# Finite Playground

## MA-SETH is false

Ryan Williams just posted a new paper Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation on ECCC, in which he disproves the MA analog of the Strong Exponential Time Hypothesis (MA-SETH), which is motivated by the paper Nondeterministic extensions of the Strong Exponential Time Hypothesis and consequences for non-reducibility by Carmosino, Gao, Impagliazzo, Mikhailin, Paturi, and Schneider, proving that assuming Nondeterministic Strong Exponential Time Hypothesis (NSETH) then some problems like 3SUM and APSP cannot be SETH-hard.

## NEXP do not have ACC0 circuits

$\mathsf{NTIME}(2^n)$不能用$\mathsf{ACC}^0$circuits – 也就是 constant-depth, poly-size circuits with AND, OR, NOT, and Mod_m gates for any m 解掉.