Does every language in BPP have a mapping reduction to ATM?

Does every language $C$ in the class $BPP$ have a mapping reduction to $A_{TM}$? $(C\leq _{m} A_{TM})$

$BPP$ is the class of languages that have a probabilistic $TM$ that accepts them with an error $\epsilon$ less than 1/3.

$A_{TM}$ is the acceptance language, takes as input a $TM$ description of $M$ and a word w, then determines if w is in $M$'s langugae. $A_{TM}$ is of course undecidable!

• Note BPP is a subset of EXP. – xskxzr Mar 15 '18 at 9:06

Every decidable language reduces to $A_{\mathrm{TM}}$.
• A $L$ language is decidable if ______. A string $x$ is in $L$ if ______. Now relate that to the definition of $A_{\mathrm{TM}}$. – David Richerby Mar 16 '18 at 10:47