# 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