CS150 HW5
       	                 Set Nov 19, Wednesday
                         Due Dec 4, Thursday, at 5pm
                         Total: 100 pts


Q1 [10 pts] Convert the grammar

               S -> aAbB| ab
               A -> aSb | abab
               B -> bSa | ba

   to a PDA that accepts the same language by final state. Please
   represent the PDA as a transition diagram.

Q2 [20 pts] Let us pretend the PDA of Exercise 6.1.1 (on P.233-234
   or P.228 in the 2nd ed) is an empty-stack PDA. Convert it to a CFG.

Q3 [20 pts] P.277 (or P.271 in the 2nd ed)  Ex.7.1.4
   Repeat Exercise 7.1.2 for the following grammar.
   ...

   Please note that you need show the resulting CFG after each major step
   of the conversion procedure.

Q4 [20 pts] Use the CFL Pumping Lemma to show each of the following
   language not to be context-free:
         
    a) {a^n b^n c^i | i < n}
    b) {www | w is a binary string over {0,1}}

Q5 [20 pts] P.297 (or P.292 in the 2nd ed)  Ex.7.3.2
   Consider the following two languages: ...

Q6 [10 pts] For the grammar G of Example 7.34 on P.306 (or P.301 in the 2nd ed), 
   use the CYK algorithm to determine 
   if each of the following strings is in L(G):

   a) bbaaa
   b) aaaaa