Theory of Computation | Chomsky Hierarchy

Question

A general query,

If Regular expression (a+b)* covers the all possible languages over $\sum$= {a,b} then, why we need other type of languages?

1. Are they here only to distinguish complex patterns due to limitation of DFA.
2. Or to increase readbility of language.

I found these two reasons on internet and nothing else is there any other reasons here?

Comments

(a+b)* - is covers all the possible strings but not the all possible languages.

Regular expression (a+b)* is only one language. That is universal language on input symbol set {a,b}.

All possible languages = power set of universal language.

---

Yes,
what you'r saying is right but

what i mean is that {$a^n b^n$ | n>=0} is a CFL and that is proper subset of language generated by the $(a + b)*$ and same, somewhere you can definately find any string that is generated by any language in $(a + b)*$,

for eg.

{ab, aabb, aaabbb, aaaabbbb, .....} $\subset$ {$\epsilon$, a, b, aa, ab, ba, bb, aaa, aab, aba, abb,.....}
So why we need other types of language ? except the fact that DFA have limitations.

---

It's all started from Regular grammar. The languages generated by Regular grammars are called Regular languages.

The nature of production in regular grammar not allow to generate the language some languages such as  "no.of a's = no.of b's in a string."

 

Hence, there is a new type of grammars called context free grammars which generate context free languages.