CS 162 - Automata Theory Homework 4, 25 Points
Due: Friday, February 10, 11:55pm

  1. 5 points. Let L={0n12n | n > 0}. Give a CFG for L.
  2. 5 points. Show that every regular language, L, is also context free. Hint: use a proof by induction on the number of operators in a regular expression for L.
  3. 5 points. Exercise 2.5(b,c,e) in Sipser.
  4. 5 points. Exercise 2.14 in Sipser.
  5. 5 points. Let L be the language of all strings, w, of 0's and 1's such that w has an equal number of 0's and 1's (in any order). Give a PDA for L. Include comments in your answer describing your PDA in English as well as using a transition function.