State which of the following languages are 1 not contextfree

State which of the following languages are (1) not context-free (2) context-free but not regular or (3) regular and context-free. If a language is not context-free then give a string, s, for that language that could be used in a proof using the Pumping Lemma for context-free languages.

A = { b^mw | m 0 and w Î {a, b}* and |w| = m}

B = { (ab)ⁿ(ab)^m | m, n > 0 and m n}      

C = {(ab)ⁿ(ab)^m| m, n > 0}

D = { wbⁿw | n 0, w Î {a, b}* }

E = { w | w is in {a, b, c}* and w has an equal number of a’s, b’s and c’s}. So abbcac is in E.

Solution

Answer :-

The Pumping Lemma for context-free languages .

C = {(ab)n(ab)m| m, n > 0} .