Special Cases: Examples



As we already solve lots of problems in all previous examples.

Where Languages are same like

But ranges of ω and x are different. 

For infinite language, it may or may not be regular. It depends on it is possible to Regular Expression (RE) for language or not.


But in the case of finite range, we can directly say it is the regular language because any language with finite range is under regular language.


So, in our given all problems

In that case every range of ω and x is finite i.e. ∑, x ϵ ∑,   

where ∑ = {a, b} means  = (a + b)



Important Notes: 

Carefully notice the range of the language in your examinations because the range of the language can change the type of the given language.

Sometimes two or more languages look like same but the range is different which changes the type of the languages. So, do not identify the languages before notice the range which is important. 



Let two languages 

But the range of ω is different that’s why the types of the languages are different.


# But it is not right that all infinite range of languages is not regular it depends on the nature of languages for details see previous chapter Regular Expression  and  Languages Identification