# CFG of odd Length strings {w | the length of w is odd}

## CFG of odd Length strings {w | the length of w is odd}

Context-free grammar for the language of odd length strings is mentioned below;

L = {w | the length of w is odd}:

S → aX | bX

X→ aS | bS | ε

Now we can read any kind of odd length string.

## Examples of CFG of odd Length strings

**To read a;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ aX //Read first a.

X⇒ε //Read first aε.

finally, we can read it as a.

**Congratulation,** the string can be read and the machine can be stoped after successfully completing its task.

**To read b;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ bX //Read first b.

X⇒ε //Read first bε.

finally, we can read it as b.

**Congratulation,** the string can be read and the machine can be stoped after successfully completing its task.

**To read ab;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ aX //Read first a.

X = bS //Read first ab.

Finally, Read the ab but S is forcing to reading some unknown alphabets.

Oh sorry, the string ab can be read but machine cant stop here because machine again force the CFG to read from S as mentioned in X=bS

**To read ba;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ bX //Read first b.

X = aS //Read the first ba.

Finally, Read the ba but S is forcing to reading some unknown alphabets.

Oh sorry, the string ba can be read but machine cant stop here because machine again force the CFG to read from S as mentioned in X=bS

**To read aba;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ aX //Read first a.

X = bS //Read first ab.

S = aX //Read first aba.

X = ε //Read first abaε.

finally, we can read it as aba.

**Congratulation,** the string can be read and the machine can be stoped after successfully completing its task.

**To read babaa;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ bX //Read first b.

X = aS //Read first ba.

S = bX //Read first bab.

X = aS //Read first baba.

S = aX //Read first babaa.

X = ε //Read first babaaε.

finally, we can read it as babaa.

**Congratulation,** the string can be read and the machine can be stoped after successfully completing its task.

**To read ababb;**

**CFG: **

S → aX | bX

X→ aS | bS | ε

**Path to Read the String**

S ⇒ aX //Read first a.

X = bS //Read first ab.

S = aX //Read first aba.

X = bS //Read first abab.

S = bX //Read first ababb.

X = ε //Read first ababbε.

finally, we can read it as ababb.

**Congratulation,** the string can be read and the machine can be stoped after successfully completing its task.

**Conclusion:**

Final CFG of odd Length strings is

S → aX | bX

X→ aS | bS | ε

This CFG can accept all the 100% strings of the mentioned language and rejects the all 100% strings that are not part of the language of odd length strings.

## More Examples of CFG

- Intro to Context Free Grammar with 12 Examples
- CFG of Language of all even and odd length palindromes
- Context Free Grammar CFG for language of all even length strings
- CFG for the language of all non Palindromes
- CFG for strings with unequal numbers of a and b
- CFG of odd Length strings {w | the length of w is odd}
- CFG of Language contains at least three 1’s or three a’s {w | w contains at least three 1’s}
- CFG for the language L = 0
^{n}1^{n}where n>=1 - CFG for the language L = 0
^{n}1^{2n}where n>=1 - Write a CFG for the language L = 0
^{n}1^{4n}where n>=1 - CFG for {a
^{n }b a^{n+1}| n >=0} - CFG for {a
^{n }b a^{n+2}| n >=0} - CFG for {a
^{n }b a^{n+3}| n >=0}