
SIAM Journal on Computing
Communication complexity and quasi randomness
SIAM Journal on Discrete Mathematics
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Communication complexity
The BNS-chung criterion for multi-party communication complexity
Computational Complexity
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Communication Complexity of Simultaneous Messages
SIAM Journal on Computing
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Hadamard tensors and lower bounds on multiparty communication complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Lower bounds for lovász-schrijver systems and beyond follow from multiparty communication complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The multiparty communication complexity of exact-T: improved bounds and new problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Improved Separations between Nondeterministic and Randomized Multiparty Communication
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Improved Separations between Nondeterministic and Randomized Multiparty Communication
ACM Transactions on Computation Theory (TOCT)
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We solve some fundamental problems in the number-onforehead (NOF) k-party communication model. We show that there exists a function which has at most logarithmic communication complexity for randomized protocols with a one-sided error probability of 1/3 but which has linear communication complexity for deterministic protocols. The result is true for k = nO(1) players, where n is the number of bits on each players' forehead. This separates the analogues of RP and P in the NOF communication model. We also show that there exists a function which has constant randomized complexity for public coin protocols but at least logarithmic complexity for private coin protocols. No larger gap between private and public coin protocols is possible. Our lower bounds are existential and we do not know of any explicit function which allows such separations. However, for the 3-player case we exhibit an explicit function which has Ω(log log n) randomized complexity for private coins but only constant complexity for public coins. It follows from our existential result that any function that is complete for the class of functions with polylogarithmic nondeterministic k-party communication complexity does not have polylogarithmic deterministic complexity. We show that the set intersection function, which is complete in the number-in-hand model, is not complete in the NOF model under cylindrical reductions.