# Homework Assignment #7

#### 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.

• 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.)