# Language Ambiguity | Ambiguous Language

## Language Of Grammar-

Before you go through this article, make sure that you have gone through the previous article on Language of Grammar.

We have discussed-

• Language of grammar is the set of all strings that can be generated from that grammar.
• Finite language consists of finite number of strings.
• Infinite language consists of infinite number of strings.

## Language Ambiguity-

 If every grammar that generates language L is ambiguous, then language L is called as Inherently ambiguous language. OR A language is inherently ambiguous if all the grammars which generate that language are ambiguous.

## NOTE-

• The term “inherently ambiguous language” is used instead of “ambiguous language”.
• This is because all the grammars which generate that language are ambiguous.

## Important Points-

• If a grammar is ambiguous, it does not imply that its language will be ambiguous too.
• If a grammar is ambiguous, its language may be unambiguous.
• If a grammar is ambiguous, its language will be unambiguous when there exists at least one unambiguous grammar which generates that language.

## Example Of Not An Inherently Ambiguous Language-

Consider the following language-

L = an , n>=0

• This language consists of strings having any number of a’s.
• Few grammars which generate this language are-

### Grammar-01:

S → aS / ∈

(Unambiguous Grammar)

### Grammar-02:

S → aS / a / ∈

(Ambiguous Grammar)

### Grammar-03:

S → aS / Sa / ∈

(Ambiguous Grammar)

### Grammar-04:

S → aS / a / Sa / ∈

(Ambiguous Grammar)

• All the above grammars generate the same language L = an , n>=0.
• Grammar-01 is unambiguous.
• Since there exists at least one unambiguous grammar which generates language L.
• Therefore, L is not an inherently ambiguous language.

## Example Of An Inherently Ambiguous Language-

Consider the following language-

L = { anbncm } ∪ { anbmcm }

There exists only one grammar which generates this language L.

The grammar is-

S → S1 / S2

S1 → S1C / A

A → aAb / ∈

S2 → aS2 / B

B → bBc / ∈

This grammar is ambiguous in nature.

This is because following two parse trees exist for string w = abc-

• There exists no language that generates this language L and is unambiguous.
• Therefore, L is an inherently ambiguous language.

Next Article- Context Free Grammar

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Summary
Article Name
Language Ambiguity | Ambiguous Language
Description
A language is called inherently ambiguous language if every grammar which generates that language is ambiguous. Ambiguous Language Examples. Language Ambiguity is closely related to grammar ambiguity.
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Gate Vidyalay
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