Correct Many-One Reduction

computation

Definition

Correct Many-One Reduction

A many-one reduction $R:I_A\to I_B$ between problems $A$ and $B$ is correct if it preserves the answer to the problem instance.

That means:

$$x\in I_A^{+}⟺R(x)\in I_B^{+}$$

In other words, $x$ and $R(x)$ are equivalent as problem instances.