CS150 HW3
       	                  Set April 30, Tuesday
                          Due May 10, Friday, at 5pm
                          Total: 60 pts


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

   (d) {0^n 1 2^m | n and m are arbitary (nonegative) integers with m <= n}
   (f) {0^{n+1} 1^n | n > 0}

   Note that your proof should not assume specific values of x and y 
   in the partition.

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.

   Again, your proof should not assume specific values of x and y in 
   the partition.

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.