Q:

Among regular and context-free grammars which one is more powerful. Please give me the reason too

I was just going through the principles of programming languages. I know the concepts of regular and context-free grammars and their usage. But still I am unable to decide which one is more powerful and why. Please help
Thanks in advance.

A:

Every regular language is context-free, but some context-free languages are not regular. In that sense, the context-free languages are more "powerful" than the regular languages.
As one example of a nonregular language that is context-free, consider the language of all palindromes made up of the characters x and y. You can prove that this language is nonregular by using the pumping lemma or the Myhill-Nerode theorem. However, it is context-free, since it's generated by the grammar

S → aSa | bSb | a | b | ε

Intuitively, regular languages correspond to yes/no questions that can be solved on a computer with finite memory (the Myhill-Nerode theorem is one way of formalizing this intuition). This means that any yes/no problem that can't be solved with only finite memory therefore won't correspond to regular languages. Context-free languages occupy a strange middle ground - they correspond to problems that can be solved on computers with finite memory and an unbounded stack.
If you're interested in learning more about this, I'd recommend reading through a book on formal languages and computability. There's a lot of amazingly beautiful results about these classes of languages and there's no way I can compress it into a single answer.
Hope this helps!

