HIERARCHY
For any space constructible function f : N ?N, there exists a language A that is decidable in space O( f(n) ) but not in space o( f(n) ).
For any time constructible function f : N ?N, there exists a language A that is decidable in time O( f(n) ) but not in time o( f(n) / log f(n) )
P ? NP ? PSPACE = NPSPACE ? EXPTIME
- Researchers believe each containment is proper