Type 0 > Type 1 > Type 2 > Type 3
Unrestricted Grammar > Context Sensitive Grammar > Context Free Grammar > Regular Grammar.
Power of Language which is generated by above grammer:
Recursive Enumerable > Recursive > Context Sensitive > Context Free > Regular
Power of the machine:
TM > LBA > PDA > F.A.
Type 0 or Unrestricted Grammar is superset of all grammars.
Context-Sensitive Grammar ⊆ Unrestricted Grammar
Context-Free Grammar ⊆ Context Sensitive Grammar
Regular Grammar ⊆ Context-Free Grammar
Important points: (This concept is very important to solve problems regarding grammar identification)
Context Sensitive Grammar → Unrestricted Grammar. [→ Implies]
Context Free Grammar → Context Sensitive Grammar → Unrestricted Grammar.
Regular Grammar → Context Free → Context Sensitive → Unrestricted Grammar.
But Opposite is not true because if P → Q is true then Q → P is not necessarily true.
At that same time P → Q ≈ Q′→ P′
For example: If a grammar is not a context free grammar then obviously it is not a regular grammar also.
(Context Free Grammar)' → (Regular Grammar)′