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5 points.
Let L be the language of all strings of balanced parentheses.
That is,
all strings of the characters "(" and ")" such that each "(" has a matching ")".
Use the Pumping Lemma to show that L is not regular.
5 points.
Let L={0^{n}1^{2n} | n > 1}.
Show that L is not regular.
5 points.
Given two languages, L and M,
define the exclusive-or of L and M as the set of all strings,
w, such that w is in L and not in M or w is in M and not in L.
Show that the exclusive-or of two regular languages is regular.