Lower bounds for randomized and quantum query complexity using Kolmogorov arguments

S. Laplante, F. Magniez
Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.  
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( nC 0
more » ... f in O(min( nC 0 (f ), nC 1 (f ))), where C 0 , C 1 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.
doi:10.1109/ccc.2004.1313852 dblp:conf/coco/LaplanteM04 fatcat:7mlg5ylqubgilhtnofmo46mhu4