# CMPSCI 401: Theory of Computation

### David Mix Barrington

### Spring, 2011

# Homework Assignment #1

#### Posted Monday 24 January 2011

#### Due on paper in class, Monday 7 February 2010

There are twelve questions for 100 total points.
All but one are
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 0.5 (5) Prove your answer by induction on the size of
C. That is, for your answer function f(n), prove "for any non-negative
integer n, for any set C of size n, the power set of C has f(n)
elements"
by induction on n.
- Problem 0.12 (5)
- Exercise 1.3 (5)
- Problem A-1 (10) Find a regular expression for the language
L(M)
of Exercise 1.3.
- Exercise 1.4 parts a and g only (10)
- Exercise 1.6 parts d, i, k, and l only (10)
- Exercise 1.10 (5)
- Exercise 1.17 (5)
- Exercise 1.28 (5)
- Problem 1.38 (10) You should prove that any language is regular
if and only if it is the language of some all-NFA. One direction of
this is very easy.
- Problem 1.45 (10)
- Problem 1.48 (10)
- Problem 1.49 part a only (10)

Last modified 24 January 2011