CS 321 HW 5
Due **Wednesday Oct 28**, 5pm, on Canvas.

The important problems for Midterm are: 2--6.

1. Prove that there is one unique partition of states into equivalence classes in DFA,
   where in each class A, all states p in A are equivalent, but across any two classes
   A and B, any state p from A is not equivalent from any state q from B.

   The uniqueness is basically saying the order of splitting does not matter.

   Show that this immediately implies that the new DFA according to the partition
   is the smallest possible.

2. Now revisit problem 1 of HW 4. Which DFAs converted from NFAs can be minimized?

3. Write the regular expressions for bitstrings; if impossible, explain.

   (1) same number of 0s and 1s
   (2) all 0s are before all 1s
   (3) contains at least two disjoint occurances of 010
   (4) every 1 must be followed by at least two 0s
   (5) palindrome
   (6) starts and ends with different letters
   (7) divisible by 3
   (8) odd number of 0s
   *(9) odd number of 0s and even number of 1s
   (10) the difference between the numbers of 0s and 1s is even

* possible to result in HUGE REs.

4. Convert the above REs to NFAs.

5. Convert the minimal DFAs from problem 1 of HW4 to GNFAs and then REs.

6. Convert the NFAs from problem 4 back to REs. Do you get the same REs?


Debriefing (required!): --------------------------

1. Approximately how many hours did you spend on this assignment?
2. Would you rate it as easy, moderate, or difficult?
3. Did you work on it mostly alone, or mostly with other people?
4. How deeply do you feel you understand the material it covers (0%–100%)? 
5. Any other comments?