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• W2964640665 abstract "The communication class UPPcc is a communication analog of the Turing Machine complexity class PP. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f, let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPPcc(f) = O(log n), and UPPcc(f ∧ f) = Θ (log2 n). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPPcc, the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity nOmegaΩ(log n). This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time." @default.
• W2964640665 created "2019-08-13" @default.
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• W2964640665 date "2019-01-01" @default.
• W2964640665 modified "2023-09-24" @default.
• W2964640665 title "Sign-Rank Can Increase Under Intersection." @default.
• W2964640665 hasPublicationYear "2019" @default.
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