We consider the problem of amplifying uniform average-case hardness
of languages in $\NP$, where hardness is with respect to $\BPP$
algorithms. We introduce the notion of \emph{monotone}
error-correcting codes, and show that hardness amplification for
$\NP$ is essentially equivalent to constructing efficiently
\emph{locally} encodable and \emph{locally} list-decodable monotone
codes. The ... more >>>

In a seminal paper from 1985, Sistla and Clarke showed
that satisfiability for Linear Temporal Logic (LTL) is either
NP-complete or PSPACE-complete, depending on the set of temporal
operators used

If, in contrast, the set of propositional operators is restricted, the
complexity may ... more >>>

We prove that the integrality gap after tightening the standard LP relaxation for Vertex Cover with Omega(sqrt(log n/log log n)) rounds of the SDP LS+ system is 2-o(1).

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