Recently, Moser and Tardos [MT10] came up with a constructive proof of the Lovász Local Lemma. In this paper, we give another constructive proof of the lemma, based on Kolmogorov complexity. Actually, we even improve the Local Lemma slightly.

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$\mbox{ACC}_m$ circuits are circuits consisting of unbounded fan-in AND, OR and MOD_m gates and unary NOT gates, where m is a fixed integer. We show that there exists a language in non-deterministic exponential time which can not be computed by any non-uniform family of $\mbox{ACC}_m$ circuits of quasi-polynomial size and ... more >>>

Hardness amplification results show that for every function $f$ there exists a function $Amp(f)$ such that the following holds: if every circuit of size $s$ computes $f$ correctly on at most a $1-\delta$ fraction of inputs, then every circuit of size $s'$ computes $Amp(f)$ correctly on at most a $1/2+\eps$ ... more >>>