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Paper:

TR19-043 | 12th March 2019 20:55

Nondeterministic and Randomized Boolean Hierarchies in Communication Complexity

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TR19-043
Authors: Toniann Pitassi, Morgan Shirley, Thomas Watson
Publication: 24th March 2019 09:12
Downloads: 299
Keywords: 


Abstract:

We study the Boolean Hierarchy in the context of two-party communication complexity, as well as the analogous hierarchy defined with one-sided error randomness instead of nondeterminism. Our results provide a complete picture of the relationships among complexity classes within and across these two hierarchies. In particular, we prove a query-to-communication lifting theorem for all levels of the Boolean Hierarchy and use it to resolve an open problem stated in the paper by Halstenberg and Reischuk (CCC 1988) which initiated this topic.



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