Information and Computation
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
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
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
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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 f1, ..., fk and Alice and Bob have k inputs x1,..., xk and y1,..., yk, respectively. In the eliminate problem, Alice and Bob should output a vector σ1,..., σk such that fi(xi) ≠ σi for at least one i (i.e., their goal is to eliminate one of the 2k output vectors); in choose, Alice and Bob should return (i, fi(xi,yi)) and in agree they should return fi(xi, yi), for some i. 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.