$ \newcommand{\DSPACE}{\mathsf{DSPACE}} \newcommand{\L}{\mathsf{L}} \newcommand{\P}{\mathsf{P}} \newcommand{\DTIME}{\mathsf{DTIME}} $ $\L^2 \subseteq \P$ would refute the Exponential Time Hypothesis. ...

This problem is hard, in various settings. As stated in the other answers to this question, the problem is NP-complete over the integers. In signal processing, the matrix and the vectors have ...

The title of this question does not match the content. As stated in the comments, there are some NP optimization problems for which any polynomial time approximation algorithm implies P = NP. Maybe ...

Like the Boolean Formula Isomorphism problem, the Group Equations Isomorphism problem is $\mathsf{coNP}$-hard and in $\mathsf{\Sigma_2P}$, for any fixed non-abelian group. See The Complexity of ...

This is not an answer to your exact question, but perhaps you may find this helpful. You might have a slightly easier time finding results for the class of languages decided by nondeterministic $\...

This is a partial answer; maybe it will inspire someone else to provide a better one. $\newcommand{\EBPP}{\mathsf{EBPP}}$ $\newcommand{\CP}{\mathsf{C}_=\mathsf{P}}$ Your class $\EBPP$ is a special ...