We introduce the notion of {\em natural} proof.
We argue that the known proofs of lower bounds on the complexity of explicit
Boolean functions in non-monotone models
fall within our definition of natural.
We show based on a hardness assumption
that natural proofs can't prove superpolynomial lower bounds for
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We introduce a new approach to construct extractors -- combinatorial
objects akin to expander graphs that have several applications.
Our approach is based on error correcting codes and on the Nisan-Wigderson
pseudorandom generator. An application of our approach yields a
construction that is simple to describe ... more >>>

We give the first construction of a pseudo-random generator with
optimal seed length that uses (essentially) arbitrary hardness.
It builds on the novel recursive use of the NW-generator in
a previous paper by the same authors, which produced many optimal
generators one of which was pseudo-random. This is achieved ... more >>>

We consider tautologies formed from a pseudo-random
number generator, defined in Kraj\'{\i}\v{c}ek \cite{Kra99}
and in Alekhnovich et.al. \cite{ABRW}.
We explain a strategy of proving their hardness for EF via
a conjecture about bounded arithmetic formulated
in Kraj\'{\i}\v{c}ek \cite{Kra99}. Further we give a
purely finitary statement, in a ... more >>>

We present a weaker variant of the PCP Theorem that admits a
significantly easier proof. In this
variant the prover only has $n^t$ time to compute each
bit of his answer, for an arbitray but fixed constant
$t$, in contrast to
being all powerful. We show that
3SAT ... more >>>