CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2015

Homework Assignment #1

Posted Monday 9 February 2015

Due on paper in class, Wednesday 18 February 2015

There are twelve questions for 80 total points plus 10 extra credit. All but one 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 B-1 (10): Find minimal DFA's for the languages of Exercises 1.6h and 1.28c. Describe all the Myhill-Nerode equivalence classes for each of the two languages.

• Exercise 1.29 part b only (5): Use either the Pumping Lemma or Myhill-Nerode.

• Problem 1.40 part b only (10)

• Problem 1.67 (10XC). This problem is not in the second edition, it reads: "Let the rotational closure of language A be RC(A) = {yx: xy ∈ A}. Part (a): Show that for any language A, we have that RC(A) = RC(RC(A)). Part (b): Show that the class of regular languages is closed under rotational closure (that is, show that if A is any regular langauge, RC(A) is also regular)."

• Exercise 2.4 parts b, e, f only (5).

• Exercise 2.5 parts b, e, f only (5): You need not use the construction on your results from 2.4.

• Exercise 2.6 part d only (5)

• Exercise 2.11 (5)

• Problem 2.23 (10)

• Problem 2.25 (10).

• Problem 2.26 (5)

• Problem 2.44 (10)

Last modified 11 February 2015