FOR FREE CONTENT

Special Cases: Examples

Identify the languages:

It is better to see Part 1, Part 2, Part 3, Part 4, Part 5 of Special Case Examples before following the answers to the given questions.

Answer:

This is language is exactly the same as the language

The only difference that in our given language it has a symbol x which represents some string but it does not matter because x is not part of this language.

Answer:

In this language range of x is finite i.e. x ϵ ∑so, either x will be ‘a’ or ‘b’ because ∑ = {a, b}. 

Now, we can write the language,

Or 

In that case if neglect ‘a’ or ‘b’ then

For details please follow the previous example Special Case Examples: Example 1.

Answer:

This language is the same as previous Example 2 

the only position of x is different but it does not matter in that case language is the same.

So, we can write in this way, 

In that case if neglect ‘a’ or ‘b’ then

For details please follow the previous example Special Case Examples: Example 1.

Answer: 

If you see all previous examples (Example 3, Example 4, Example 4, Example 4,  Example 4, Example 4) all languages of the previously given examples look like the same i.e.

In all previous examples, these languages are identified as regular language because the range of x is infinite every time. 

For details please see any of the previous examples like Example 3.

Now, if we come to our given question language, 

is the same as all languages which are described in previous examples but the only difference, in this case, is the range of x is finite i.e. x ϵ ∑.

So, x is finite i.e. x ϵ ∑ and we cannot expand x on both sides in this language and for this reason, we cannot write a regular expression for this given language. 

Note: To make this concept clear please follow any of the above previous examples like Example 3.

So, in that case, we can write the language, 

Or 

Now, if we neglect ‘a’ or ‘b’ then