Information and Computation
Private vs. common random bits in communication complexity
Information Processing Letters
Communication complexity towards lower bounds on circuit depth
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
Terse, superterse, and verbose sets
Information and Computation
Fractional Covers and Communication Complexity
SIAM Journal on Discrete Mathematics
Information and Computation
Amortized Communication Complexity
SIAM Journal on Computing
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
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Products and Help Bits in Decision Trees
SIAM Journal on Computing
Journal of Computer and System Sciences
Theory of Semi-Feasible Algorithms
Theory of Semi-Feasible Algorithms
An Information Statistics Approach to Data Stream and Communication Complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Distributional Complexity of Disjontness
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
P-Selective Sets, Tally Languages, and the Behavior of Polynomial Time Reducibilities on NP
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Realizing Boolean Functions on Disjoint Sets of Variables
Realizing Boolean Functions on Disjoint Sets of Variables
Towards Proving Strong Direct Product Theorems
CCC '01 Proceedings of the 16th 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
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
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
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We consider several questions inspired by the direct-sum problem in (two-party) communication complexity. In all questions, there are k fixed Boolean functions f 1,驴,f k and each of Alice and Bob has k inputs, x 1,驴,x k and y 1,驴,y k , respectively. In the eliminate problem, Alice and Bob should output a vector 驴1,驴,驴 k such that f i (x i , y i ) 驴 驴 i for at least one i (i.e., their goal is to eliminate one of the 2 k output vectors); in the choose problem, Alice and Bob should return (i, f i (x i , y i )), for some i (i.e., they choose one instance to solve), and in the agree problem they should return f i (x i , y i ), for some i (i.e., if all the k Boolean values agree then this must be the output). The question, in each of the three cases, is whether one can do better than solving one (say, the first) instance. We study these three problems and prove various positive and negative results. In particular, we prove that the randomized communication complexity of eliminate, of k instances of the same function f, is characterized by the randomized communication complexity of solving one instance of f.