CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2010

Homework Assignment #3

Posted Friday 26 February 2010

Due on paper in class, Wednesday 10 March 2010

There are thirteen questions for 100 total points plus 10 extra credit. All but one are the textbook, Introduction to the Theory of Computation by Michael Sipser (second edition). The number in parentheses following each problem is its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

• Exercise 3.2, part d only (5)

• Exercise 3.6 (5)

• Exercise 3.8, part c only (5)

• Problem 3.12 (10)

• Problem 3.14 (10)

• Problem 3.16, part c only (5)

• Problem 3.19 (10)

• Problem C-1 (15) Here is your one assignment to actually construct a state table for a Turing machine. It is to decide the following language: {u#v#w₁#w₂#...#w_m: u, v, and all w_i's are in {0,1}^* and w_u = v}. The input alphabet is thus {0,1,#} and you may define the tape alphabet as you see fit. Describe your TM by a diagram as Sipser does on pages 144 and 145.

• Exercise 4.3 (10)

• Exercise 4.4 (10)

• Exercise 4.7 (5)

• Problem 4.12 (10)

• Problem 4.14 (10XC)

Last modified 28 February 2010