Abstract
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,...,f k and Alice and Bob have k inputs x 1,...,x k and y 1,...,y k , respectively. In the eliminate problem, Alice and Bob should output a vector σ 1,...,σ k such that f i (x i ) ≠ σ i 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,f i (x i ,y i )) and in agree they should return f i (x i ,y i ), 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.
The first author is supported by ISF grant 938/09. The second author is partially supported by the Frankel Center for Computer Science. The third and fourth authors are supported by ISF grant 1310/06.
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Beimel, A., Ben Daniel, S., Kushilevitz, E., Weinreb, E. (2010). Choosing, Agreeing, and Eliminating in Communication Complexity. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_39
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DOI: https://doi.org/10.1007/978-3-642-14165-2_39
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