We show that the Hidden Subgroup Problem for black-box groups is in \mathrm{BPP}^\mathrm{MKTP} (where \mathrm{MKTP} is the Minimum \mathrm{KT} Problem) using the techniques of Allender et al (2018). We also show that the problem is in \mathrm{ZPP}^\mathrm{MKTP} provided that there is a \emph{pac overestimator} computable in \mathrm{ZPP}^\mathrm{MKTP} for the logarithm ... more >>>