Question

Kleen closure of {a^nb^n | n>=1} is DCFL

Answer 1

The Language {a^n b^n, n>=1} consists of the strings = {ab,aabb,aaabbb,aaaabbbb,…...}

If we take L* it would be

= {ab,aabb,aaabbb,aaaabbbb,…..}*

= {e,…..,abab,ababab,….abaabb, aabbab,…… aaabbbaabbab,…….}

= number of a’s read is immediately followed by equal number of b’s read and all strings should start with a and end with b

The transition diagram would be something like this:

Now, as we can draw a DPDA for the Kleene’s Closure of L it is a DCFL.

Note 1: Generally DCFL is not closed under Kleene’s Closure, this Language happens to be closed but it will not happen for all DCFL Languages. On the other hand NCFL is always closed under Kleene’s Closure.

Note 2: Closure property is not for a particular language it’s for a class of language.

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Sure, I hid that comment as what I said was wrong so dint want to create any confusion. Cool I have reshown the comment.