Language Of Grammar | Automata

Language Of Grammar-

 

Language of Grammar is the set of all strings that can be generated from that grammar.

 

  • If the language consists of finite number of strings, then it is called as a Finite language.
  • If the language consists of infinite number of strings, then it is called as an Infinite language.

 

Also Read- Grammar in Automata

 

Example-01:

 

Consider a grammar G = (V , T , P , S) where-

  • V = { S }
  • T = { a , b }
  • P = { S → aSbS , S → bSaS , S → ∈ }
  • S = { S }

 

This grammar generates the strings having equal number of a’s and b’s.

 

So, Language of this grammar is-

 

L(G) = { ∈ , ab , ba , aabb , bbaa , abab , baba , …… }

 

  • This language consists of infinite number of strings.
  • Therefore, language of the grammar is infinite.

 

Example-02:

 

Consider a grammar G = (V , T , P , S) where-

  • V = { S , A , B , C }
  • T = { a , b , c }
  • P = { S → ABC , A → a , B → b , C → c }
  • S = { S }

 

This grammar generates only one string “abc”.

 

So, Language of this grammar is-

 

L(G) = { abc }

 

  • This language consists of finite number of strings.
  • Therefore, language of the grammar is finite.

 

Also Read- Deciding Language Is Finite Or Infinite

 

Important Concept-

 

  • For any given grammar, the language generated by it is always unique.
  • For any given language, we may have more than one grammar generating that language.

 

 

Example-

 

Consider the following two grammars-

 

Grammar G1-

 

S → AB

A → a

B → b

The language generated by this grammar is-

L(G1) = { ab }

 

Grammar G2-

 

S → AB

A → 

B → ab

The language generated by this grammar is-

L(G2) = { ab }

 

Here,

  • Both the grammars generate a unique language.
  • But given a language L(G) = { ab }, we have two different grammars generating that language.

This justifies the above concept.

 

Next Article- Language Ambiguity

 

Get more notes and other study material of Theory of Automata and Computation.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
Language Of Grammar | Automata
Article Name
Language Of Grammar | Automata
Description
In Automata, Language of Grammar is the set of all strings that can be generated from that grammar. Examples. Finite and Infinite Language- If language consists of finite number of strings, then it is called as a finite language otherwise an infinite language.
Author
Publisher Name
Gate Vidyalay
Publisher Logo
Liked this article? Share it with your friends and classmates now-