Polynomial Reduction

A polynomial reduction from a problem $X$ to problem $Y$ is a function $f:{\Sigma }^{\ast }\to {\Sigma }^{\ast }$ computable in polynomial-time such that:

$$\begin{array}{c}w\in X⟺f(w)\in Y\\ X{\le }_{p}Y\text{ means }X\text{ is polynomially reducible to }Y\end{array}$$