CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2013

Homework Assignment #6

Posted Wednesday 3 April 2013

Due on paper in class or to me or to the main office by 4:00 pm, Wednesday 1 May 2013

There are fourteen questions for 100 total points plus 20 extra credit. All are more or less from 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 8.1 (5)

• Exercise 8.3 (5)

• Exercise 8.6 (5)

• Problem 8.8 (10) This is fairly challenging. It would be natural to convert the regular expressions to DFA's, but you don't have enough space to write down these DFA's. You can write down the NFA's, and since the DFA's are defined in terms of the NFA's, you can in effect use "virtual memory" to operate on the DFA's.

• Problem 8.9 (10)

• Problem 8.11 (5)

• Problem 8.13 (10)

• Problem 8.18 (10)

• Problem 8.25 (10)

• Problem 8.30 (10)

• Problem 9.24 (10) Also determine the depth of your circuits as a function of n.

• Problem 9.25 part (a) (10) In case you mess up the extra-credit questions, make sure you have a solution to this one that you are sure of.

• Problem 9.25 part (b) (10XC) For full credit on this problem, your circuit family should have depth O(log n) as well as size O(n log n). (You get 9 points out of ten for depth O(log n log log n).)

• Problem 9.26 (10XC) Determine the depth of your circuits (though it need not be O(log n) this time -- as best I remember that is not known and believed (but not proved) to be impossible).

• Hint for both 9.25 (b) and 9.26 -- remember the Master Theorem from CMPSCI 311.

Last modified 17 April 2013