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 >>>

The class QMA(k), introduced by Kobayashi et al., consists
of all languages that can be verified using k unentangled quantum
proofs. Many of the simplest questions about this class have remained
embarrassingly open: for example, can we give any evidence that k
quantum proofs are more powerful than one? Can ... more >>>

Dinur's celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the ... more >>>