CS 162 - Automata Theory Homework 5, 50 Points
Due: Monday, May 13, 11:55pm

  1. 10 points. Consider the following grammar:
    S -> AB | BC
    A -> BA | a
    B -> CC | b
    C -> AB | a
    Show the table that results from running the CYK algorithm discussed in class to CFG membership for each of the following strings (and say whether or not the string is in the language generated by the CFG above):
    (a) baaab
    (b) aabab
  2. 10 points. Exercise 3.2(d,e) in Sipser.
  3. 10 points. Exercise 3.8(b) in Sipser.
  4. 10 points. Give a high-level description of a Turing machine for deciding the language of all strings of the form anbncn, where n is at least 1.
  5. 10 points. Give a high-level description of a Turing machine for deciding the language of all strings of the form aibj, where j = i2 and i is at least 1.