Formally, for a problem H in the class of NP-Hard, there is a problem L in NP-complete such that L is polynomial turing reducible to H. In other words, there is an algorithm which solves H in polynomial time which involves calling a subroutine , that solves L in polynomial time. Since L is NP-complete, then there is a non-deterministic algorithm which solves L in poly-time. Hence, the problem H is called NP-Hard, because it is as hard as the hardest problem in NP. However, there are clearly problems that cannot be solved in polynomial time even with non-deterministic algorithms.