CS 162 Homework 3, 25 Points
Due: Friday, January 27, 11:55pm

Please submit your solutions in pdf format via dropbox on eee.
Note: scanned copies of handwritten solutions will not be graded. Solutions must be typed.
(You may use bold circles to denote final states.)

  1. 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.
  2. 5 points. Let L={0n12n | n > 1}. Show that L is not regular.
  3. 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.
  4. 5 points. Problem 1.41 on page 89 of Sipser.
  5. 5 points. Problem 1.70 on page 93 of Sipser.