I am looking for a reference on `reducing' Turing reductions to many-one reductions.  I have in mind a statement of the following form (similar enough statements would also satisfy me):Theorem.  If $\mathsf{A}\leq_T^f \mathsf{B}$, then $\mathsf A\leq_m^{2^f}\mathsf B^{tt}$.where $\leq_T^f$ and $\leq_m^f$ denote respectively Turing and many-one reductions in deterministic time $f(n)$, and $\mathsf{B}^{tt}$ denotes a `truth table' variant of the language $\mathsf{B}$, which evaluates a Boolean combination of checks $x\in\mathsf{B}$.Proof idea for the statement:  Simulate the $f(n)$-time bounded oracle Turing machine used in the Turing reduction: it's easy enough to obtain a nondeterministic Turing transducer also in time $f(n)$ that guesses the answers of the $\mathsf B$ oracle and writes a conjunction of checks $x\in\mathsf B$ or $x\not\in\mathsf{B}$ on the output, to be evaluated by an $\mathsf B^{tt}$ machine.  This transducer can be determinized by exploring both outcomes of the oracle calls, and handling them through disjunctions in the output; it now works in time $2^{f(n)}$.Oddly enough, I cannot seem to find any related result in complexity textbooks.Edit: renamed $A\mathsf B$ into $\mathsf B^{tt}$ to emphasize the relation with truth tables, as pointed out by @MarkusBlser.
Reference for Turing to many-one reductions
cc.complexity theory;reference request;complexity classes