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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)

- S. Ben-David, K. Meer, C. Michaux
- 2000

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)