CS150 HW3
       	                  Set April 29, Tuesday
                          Due May 9, Friday, at 6pm
                          Total: 60 pts


Q1 [10 pts] Prove that the following languages are not regular:

   (a) {0^n 1^m 2^n | n and m are arbitary (nonegative) integers}
   (b) {0^{2n} 1^n | n > 0}

Q2 [10 pts] Prove that the following language (called squares) is not regular:

   The set of binary strings of the form ww, that is, the same string repeated.
   
   E.g., 00, 0101, 010010, 011011 are squares but 010, 0011, 0110 are not.

Q3 [10 pts] P. 147 (or P. 146 in 2nd ed)  Ex.4.2.3.
   If L is a language, and a is symbol, then a\L is the set of ...
  
   You may consult Ex. 4.2.2 for ideas.

Q4 [10 pts] Give an algorithm to tell whether a regular language L 
   contains at least 100 strings.

   Note that you may assume that the regular language is represented
   as a DFA, and the pumping lemma constant n is the size of the DFA.

   Hint: You may use the algorithm for Ex. 4.3.1 to decide if the 
   input DFA accepts an infinite language, and focus on the case when 
   the language is finite.

Q5 [20 pts] P. 165-166 (or P. 164 in 2nd ed)  Ex.4.4.2.
   Repeat Ex. 4.4.1 for the DFA of Fig. 4.15.