Computational Theory Homework Assignment

To go over in class, Wednesday, 11/28/2005:

1. Draw the state diagram for the TM represented by the following serial number. For this and all other problems, you should assume that the alphabet is {0, 1, b} unless explicitly stated otherwise.

   11101001001001011010100100100110010010010010011001000100010100011000100100010010000111

2. Draw the state diagram for the TM represented by the following set of 5-tuples.

   {(1,0,0,R,2), (1,1,1,R,2), (2,1,1,R,3), (3,0,0,R,3), (3,b,b,R,4), (3,1,1,R,3)}

3. What is the serial number for the TM in question 2?
   

4. What does the TM in question 2 do? In other words, what types of input does it accept? Remember "accept" means halt without crashing.
   

5. Examine the TM whose state diagram is shown below.

   a. Rewrite this TM as a list of 5-tuples.
   
   b.Try it on some sample strings to see if you can determine when it accepts:
   

   Hint: try all strings of length 3, then a few strings of length 4. What kind of strings cause the tape to clear and the machine to halt?