# CMPSCI 601: Theory of Computation

### Homework Assignment #4

#### 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)