Year: 2014
Type: preprint
Abstract: The Element Distinctness problem is to decide whether each character of an input string is unique. The quantum query complexity of Element Distinctness is known to be $Θ(N^{2/3})$; the polynomial method gives a tight lower bound for any input alphabet, while a tight adversary construction was only known for alphabets of size $Ω(N^2)$. We construct a tight $Ω(N^{2/3})$ adversary lower bound for Element Distinctness with minimal non-trivial alphabet size, which equals the length of the input. This result may help to improve lower bounds for other related query problems.
Source: arXiv (Cornell University)
Author: Rosmanis, Ansis
Institution: University of Waterloo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1902551940