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