CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2011

Homework Assignment #2

Posted Sunday 6 February 2011

Due on paper in class, Monday 14 February 2010

There are ten questions for 80 total points. All but two are 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.

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

• Problem B-1 (10) Show the steps of the state minimization algorithm on the eight-state DFA for Exercise 1.6 part (l). Is this DFA minimal? If you are using the solutions for HW#1, note that the diagram there is missing a 1-loop on state q1d.

• Problem B-2 (10) Create a DFA from the NFA of Exercise 1.10 part (a). Find a minimal DFA for this language, and describe the classes of the Myhill-Nerode equivalence relation. If you are using the solutions for HW#1, note that you must add a 1-loop on state q5 to make the NFA correct.

• Problem 1.35 (10)

• Problem 1.49 part (b) only (10)

• Problem 1.51 (5)

• Problem 1.62 (5)

• Exercise 2.1 part (c) only (5)

• Exercise 2.9 (10)

• Exercise 2.13 (10)

• Exercise 2.16 (5)

Last modified 12 February 2011