P vs. NP - Polynomial time solution - nondeterministic polynomial time - verifiable vs solvable. - What is known? P <= NP Suspected: P < NP - It should be somewhat surprising that this is an open problem. Perhaps the solution is not recognizable? Is there some paradox wrapped up in this? Shouldn't we be able to diagonalize it? PSPACE vs NSPACE - known to be equal - known P <= NP <= PSPACe = NPSPACE