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Large databases with uncertain information are becoming more common in many applications including data integration, location tracking, and Web search. In these applications , ranking records with uncertain attributes introduces new problems that are fundamentally different from conventional ranking. Specifically, uncertainty in records' scores induces a… (More)

We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate… (More)

While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the disjointness function. We give the first super-quadratic separation between quantum and randomized communication… (More)

We construct a total Boolean function f satisfying R(f) = ˜ Ω(Q(f) 5/2), refuting the long-standing conjecture that R(f) = O(Q(f) 2) for all total Boolean functions. Assuming a conjecture of Aaronson and Ambainis about optimal quantum speedups for partial functions, we improve this to R(f) = ˜ Ω(Q(f) 3). Our construction is motivated by the… (More)

We provide new query complexity separations against sensitivity for total Boolean functions: a power 3 separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power 2.1 separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a… (More)

We study the composition question for bounded-error randomized query complexity: Is R(f • g) = Ω(R(f)R(g)) for all Boolean functions f and g? We show that inserting a simple Boolean function h, whose query complexity is only Θ(log R(g)), in between f and g allows us to prove R(f • h • g) = Ω(R(f)R(h)R(g)). We prove this using a new lower bound measure for… (More)

The fisherman caught a quantum fish. Fisherman, please let me go, begged the fish, and I will grant you three wishes. The fisherman agreed. The fish gave the fisherman a quantum computer, three quantum signing tokens and his classical public key. The fish explained: to sign your three wishes, use the tokenized signature scheme on this quantum computer, then… (More)

One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially equivalent to the approximate γ 2 norm and generalized discrepancy, and subsumes several other lower bounds. All known lower… (More)