Lower bounds for constant-depth circuits in the presence of help bits
Information Processing Letters
Elements of information theory
Elements of information theory
Monotone circuits for matching require linear depth
Journal of the ACM (JACM)
On the distributional complexity of disjointness
Theoretical Computer Science
Rounds in communication complexity revisited
SIAM Journal on Computing
Communication complexity and quasi randomness
SIAM Journal on Discrete Mathematics
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
The BNS lower bound for multi-party protocols is nearly optimal
Information and Computation
Direct product results and the GCD problem, in old and new communication models
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
SIAM Journal on Computing
Products and Help Bits in Decision Trees
SIAM Journal on Computing
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
The BNS-chung criterion for multi-party communication complexity
Computational Complexity
Space lower bounds for distance approximation in the data stream model
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Towards Proving Strong Direct Product Theorems
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Information Theory Methods in Communication Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Communication Complexity of Simultaneous Messages
SIAM Journal on Computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Computational complexity questions related to finite monoids and semigroups
Computational complexity questions related to finite monoids and semigroups
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
A direct sum theorem in communication complexity via message compression
ICALP'03 Proceedings of the 30th 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
An axiomatic approach to algebrization
Proceedings of the forty-first annual ACM symposium on Theory of computing
Kolmogorov Complexity and Combinatorial Methods in Communication Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Kolmogorov complexity and combinatorial methods in communication complexity
Theoretical Computer Science
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
An optimal lower bound on the communication complexity of gap-hamming-distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
A little advice can be very helpful
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Communication lower bounds using directional derivatives
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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 驴(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 驴(n 1/(k驴1)/(k 驴 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 驴(log n/(k 驴 1)) bits of communication to compute the disjointness function.