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10 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.
10 points.
Excercise 1.20 parts a,b,c,d on page 86 of Sipser
10 points.
Problem 1.38 on page 89 of Sipser
10 points.
Problem 1.46 part c on page 90 of Sipser
10 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.