# 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 Π
_{2} 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 Π_{2}.
- Problem D-2 (10XC)
Prove that if C is
any
language in Π
_{2}, then C ≤_{m} ALL_{TM}.

Last modified 8 March 2013