# CMPSCI 601: Theory of Computation

### David Mix Barrington

### Spring 2010

### Homework Assignment #1

#### Posted Friday 22 January 2010

#### Due in class Wednesday 3 February 2010

All these questions are from the textbook, *Computational
Complexity: A Modern Approach* by Arora and Barak. There are five
questions for 50 total points.

- Exercise 0.3 (5) Be quantitative as well as qualitative in your
answer. Would the same effect hold with fewer than 13 gears and the other
parameters the same?
- Exercise 1.5 (10) Of course this solution will need considerable
detail about tapes and heads.
- Exercise 1.9 (10) As will this.
- Exercise 1.14 (15) Pick any three of the four parts. Here you may be
somewhat less detailed about tapes and heads, particularly if you quote
results that allow you to use a more natural model than an ordinary TM.
But your arguments should be complete and convincing that each problem is
solvable in poly time on an ordinary multitape TM.
- Exercise 1.15 (10) As in 1.14, you do not need so much
detail about tapes and heads.

Last modified 22 January 2010