| Grammar accepted | Language accepted | Automaton / Machine |
Type 0 | Unrestricted grammar | Recursively enumarable language | Touring machine (Deterministic (DTM) vs Non-deterministic (NTM), the default being DTM |
Type 1 | Context sensitive grammar | Context sensitive language | Linear bounded automata (LBA) (also deterministic vs. non-deterministic) |
Type 2 | Context free grammar | Context free lanuage | Push down automata (PDA), also D vs N, the default being NPDA |
Type 3 | Regular grammar | Regular language | Finite automata (FA), also DFA vs NFA, the default being DFA |
Expressive power
Type 0 grammars have the most expressive power, Type 3 the least expressive power.
The expressive power of of DFAs is equal to the expressive power of NFAs. Therefore, every NFA can be converted into a DFA.
The expressive power of NPDAs is greated than the expressive power of DPDAs. Therefore, some NPDAs can't be converted into a DPDA.
The expressive power of DTMs is equal to the expressive power of NTMs.