CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2016

Homework Assignment #6

Posted Thursday 14 April 2016

Due on paper in class, Wednesday 27 April 2016

Or on paper to the CICS main office by 4:00 pm that day

There are ten questions for 80 total points plus 10 extra credit. (Though the point total is lower, this assignment counts the same as the first five.) All are from the textbook, Introduction to the Theory of Computation by Michael Sipser (third edition, with second edition numbers given where different). The number in parentheses following each problem is its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

Corrections in red made on 20 April 2016.

Correction in purple added on 26 April 2016.

• Problem 8.8 (both) (10) (Remember that you may use nondeterminism because of Savitch's Theorem.)

• Problem 8.15 (second)/8.14 (third) (10)

• Problem 8.20 (both) (10)

• Problem 8.24 (both) (10)

• Problem 8.26 (both) (10) (The second edition asks you to show BIPARTITE ≤_L UPATH. The third edition corrects this to ask you to show that BIPARTITE-bar ≤_L UPATH. You should do the latter.)

• Problem 8.32 (second)/8.33 (third) (10XC)

• Problem 9.25 (second)/9.24 (third) (10)

• Exercise 10.1 (both) (5) (I said that here you are asked to show NC¹ ⊆ LOGSPACE, but that is not true. This question just asks you to show that log-depth circuits (of ordinary binary AND and OR gates, and unary NOT gates) must have polynomial size.)

• Exercise 10.5 (both) (5)

• Problem 10.8 (both) (10) This result implies that all regular languages are in NC¹. My thesis shows that there exist regular languages that are complete for NC¹ under the appropriate reductions.

Last modified 26 April 2016