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COCO
2004
Springer

Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments

10 years 5 months ago
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique generalizes the weighted, unweighted methods of Ambainis, and the spectral method of Barnum, Saks and Szegedy. As an immediate consequence of our main theorem, it can be shown that adversary methods can only prove lower bounds for boolean functions f in O(min( nC0(f), nC1(f))), where C0, C1 is the certificate complexity, and n is the size of the input. We also derive a general form of the ad hoc weighted method used by Høyer, Neerbek and Shi to give a quantum lower bound on ordered search and sorting.
Sophie Laplante, Frédéric Magniez
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where COCO
Authors Sophie Laplante, Frédéric Magniez
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