Under the assumption that $P \ne NP$, why is it impossible to reduce a problem that is known to be NP-complete to a problem that is known to be of polynomial time complexity? What kind of fundamental theorems would this contradict if it was possible?
Why can there be no reductions from NP-complete problems to P problems under P  NP
complexity theory;np complete;reductions;np;p vs np
It would contradict the assumption that P$\,\neq\,$NP. You could solve the NP-complete problem in polynomial time by reducing it to a problem in P and solving that.