We construct a PCP based on the hyper-graph linearity test with 3 free queries. It has near-perfect completeness and soundness strictly less than 1/8. Such a PCP was known before only assuming the Unique Games Conjecture, albeit with soundness arbitrarily close to 1/16.

At a technical level, our ... more >>>

We formulate a new connection between instance compressibility \cite{Harnik-Naor10}), where the compressor uses circuits from a class $\C$, and correlation with
circuits in $\C$. We use this connection to prove the first lower bounds
on general probabilistic multi-round instance compression. We show that there
is no
probabilistic multi-round ... more >>>

We consider a model of teaching in which the learners are consistent and have bounded state, but are otherwise arbitrary. The teacher is non-interactive and ``massively open'': the teacher broadcasts a sequence of examples of an arbitrary target concept, intended for every possible on-line learning algorithm to learn from. We ... more >>>