The Chomsky hierarchy arranges formal languages based on the type of grammar needed to describe them. Type-0 languages are the most powerful, including all recursively enumerable languages and are described by unrestricted grammars. Type-1 languages are context-sensitive and described by context-sensitive grammars. Type-2 languages are context-free and accepted by pushdown automata using context-free grammars. Type-3, the least powerful type, are regular languages described by regular grammars and recognized by finite state automata. Each language type in the hierarchy includes all languages of less restrictive types.

1. Chomsky Hierarchy
Presented By : Urfi Khurshaid
Roll no : 182146

2. Chomsky Hierarchy
• Chomsky Hierarchy represents the class of languages
that are accepted by the different machine. The
category of language in Chomsky's Hierarchy is as
given below:
1. Type 0 known as Unrestricted Grammar.
2. Type 1 known as Context Sensitive Grammar.
3. Type 2 known as Context Free Grammar.
4. Type 3 Regular Grammar.

3. This is a hierarchy. Therefore every language of type 3 is also of type 2, 1 and 0.
Similarly, every language of type 2 is also of type 1 and type 0, etc.

4. Type 0 Grammar:
• Type-0 grammars include all formal grammar. Type 0
grammar languages are recognized by turing
machine. These languages are also known as the
Recursively Enumerable languages.
• Grammar Production in the form of α→β
where alpha is ( V + T)* V ( V + T)*
V : Variables T : Terminals.
βis ( V + T )*.
• In type 0 there must be at least one variable on the
Left side of production.

5. For example:
Sab --> ba
A --> S
Here, Variables are S, A, and Terminals a, b.

6. Type 1: Context-Sensitive Grammar:
Type 1 grammar is known as Context Sensitive Grammar.
The context sensitive grammar is used to represent
context sensitive language. The context sensitive
grammar follows the following rules:
• The context sensitive grammar may have more than one
symbol on the left hand side of their production rules.
• The number of symbols on the left-hand side must not
exceed the number of symbols on the right-hand side.
• The rule of the form A → ε is not allowed unless A is a
start symbol. It does not occur on the right-hand side of
any rule.

7. • The Type 1 grammar should be Type 0. In type 1, Production is
in the form of V → T
Where the count of symbol in V is less than or equal to T.
α→β
|alpha |<=|beta |
Also β ∈ (V + T)+
i.e. β can not be ε.
• For Example:
S --> AB
AB --> abc
B --> b

8. Type 2: Context-Free Grammar:
• Type-2 grammars generate context-free languages. The
language generated by the grammar is recognized by
a Pushdown automata. In Type 2:
• First of all, it should be Type 1.
• The left-hand side of production can have only one variable
and there is no restriction on β.
• The production rule is of the form
A → α
Where A is any single non-terminal and is any combination of
terminals and non-terminals.

9. • For example:
A → aBb
A → b
B → a

10. Type 3 Grammar:
• Type 3 Grammar is known as Regular Grammar. Regular
languages are those languages which can be described using
regular expressions. These languages can be modeled by NFA
or DFA.
• Type 3 is most restricted form of grammar. The Type 3
grammar should be Type 2 and Type 1.
• Type 3 should be in the given form only :
• V --> VT / T (left-regular grammar)
(or)
• V --> TV /T (right-regular grammar)

11. • For example:
S --> a
The above form is called strictly regular
grammar.

12. THANK YOU