Eli Ben-Sasson, Prahladh Harsha

We present a simple proof of the bounded-depth Frege lower bounds of

Pitassi et. al. and Krajicek et. al. for the pigeonhole

principle. Our method uses the interpretation of proofs as two player

games given by Pudlak and Buss. Our lower bound is conceptually

simpler than previous ones, and relies ...
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Emanuele Viola

We exhibit an explicitly computable `pseudorandom' generator stretching $l$ bits into $m(l) = l^{\Omega(\log l)}$ bits that look random to constant-depth circuits of size $m(l)$ with $\log m(l)$ arbitrary symmetric gates (e.g. PARITY, MAJORITY). This improves on a generator by Luby, Velickovic and Wigderson (ISTCS '93) that achieves the same ... more >>>

Luca Trevisan

We describe a new pseudorandom generator for AC0. Our generator $\epsilon$-fools circuits of depth $d$ and size $M$ and uses a seed of length $\tilde O( \log^{d+4} M/\epsilon)$. The previous best construction for $d \geq 3$ was due to Nisan, and had seed length $O(\log^{2d+6} M/\epsilon)$.

A seed length of ...
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Oded Goldreich, Avi Wigderson

{\em Does derandomization of probabilistic algorithms become easier when the number of ``bad'' random inputs is extremely small?}

In relation to the above question, we put forward the following {\em quantified derandomization challenge}:

For a class of circuits $\cal C$ (e.g., P/poly or $AC^0,AC^0[2]$) and a bounding function $B:\N\to\N$ (e.g., ...
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Johan Hastad

We prove that a small-depth Frege refutation of the Tseitin contradiction

on the grid requires subexponential size.

We conclude that polynomial size Frege refutations

of the Tseitin contradiction must use formulas of almost

logarithmic depth.

Marshall Ball, Dana Dachman-Soled, Siyao Guo, Tal Malkin, Li-Yang Tan

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e.~$\mathsf{AC^0}$ tampering functions), our codes have codeword length $n = k^{1+o(1)}$ for a $k$-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay ... more >>>

Shachar Lovett, Kewen Wu, Jiapeng Zhang

A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whole term is satisfied by the input. Decision ... more >>>