I am reading a paper called "Rational Proof". It mentioned the following one-to-one reduction. I cannot google an introduction of it.
An excerpt from the paper. "Recall that a one-to-one reduction from a function $f$ to another function $g$ is a triple of polynomial time computable functions ($\alpha$, $\beta$, $\gamma$) such that:
- For all $x$ in the domain of $f$ we have $y=f(x)$ if and only if $g(\alpha(x))=\beta(y)$
- For all $x$ in the domain of $f$, let $w=\alpha(x)$. Then we have $g(w)=z$ if and only if $f(x)=\gamma(z)$. "
Any reference for the formal definiton of the so-called "one-to-one reduction" is appreciated. Thanks.