We initiate the study of the tradeoff between the {\em length} of a
probabilistically checkable proof of proximity (PCPP) and the
maximal {\em soundness} that can be guaranteed by a $3$-query
verifier with oracle access to the proof. Our main observation is
that a verifier limited to querying a short ... more >>>

Given a family X of subsets of [n] and an ensemble of local functions $\{f_s:s\to\Sigma \;|\; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\to\Sigma$ such that $f_s=G|_s$ for many sets $s$. For example, the V-test chooses ... more >>>