# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2012

# Homework Assignment #7

#### Posted Thursday 5 April 2012

#### Due on paper in lecture, Friday 13 April 2012.

There are eight questions for 60 total points plus 10 extra credit.
All but one are from
the textbook, *
Mathematical Foundation for Computer Science*. Note that the book has
both Exercises and Problems -- make sure you are doing a Problem and not the
Exercise with the same number. 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 9.9.1 (10) Note that if you have a green or blue
textbook, you will need to look at a yellow one to get the correct
statement
of this problem.
- Problem 9.10.3 (10XC) Determine the winner for all positions of
the game (with either player to move) that are legitimate -- the two
kings cannot be on adjacent squares. You may or may not find a
computer useful -- if you find the answer by running a program,
include your code.
- Problem 5.1.1 (5)
- Problem G-1 (10): Give (and justify) a regular expression for
the strings in (a+b+c)* that do not contain the same letter twice in
a row (that is, the complement of the language Σ
^{*}(aa+bb+cc)Σ^{*}).
- Problem 5.2.1 (10)
- Problem 5.4.1 (5)
- Problem 5.5.4 (10)
- Problem 5.5.5 (10) (Hint: Prove that if L is any such language,
and Δ is the set of all letters that ever occur in any string
in L, then all of Δ
^{*} is contained in L.)

Last modified 5 April 2012