glauberdebona comments on Amplifying the Computational No-Coincidence Conjecture

[glauberdebona]

For the time-complexity of the verifier to grow only linearly with $O\left(\log 1/\epsilon \right)$, we need also to assume the complexity of the reduction $f_m$ is $O\left(|C{|}^{\gamma }\right)$ for a fixed $\gamma$, regardless of $m$, which I admit is quite optimistic. If the time-complexity of the reduction $f_m$ is doubly exponential in $m$, the (upper bound of the) time-complexity of the verifier will be exponential in $1/\epsilon$, even with the stronger version of Reduction-Regularity.

[glauberdebona]

Correcting myself: “doubly” just added above.