CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2009

Homework Assignment #2

Posted Tuesday 17 February 2009

Due on paper in class, Friday 27 February 2009

There are fifteen questions for 100 total points plus 10 extra credit. All but two are from the textbook, Introduction to the Theory of Computation by Michael Sipser (second edition). The number in parentheses following each problem is its individual point value.

Correction 22 February: 2.43 instead of 2.42!

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

• Problem B1 (5): Let Q be the language {u$v: u and v are binary strings and the integer denoted by v is exactly three times the integer denoted by u}. Prove that q is not regular.

• Problem 1.46 part d only (5)

• Problem 1.53 (5) (This is much easier with Myhill-Nerode.)

• Problem 1.54 (10)

• Problem B-2 (10) For each of the languages of Problem 1.55, give a DFA that uses the minimum possible number of states for that language. For five of those languages (of your choice) show that your DFA has the minimum number of states for that language.

• Exercise 2.1 (5)

• Exercise 2.9 (10)

• Exercise 2.10 (5)

• Exercise 2.12 (10)

• Exercise 2.13 (5)

• Problem 2.21 (10 extra credit)

• Problem 2.32 (5)

• Problem 2.39 (10)

• Problem 2.43 part a (10) (corrected 22 February, recorrrected 26 February)

• Problem 2.43 part b (5) (corrected 22 February, recorrected 26 February)