The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
Trade-offs between communication and space
Journal of Computer and System Sciences
Communication-Space Tradeoffs for UnrestrictedProtocols
SIAM Journal on Computing
Non-deterministic communication complexity with few witnesses
Journal of Computer and System Sciences
Fractional Covers and Communication Complexity
SIAM Journal on Discrete Mathematics
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
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
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Towards Proving Strong Direct Product Theorems
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Quantum Search of Spatial Regions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
SIAM Journal on Computing
Lower Bounds for Quantum Communication Complexity
SIAM Journal on Computing
One-Way Multi-Party Communication Lower Bound for Pointer Jumping with Applications
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A Direct Product Theorem for Discrepancy
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A time-space tradeoff for Boolean matrix multiplication
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Products and help bits in decision trees
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds in communication complexity based on factorization norms
Random Structures & Algorithms
Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak
A Probabilistic Inequality with Applications to Threshold Direct-Product Theorems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
ACM SIGACT News
Quantum one-way communication can be exponentially stronger than classical communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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
Direct product via round-preserving compression
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Direct sum fails for zero error average communication
Proceedings of the 5th conference on Innovations in theoretical computer science
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A strong direct product theorem states that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then the overall success probability will be exponentially small in k. We establish such a theorem for the randomized communication complexity of the Disjointness problem, i.e., with communication const• kn the success probability of solving k instances of size n can only be exponentially small in k. This solves an open problem of [KSW07, LSS08]. We also show that this bound even holds for $AM$-communication protocols with limited ambiguity. The main result implies a new lower bound for Disjointness in a restricted 3-player NOF protocol, and optimal communication-space tradeoffs for Boolean matrix product. Our main result follows from a solution to the dual of a linear programming problem, whose feasibility comes from a so-called Intersection Sampling Lemma that generalizes a result by Razborov [Raz92].