CS150 HW2
                        Set April 18, Thursday
                        Due April 30, Tuesday, at 5pm
                        Total: 65 pts


Q1 [15 pts] Consider the following e-NFA with 3 states p, q and r:

           ||  e    | a   | b     | c
      =======================================
      -> p || {q,r} | {}  | {r}   | {q}
         q || {}    | {p} | {p,q} | {r}
        *r || {}    | {}  | {}    | {}

   (a) Compute the e-closure of each state.
   (b) Give all strings of lengths three or less accepted by the automaton.
   (c) Convert the automaton to a DFA.

Q2 [10 pts] Write a regular expression for the following language:
   The set of all binary strings whose number of 0's is divisible by four.

    E.g., 111, 110101001, and 0010010101010111 are accepted but 
          00000111, 11001111, and 00011110000 are not.

Q3 [10 pts] P. 107 in HMU (or P. 106 in 2nd edition)  Ex.3.2.3
   Convert the following DFA to a regular expression, ...
   
   For the convenience of grading, please eliminate states in 
   the order q,r,s.

   Again, please be careful with the page and exercise numbers if you are 
   using an international edition of the book!!!

Q4 [10 pts] P. 108 in HMU (or P. 107 in 2nd edition) Ex.3.2.6: c), d)
   You may describe the languages using a combination of plain English 
   and mathematics notations (such as set notations). Please also 
   consult the answers for parts a) and b) available on the textbook
   homepage: http://www-db.stanford.edu/~ullman/ialc.html

Q5 [20 pts] P. 121-122 in HMU (or P. 120-121 in 2nd ed) Ex.3.4.1: c), d)
   You may use the test technique in Section 3.4.7 (also see the 
   sample solution for part a) on the textbook homepage), or the general 
   proof technique used in the proof of Theorem 3.11.