Bill Fefferman, Ronen Shaltiel, Chris Umans, Emanuele Viola

The {\em hybrid argument}

allows one to relate

the {\em distinguishability} of a distribution (from

uniform) to the {\em

predictability} of individual bits given a prefix. The

argument incurs a loss of a factor $k$ equal to the

bit-length of the

distributions: $\epsilon$-distinguishability implies only

$\epsilon/k$-predictability. ...
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Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Avishay Tal

Minimum Circuit Size Problem (MCSP) asks to decide if a given truth table of an $n$-variate boolean function has circuit complexity less than a given parameter $s$. We prove that MCSP is hard for constant-depth circuits with mod $p$ gates, for any prime $p\geq 2$ (the circuit class $AC^0[p])$. Namely, ... more >>>