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Revision #1 to TR13-029 | 18th July 2013 07:25

A {\huge ${o(n)}$} monotonicity tester for Boolean functions over the hypercube

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Revision #1
Authors: Deeparnab Chakrabarty, C. Seshadhri
Accepted on: 18th July 2013 07:25
Downloads: 1264
Keywords: 


Abstract:

Given oracle access to a Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$, we design a randomized tester that takes as input a parameter $\eps>0$, and outputs {\sf Yes} if the function is monotone, and outputs {\sf No} with probability $>2/3$, if the function is $\eps$-far from monotone. That is, $f$ needs to be modified at $\eps$-fraction of the points to make it monotone. Our non-adaptive, one-sided tester makes $\widetilde{O}(n^{7/8}\eps^{-3/2})$ queries to the oracle.



Changes to previous version:

Fixed a bug in previous version. The running time is now $n^{7/8}$ instead of $n^{5/6}$.

More discussion on directed isoperimetry.


Paper:

TR13-029 | 19th February 2013 08:52

A {\huge ${o(n)}$} monotonicity tester for Boolean functions over the hypercube





TR13-029
Authors: Deeparnab Chakrabarty, C. Seshadhri
Publication: 19th February 2013 10:16
Downloads: 2236
Keywords: 


Abstract:

Given oracle access to a Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$, we design a randomized tester that takes as input a parameter $\eps>0$, and outputs {\sf Yes} if the function is monotone, and outputs {\sf No} with probability $>2/3$, if the function is $\eps$-far from monotone. That is, $f$ needs to be modified at $\eps$-fraction of the points to make it monotone. Our non-adaptive, one-sided tester makes $\widetilde{O}(n^{5/6}\eps^{-5/3})$ queries to the oracle.



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