منابع مشابه
Element Distinctness Revisited
The element distinctness problem is the problem of determining whether the elements of a list are distinct. Classically, it requires N queries, where N is the number of elements. In the quantum case, it is possible to solve the problem in O(N) queries. The problem can be extended by asking whether there are k colliding elements, known as element k-distinctness. This work obtains optimal values ...
متن کاملPRAM Lower Bound for Element Distinctness Revisited
This paper considers the problem of element distinctness on CRCW PRAMs with unbounded memory. A complete proof of the optimal lower bound of ? n log n= ? p log(n p log n + 1) steps for n elements problem on p processor COMMON PRAM is presented. This lower bound has been previously correctly stated by Boppana, but his proof was not complete. Its correction requires some additional observations a...
متن کاملQuantum Algorithms for Element Distinctness
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Høyer, and Tapp, and imply an O(N3=4 logN) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with (N logN) classical complexity. We also prove a lower bound of ...
متن کاملA Time-Space Tradeoff for Element Distinctness
In a time-space tradeoff for sorting on non-oblivious machines, Borodin et. Al. [J. Comput. System Sci., 22(1981), pp. 351-364] proved that to sort $n$ elements requires $TS=\Omega(n^2)$ where $T=time$ and $S=space$ on a comparison based branching program. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately fol...
متن کاملDual Polynomials for Collision and Element Distinctness
The approximate degree of a Boolean function f : {−1, 1} → {−1, 1} is the minimum degree of a real polynomial that approximates f to within error 1/3 in the `∞ norm. In an influential result, Aaronson and Shi (J. ACM 2004) proved tight Ω̃(n) and Ω̃(n) lower bounds on the approximate degree of the Collision and Element Distinctness functions, respectively. Their proof was non-constructive, using a...
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ژورنال
عنوان ژورنال: Quantum Information Processing
سال: 2018
ISSN: 1570-0755,1573-1332
DOI: 10.1007/s11128-018-1930-x