Noam Chomsky developed a hierarchy of formal languages in 1956 that consists of four types of languages based on the computational devices required to describe them: Type-0 languages, also known as recursively enumerable languages, include all languages that can be recognized by a Turing machine. Type-1 languages are context-sensitive and can be recognized by a linear bounded automaton. Type-2 languages are context-free and can be recognized by a pushdown automaton. Type-3, or regular languages, are the simplest and can be recognized by a finite state automaton. The Chomsky hierarchy arranges the language types from the most complex computational descriptions to the simplest.

1. By Ashutosh kumar (cse-1)
CHOMSKY
CLASSIFICATION

2. Topic of Discussion:
➢ Introduction
➢ Chomsky Hierarchy of Languages
➢ Type of Languages
o TYPE-0
o TYPE-1
o TYPE-2
o TYPE-3

3. Introduction
▪ Noam chomsky is an American linguist ,philospher,scientist and social
activist.
▪ Chomsky hierarchy of grammers was described by Noam chomsky in
1956 and sometimescalled as father of modern linguistics.
▪ Grammar Definition: It is defined by four tuples: G={V,T,P,S} where
❖ V=Non Terminal
❖ T=Terminals
❖ P=Production Rule
❖ S=Start Symbol
Production Rule:
S-AB
A-a
B-b

4. Chomsky Hierarchy of languages:
Venn Diagram of Grammar Types:
Iuhiuhdiujkhffjkjkfss
Type0-Recursively enumerable Language
Type1-Context sensitive
Type3
-
Regular
Type0-Turningmachine
Type1-Linear Bounded
Automata
Type2-push down
Automata
Type3-
Finite
automata
Type2-Context
Free

5. Type of Languages
❑ Recusively enumerableLanguage(Type-0)
❑ Context-Sensitive Language(Type-1)
❑ Context-free Language(Type-2)
❑ Regular language(Type-3)

6. Type-0:
▪ Type-0 Languages included all type of formal grammers.
▪ It generates the languages that are recognised by a turning machine.
▪ This languages are also known as recursively enumerable languages
▪ This grammar have rules in form of α → β (where α contains Non terminal
And β contains terminal or Non terMinals)
▪ Example-AB-A
▪ AB-aB
▪ S-^
▪ a-AB
▪ ^-a

7. Type-1:
 -Type-1 grammar generate the context –Sensitive languages.
 The language described by these grammar are exactly all
languages that can be recognised by a linear bounded
automaton.
 These grammars have rules of the form α → β with a restriction that
length of |α |<=| β|.
 Example:
aAb-bbb
 aA-bbb
 aAb-bb

8. Type-2:
 Type-2 Languages generate the context -free languages.
 These languages are exactly all languages that can be recognised by
a non-deterministic pushdown automaton.
 Context-free languages are the theoretical basis for the syntax of most
programming languages.
 These are defined by rules of the form A-α where A is a nonterminal and α
is a string of terminals and nonterminal (there will be no context on the left
and right of nonterminal).
 Example:
 A-BCD
 A-aBC
 A-AbC

9. Type-3:
 Type-3 Languagesgeneratethe regular languages.
 These languagesare exactly all languagesthat can be decided by a finite state automaton.
 Regular languagesare commonly used to define search patternsof programming languages.
 It can be classified into two types. 1. Right linear 2.Left linear.
 If we haverepetition of non terminal on right side [A-xB|x] then it is known as Right linear.
 If we haverepetition of non terminals on left side[A-Bx|x] then it is known as Left Linear .(A,B €
non terminals and x € )
 Example:
 S – a S |b
 S – a S |c
 S – S a |b
 A - b a

10. THANK YOU