CMPSCI 501: Theory of Computation

David Mix Barrington

Spring, 2016

Homework Assignment #3

Posted Tuesday 23 February 2016

Due on paper in class, Friday 4 March 2016

There are eleven questions for 90 total points plus 20 extra credit. All but one 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 2.31 (10)

• Problem 2.50 (10XC) (not in second edition so repeated here): We defined the CUT of language A to be CUT(A) = {yxz: xyz ∈ A}, Show that the class of CFL's is not closed under CUT.

• Problem 3.9 (10).

• Problem 3.12 (10).

• Problem 3.14 (10).

• Problem 3.16 parts b, c, d only (10)

• Problem C-1 (20): Let BU be the language {w#1ⁿ: w is a binary string that represents the number n in binary}.
  • (a, 10) Give a high-level description of a one-tape Turing machine that decides UB.
  • (b, 10) Give a complete diagram for such a Turing machine, following the model of Figures 3.8 and 3.10 in Sipser.

• Exercise 4.3 (5)

• Exercise 4.4 (5)

• Problem 4.12 (second) or 4.13 (third) (10)

• Problem 4.25 (second) or 4.27 (third) (10XC)

Last modified 23 February 2016