CS4311: Introduction to Computation Theory hw12
CS 4311 Introduction to Computation Theory
Homework 12: Chapter 5
Due: Wednesday, 12/06/06, beginning of class
(Assigned: Wednesday, 11/29/06)
You are required to turn in answers to all the questions. However, only a random
subset of the questions will be graded.
While discussion with others is permitted and encouraged, the final work
should be done individually. You are not allowed
to work in groups.
The answers, comments, and programs (if any) must be the original
work of the author.
You are allowed to build on material supplied in the class. If you use
any other source than the current class notes and the textbook, specify it
clearly.
1. (Exercise 5.5) Show that ATM is not mapping
reducible to ETM.
2. (Exercise 5.6)
Show that ≤m is a transitive relation.
3. (Exercise 5.7)
Show that if A is Turing-recognizable and
A ≤m A-complement, then A is decidable.
4. (Exercise 5.9 in the first edition)
Show that all Turing-recognizable problems mapping reduce to
ATM.
5. (Exercise 5.22 in the second edition)
Show that A is Turing recognizable iff A mapping reduces to
ATM.