CS 162 Homework 3, 50 Points
Due: Friday, Feburary 2, 11:55pm

Please submit your written solutions to the first two problems in pdf format via dropbox on eee.
Note: scanned copies of handwritten solutions will not be graded. Solutions must be typed.

  1. 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.
  2. 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.
  3. 30 points. Complete the following problems about CFGs on The RASCO Online Automata Grader. Note: The solutions to these problems should not be submitted on EEE.