# CMPSCI 501: Theory of Computation

### David Mix Barrington

### Spring, 2015

# Homework Assignment #4

#### Posted Monday 9 March 2015

#### Due on paper in class, Wednesday 25 March 2015

There are thirteen
questions for 100 total points plus
10
extra credit.
All are from
the textbook, *Introduction to the Theory of Computation*
by Michael Sipser (second/third edition). though some are adapted as
indicated.
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 4.12 (2nd)/4.13 (3rd) (5):
- Problem 4.24 (2nd)/4.26 (3rd) (10):
- Problem 4.28 (2nd)/4.30 (3rd) (10):
- Exercise 5.3 (5):
- Exercise 5.4 (5):
- Problem 5.9 (10):
- Problem 5.15 (10):
- Problem 5.20 (5):
- Problem 5.24 (10):
- Problem 5.30 part b only (5): You will need to read Problem 5.28 and
its solution in the back of the book.
- Problem 5.35 (2nd)/5.34 (3rd): The Myholl-Nerode Theorem can be useful
here.
- Problem 5.36 (3rd) (not in second edition) (10):
Say that a CFG is
*minimal* if none of its rules can be removed without
changing the language generated. Let MIN_{CFG} be
{G: G is a minimal CFG}. Part (a) is to show that MIN_{CFG} is TR.
Part (b) is to show that MIN_{CFG} is undecidable.
- Problem 6.7 (5):
- Problem 6.8 (10XC):

Last modified 9 March 2015