Algorithms for Boolean function query properties (2003)
| Venue: | SIAM J. COMPUT |
| Citations: | 3 - 2 self |
BibTeX
@ARTICLE{Aaronson03algorithmsfor,
author = {Scott Aaronson},
title = {Algorithms for Boolean function query properties},
journal = {SIAM J. COMPUT},
year = {2003},
volume = {32},
pages = {2003}
}
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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.
