CMPSCI 601: Theory of Computation

Offered through the PEEAS distance learning program

Homework Assignment #6

David Mix Barrington

Assignment posted Thu 4 Dec 2003

Due Wed 10 Dec 2003, 2:00 p.m. by fax to 413-545-1249, attention Prof. Barrington.

Make sure you have read the statement on academic honesty on the homework assignment index page.

This assignment is about half the size of the first five, since you have so little time for it.

• Question 1 (15): On HW#5 you proved that n n-bit numbers can be sorted by a logspace algorithm. Prove that this problem can be solved by a TC⁰ circuit family.

• Question 2 (20): Prove Observation 20.9 on page 12 of Lecture 20 in the Spring 2003 lectures.

• Question 3 (15): Define classes Σ_iL for each positive number i, by analogy with the logtime and poly-time hierarchies. Prove that for each i, Σ_iL is equal to NL.

Last modified 4 December 2003