thumb|300px|right|Euler diagram for P, NP, NP-complete, and NP-hard set of problems. Under the assumption that P ≠ NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. Corollary 1.1.
thumb|300px|right|euler diagram for p np np-complete and np-hard set of problems under the assumption that p ≠ np the existence of problems within np but outside both p and np-complete was established by ladner corollary 11