CMPSCI 401: Theory of Computation

David Mix Barrington

Spring, 2013

Homework Assignment #4

Posted Friday 8 March 2013

Due on paper in class, Wednesday 27 March 2013

There are fourteen questions for 100 total points plus 10 extra credit. All but one 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.

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

• Exercise 4.7 (5)

• Problem 4.10 (10)

• Problem 4.14 (10)

• Problem 4.15 (5)

• Problem 4.28 (10)

• Exercise 5.3 (5)

• Exercise 5.4 (5)

• Problem 5.9 (10)

• Problem 5.15 (10)

• Problem 5.19 (5)

• Problem 5.20 (5)

• Problem 5.24 (10)

• Problem D-1 (10) The class Π₂ is the set of all languages A for which there exists another language B such that B is Turing decidable and for any string w, w ∈ A if and only if ∀x:∃y:(w,x,y) ∈ B. Prove that ALL_TM is in Π₂.

• Problem D-2 (10XC) Prove that if C is any language in Π₂, then C ≤_m ALL_TM.

Last modified 8 March 2013