Notation
DFA  =  Deterministic Finite Automaton 
NFA  =  Nondeterministic Finite Automaton 
CFL  =  ContextFree Language 
DCFL  =  Deterministic ContextFree Language 
PDA  =  Pushdown Automaton 
DPDA  =  Deterministic Pushdown Automaton 
TM  =  Turing Machine 
NTM  =  Nondeterminsistic Turing Machine 
LBA  =  Linear Bounded Automaton: NTM which cannot go beyond the input string 
Language Hierarchy
Language Class  Machine  Grammar 

Regular  decided by a DFA
accepted by an NFA 
Left or Right Linear (type 3) 
DCFL  decided by a DPDA  LR(0) 
CFL  accepted by a PDA  Context Free (type 2) 
Context Sensitive  accepted by an LBA  Context Sensitive (type 1) 
Recursive  decided by a TM
lexicographically enumerated by a TM 

Recursively Enumerable 
accepted by a TM
accepted by an NTM enumerated by a TM 
Unrestricted (type 0) 
Closure Properties under set operations
closure under  

Language Class  union  intersection  complement 
Regular  yes  yes  yes 
DCFL  no  no  yes 
CFL  yes  no  no 
Context Sensitive  yes  yes  yes 
Recursive  yes  yes  yes 
Recursively Enumerable 
yes  yes  no 