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- W2793039178 abstract "We prove several results which, together with prior work, provide a nearly-complete picture of the relationships among classical communication complexity classes between $${mathsf{P}}$$ and $${mathsf{PSPACE}}$$ , short of proving lower bounds against classes for which no explicit lower bounds were already known. Our article also serves as an up-to-date survey on the state of structural communication complexity. Among our new results we show that $${mathsf{MA} notsubseteq mathsf{ZPP}^{mathsf{NP}[1]}}$$ , that is, Merlin–Arthur proof systems cannot be simulated by zero-sided error randomized protocols with one $${mathsf{NP}}$$ query. Here the class $$mathsf{ZPP}^{mathsf{NP}[1]}$$ has the property that generalizing it in the slightest ways would make it contain $${mathsf{AM} cap mathsf{coAM}}$$ , for which it is notoriously open to prove any explicit lower bounds. We also prove that $${mathsf{US} notsubseteq mathsf{ZPP}^{mathsf{NP}[1]}}$$ , where $${mathsf{US}}$$ is the class whose canonically complete problem is the variant of set-disjointness where yes-instances are uniquely intersecting. We also prove that $${mathsf{US} notsubseteq mathsf{coDP}}$$ , where $${mathsf{DP}}$$ is the class of differences of two $${mathsf{NP}}$$ sets. Finally, we explore an intriguing open issue: Are rank-1 matrices inherently more powerful than rectangles in communication complexity? We prove a new separation concerning $${mathsf{PP}}$$ that sheds light on this issue and strengthens some previously known separations." @default.
- W2793039178 created "2018-03-29" @default.
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- W2793039178 date "2018-03-22" @default.
- W2793039178 modified "2023-09-23" @default.
- W2793039178 title "The Landscape of Communication Complexity Classes" @default.
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- W2793039178 doi "https://doi.org/10.1007/s00037-018-0166-6" @default.
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