Algorithms for Boolean Function Query Properties
Computational Complexity
2007-05-23 v1 Data Structures and Algorithms
Abstract
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,' and an O(N) algorithm for `quasisymmetry.' These algorithms are based on new insights into the structure of Boolean functions that may be of independent interest. We also give a subexponential-time algorithm for the space-bounded quantum query complexity of a Boolean function. To prove this algorithm correct, we develop a theory of limited-precision representation of unitary operators, building on work of Bernstein and Vazirani.
Cite
@article{arxiv.cs/0107010,
title = {Algorithms for Boolean Function Query Properties},
author = {Scott Aaronson},
journal= {arXiv preprint arXiv:cs/0107010},
year = {2007}
}
Comments
13 pages, no figures, earlier version submitted to SIAM J. Comp