CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2015

Homework Assignment #4

Posted Monday 9 March 2015

Due on paper in class, Wednesday 25 March 2015

There are thirteen questions for 100 total points plus 10 extra credit. All are from the textbook, Introduction to the Theory of Computation by Michael Sipser (second/third edition). though some are adapted as indicated. 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.

• Problem 4.12 (2nd)/4.13 (3rd) (5):

• Problem 4.24 (2nd)/4.26 (3rd) (10):

• Problem 4.28 (2nd)/4.30 (3rd) (10):

• Exercise 5.3 (5):

• Exercise 5.4 (5):

• Problem 5.9 (10):

• Problem 5.15 (10):

• Problem 5.20 (5):

• Problem 5.24 (10):

• Problem 5.30 part b only (5): You will need to read Problem 5.28 and its solution in the back of the book.

• Problem 5.35 (2nd)/5.34 (3rd): The Myholl-Nerode Theorem can be useful here.

• Problem 5.36 (3rd) (not in second edition) (10): Say that a CFG is minimal if none of its rules can be removed without changing the language generated. Let MIN_CFG be {G: G is a minimal CFG}. Part (a) is to show that MIN_CFG is TR. Part (b) is to show that MIN_CFG is undecidable.

• Problem 6.7 (5):

• Problem 6.8 (10XC):

Last modified 9 March 2015