CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2014

Homework Assignment #5

Posted Tuesday 1 April 2014

Due on paper in class, Wednesday 16 April 2014

There are thirteen questions for 100 total points plus 10 extra credit. All but one are from the textbook, Introduction to the Theory of Computation by Michael Sipser (second edition). Problem numbers for the third edition are given in square brackets after the original number. 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.

• Problem 6.22 [6.23] (10): (Hint: Use the Richard paradox mentioned in class to get a contradiction from the assumption that K(x) is a Turing computable function. Or look up the paradox yourself.)

• Exercise 7.7 [7.7] (5)

• Exercise 7.10 [7.10] (5)

• Problem 7.12 [7.13] (10)

• Problem 7.16 [7.17 (5)

• Problem 7.19 [7.20] (5)

• Problem 7.20 [7.21] (10)

• Problem 7.27 [7.29] (10)

• Problem 7.34 [7.35] (10)

• Problem 7.37 [7.39] (10)

• Problem 7.39 [7.41] (10)

• Problem 7.49 [7.51] (10)

• Problem [7.52] (not in second edition) (10 XC) Show that the class P is closed under homomorphism if and only if P = NP.

Last modified 1 April 2014