CS150 HW5
       	                 Set Nov. 20
                         Due Dec. 5, Thursday, 5pm
                         Total: 100 pts

Q1 [10 pts] Convert the grammar

               S -> aAbB| aabb
               A -> aSb | a
               B -> bSa | b

   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.
   ...

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