CS150 HW3
       	              Set 10/28
                      Due 11/7, Thursday, 5pm
                      Total: 60 pts


Q1 [10 pts] P.131  (or P.129 in the 2nd ed)  Ex.4.1.1: b), f)
   Prove the following languages are not regular languages. 
   ...

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


Q2 [10 pts] P.132  (or P.130 in the 2nd ed)  Ex.4.1.2: c)
   Prove the following languages are not regular languages. 
   ...

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


Q3 [15 pts] P.147  (or P.146 in the 2nd ed)  Ex.4.2.4: b), c). 
   Which of the following identities are true? ...

   You need give a simple proof for each true identity and a counterexample 
   for each false identity. Please consult Ex. 4.2.2 and Ex. 4.2.3 for 
   the definitions of the operations "/a" and "a\".


Q4 [10 pts] P.155  (or P.153 in the 2nd ed)  Ex.4.3.3
   Suppose L is a regular language with alphabet Sigma. ...

   You may assume that L is represented as a DFA.


Q5 [15 pts] PP.165-166  (or PP.164-165 in the 2nd ed)  Ex.4.4.2
   Repeat Exercise 4.4.1 for the DFA of Fig 4.15. ...