We present an alternate proof of the recent result by Gutfreund and Kawachi that derandomizing Arthur-Merlin games into $P^{NP}$ implies linear-exponential circuit lower bounds for $E^{NP}$. Our proof is simpler and yields stronger results. In particular, consider the promise-$AM$ problem of distinguishing between the case where a given Boolean circuit ... more >>>

A $k$-query locally decodable code (LDC)
$\textbf{C}:\Sigma^{n}\rightarrow \Gamma^{N}$ encodes each message $x$ into
a codeword $\textbf{C}(x)$ such that each symbol of $x$ can be probabilistically
recovered by querying only $k$ coordinates of $\textbf{C}(x)$, even after a
constant fraction of the coordinates have been corrupted.
Yekhanin (2008)
constructed a $3$-query LDC ... more >>>

The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. This hardness assumption is closely connected to the Unique Games Conjecture (Khot, STOC 2002). In particular, the Small-Set Expansion Hypothesis implies the Unique ... more >>>