BQP Updated +Created
Heck, we know nothing about this class yet related to non quantum classes!
Chomsky hierarchy Updated +Created
This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).
A good summary table that opens up each category much more can be seen e.g. at the bottom of en.wikipedia.org/wiki/Automata_theory under the summary thingy at the bottom entitled "Automata theory: formal languages and formal grammars".
NP-complete Updated +Created
A problem that is both NP and NP-hard.