CMPSCI 501: Theory of Computation
David Mix Barrington
Spring, 2014
Homework Assignment #4
Posted Monday 10 March 2014
Due on paper in class, Wednesday 26 March 2014
There are thirteen 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.
The numbering of exercises in Chapter 4 of Sipser differs
between
the second and third editions, as he inserted a new 4.5, 4.19, 4.31,
and 4.32. Nothing similar appears to have happened in Chapters 5 or 6.
- Problem 4.19 (third edition), which is not in the second
edition (10): Prove that the class
of decidable languages is not closed under homomorphism. (This
means that you must define a language X and a homomorphism f such
that X is TD and f(X) = {f(w): w ∈ X} is not TD. Homomorphisms
were defined on the first midterm.)
- Problem D-1 (10): Prove that ATM ≤m
REGTM. (The proof of Theorem 5.3, if adapted into a
mapping
reduction, shows that ATM reduces to the complement of
REGTM.)
- Problem 4.22 (second edition) or 4.24 (third edition) (10):
- Problem 4.26 (second edition) or 4.28 (third edition) (10):
- Exercise 5.1 (5):
- Exercise 5.2 (5):
- Problem 5.13 (10):
- Problem 5.17 (10):
- Problem 5.22 (5):
- Problem 5.23 (5):
- Exercise 5.25 (10):
- Problem 5.32 (10):
- Problem 6.6 (10 XC):
Last modified 10 March 2014