self-reducible

A search problem $R$ is $𝒞$ self-reducible if there is a $𝒞$ Cook reduction of $R$ to $L(R)$. That is, if the decision problem for $L(R)$ is $𝒞$ then so is the search problem for $R$.

If $R$ is polynomially self-reducible then it is called self-reducible.

Note that $L(R)$ is trivially Cook reducible to $R$.