Key points
- Regular ⊂ DCFL ⊂ CFL ⊂ CSL ⊂ Recursive ⊂ RE.
- Regular languages union, intersection, complement, concatenation, star — closed under all of them.
- CFLs are not closed under intersection or complement; CFL ∩ Regular = CFL.
- DCFLs are closed under complement, but not under union/intersection.
- Recursive languages are closed under complement; RE is not (L and L' both RE ⇒ L recursive).