CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2009

Homework Assignment #6

Posted Monday 4 May 2009

Due on paper in class or to CMPSCI main office by 4:00 p.m., Tuesday 12 May 2009

There are twelve questions for 100 total points plus 20 extra credit. All but two are 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.

• Problem 7.39 (10)

• Problem 7.44 (10)

• Exercise 8.4 (10)

• Exercise 8.6 (5)

• Problem 8.10 (10)

• Problem 8.11 (5)

• Problem 8.17 (5)

• Problem 8.20 (15)

• Problem 8.25 (10)

• Problem 8.28 (10)

• Problem F-1 (10) (refers to section 9.3) Let c be any constant and let CEVAL_c be the language of pairs (C,w) where C is a circuit of n inputs and depth at most c log n, w is a binary string of length n, and C evaluates to 1 on input w. Prove that CEVAL is in the class L.

• Problem F-2 (20 extra credit) (also refers to section 9.3) Let M be any DFA. Describe a circuit family that decides L(M), where the n-input circuit has size O(n) and depth O(log n).

Last modified 4 May 2009