Chomsky Classification of Grammars
According to Noam Chomosky, there are four types of grammars − Type 0, Type 1, Type 2, and Type 3. The following table shows how they differ from each other −
|Grammar Type||Grammar Accepted||Language Accepted||Automaton|
|Type 0||Unrestricted grammar||Recursively enumerable language||Turing Machine|
|Type 1||Context-sensitive grammar||Context-sensitive language||Linear-bounded automaton|
|Type 2||Context-free grammar||Context-free language||Pushdown automaton|
|Type 3||Regular grammar||Regular language||Finite state automaton|
Take a look at the following illustration. It shows the scope of each type of grammar −
Type - 3 Grammar
Type-3 grammars generate regular languages. Type-3 grammars must have a single non-terminal on the left-hand side and a right-hand side consisting of a single terminal or single terminal followed by a single non-terminal.
The productions must be in the form X → a or X → aY
where X, Y ∈ N (Non terminal)
and a ∈ T (Terminal)
The rule S → ε is allowed if S does not appear on the right side of any rule.
X → ε X → a | aY Y → b
Type - 2 Grammar
Type-2 grammars generate context-free languages.
The productions must be in the form A → γ
where A ∈ N (Non terminal)
and γ ∈ (T ∪ N)* (String of terminals and non-terminals).
These languages generated by these grammars are be recognized by a non-deterministic pushdown automaton.
S → X a X → a X → aX X → abc X → ε
Type - 1 Grammar
Type-1 grammars generate context-sensitive languages. The productions must be in the form
α A β → α γ β
where A ∈ N (Non-terminal)
and α, β, γ ∈ (T ∪ N)* (Strings of terminals and non-terminals)
The strings α and β may be empty, but γ must be non-empty.
The rule S → ε is allowed if S does not appear on the right side of any rule. The languages generated by these grammars are recognized by a linear bounded automaton.
AB → AbBc A → bcA B → b
Type - 0 Grammar
Type-0 grammars generate recursively enumerable languages. The productions have no restrictions. They are any phase structure grammar including all formal grammars.
They generate the languages that are recognized by a Turing machine.
The productions can be in the form of α → β where α is a string of terminals and nonterminals with at least one non-terminal and α cannot be null. β is a string of terminals and non-terminals.
S → ACaB Bc → acB CB → DB aD → Db