Emergent Mind
Boolean function monotonicity testing requires (almost) $n^{1/2}$ non-adaptive queries
(1412.5657)
Published Dec 17, 2014
in
cs.CC
Abstract
We prove a lower bound of $\Omega(n{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This improves a $\tilde{\Omega}(n{1/5})$ lower bound for the same problem that was recently given in [CST14] and is very close to $\Omega(n{1/2})$, which we conjecture is the optimal lower bound for this model.
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