# Example of reduction such that it is not many-one reduction while it is not turing reduction

I am reviewing things I learned, and I can't suddenly come up with an example of reduction that is not many-one, but Turing reduction. Can anyone present such an example?

• Your title asks for a reduction that is not many-one and not Turing, but the question asks for something that is not many-one and is Turing. Which do you want? Nov 22 '14 at 21:08

A simple example would be a reduction from e.g. $SAT$ to it's complement $\overline{SAT}$, which works as follows: given a formula $\varphi$, you can decide whether $\varphi$ is satisfiable by deciding whether $\varphi\in \overline{SAT}$, and then negating the answer. This is a Turing reduction, since you use an oracle for $\overline{SAT}$ to solve $SAT$.