CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2016

Homework Assignment #5

Posted Friday 1 April 2016

Due on paper in class, Friday 15 April 2016

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 (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.

• Problem 6.22 (second)/6.23 (third) (5) (This can be done with or without the Recursion Theorem.)

• Problem 6.24 (second)/6.25 (third) (10):

• Exercise 7.11 (third) (not in second) (10): In both parts, provide and analysis of the time complexity of your algorithm.
  • (a) Show the EQ_DFA ∈ P.
  • (b) Say that a language A is star-closed if A = A^*. Give a polynomial time algorithm to test whether a DFA recognizes a star-closed language. (Note that EQ_NFA is not known to be in P.)

• Problem 7.12 (second)/7.13 (third) (10):

• Problem 7.19 (second)/7.20 (third) (5):

• Problem 7.20 (second)/7.21 (third) (10):

• Problem 7.21 (second)/7.22 (third) (10):

• Problem 7.27 (second)/7.29 (third) (10):

• Problem 7.32 (second)/7.37 (third) (10):

• Problem 7.37 (second)/7.39 (third) (10XC):

• Exercise 8.1 (both) (5):

• Exercise 8.4 (both) (5):

• Problem 8.13 (both) (10):

Last modified 1 April 2016