# CMPSCI 601: Theory of Computation

### David Mix Barrington

### Spring 2010

### Homework Assignment #4

#### Posted Friday 26 February 2010

#### Due in class Monday 8 March 2010

All but one of these questions are from the textbook, *Computational
Complexity: A Modern Approach* by Arora and Barak. There are nine
questions for 50 total points plus 5 extra credit.

Exercise 4.3 corrected 3 March.

- Exercise 4.3 (5) (As pointed out in lecture
3 March, of course this statement is not true as written as an arbitrary
L need not be in NL and so need not be NL-complete. Replace "NL-complete"
in the problem by "NL-hard".)
- Exercise 4.4 (5)
- Exercise 4.5 (5)
- Exercise 4.6 (10)
- Exercise 4.7 (5)
- Exercise 4.12 (5) Instead of "Is SC the same as polyL ∩ P?",
which is an open question because they are equal if P = L, answer this question:
"Explain the difference between the definition of SC and PolyL ∩ P."
- Exercise X-1 (5 XC) Prove, without any conditions, that P ≠ polyL.
(Hint: You may use Theorem 6.30 on page 119 without proof.)
- Exercise 5.9 (10)
- Exercise 5.13 part a only (5)

Last modified 3 March 2010