Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

On the Probabilistic Query Complexity of Transitively Symmetric Problems

Abstract : We obtain optimal lower bounds on the nonadaptive probabilistic query complexity of a class of problems defined by a rather weak symmetry condition. In fact, for each problem in this class, given a number T of queries we compute exactly the performance (i.e., the probability of success on the worst instance) of the best nonadaptive probabilistic algorithm that makes T queries. We show that this optimal performance is given by a minimax formula involving certain probability distributions. Moreover, we identify two classes of problems for which adaptivity does not help. We illustrate these results on a few natural examples, including unordered search, Simon's problem, distinguishing one-to-one functions from two-to-one functions, and hidden translation. For these last three examples, which are of particular interest in quantum computing, the recent theorems of Aaronson, of Laplante and Magniez, and of Bar-Yossef, Kumar and Sivakumar on the probabilistic complexity of black-box problems do not yield any nonconstant lower bound.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00120934
Contributor : Natacha Portier <>
Submitted on : Tuesday, December 19, 2006 - 1:42:01 PM
Last modification on : Wednesday, September 16, 2020 - 4:52:20 PM
Long-term archiving on: : Monday, September 20, 2010 - 6:08:29 PM

Files

hal07.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00120934, version 2

Collections

Citation

Pascal Koiran, Vincent Nesme, Natacha Portier. On the Probabilistic Query Complexity of Transitively Symmetric Problems. 2006. ⟨hal-00120934v2⟩

Share

Metrics

Record views

563

Files downloads

94