$[4$ Points$]$ Computable? Consider the function $f$:$\{0,1{\}}^{*}\{0,1{\}}^{*}$ that is defined by

$f(w)=\{\begin{array}{ccc}0& if& PNP\\ 1& if& P=NP\end{array}$

Is $f$ computable in polynomial time? If not, is it computable? Explain your reasoning.