COS 550 F08 HW #3 DUE Thursday 9/25/08
p. 25 Problem 2,       15 points
p. 25 Problem 3,       15 points
p. 25 Problem 7,       15 points
p. 28 Problem 1,       10 points
p. 28 Problem 3,       15 points
Problem 1 Below,       15 points
Problem 2 Below,       15 points
********** Problem Notes *********,

For the first 5 problems, be sure to test your answer by writing a program 
in SmallBASIC or some similar language. Be sure to include a listing of 
your program and the appropriate output as part of your homework.

PROBLEM 1: In class, I described a bijection between the natural numbers 
and finite length strings over the alphabet {a, b} based on ordering the 
strings first by length, and then alphabetically. Using any reasonable 
computer language, code two functions, f and g, corresponding to the 
bijection I just described, and having the following properties. f takes a 
natural number and outputs the string corresponding to that number. g 
takes a finite length string composed of a's and b's and returns the 
number giving its place in the order we talked about. Include the source 
code and some sample output for your program.

PROBLEM 2: Let f: N -> NxN be given by f(n) = (n,0), and g: NxN -> be 
given by g(a,b) = 2^a * 3^b. In class, I described how the proof of the SB 
Theorem constructs a bijection between N and NxN. Using your favorite 
computer language, produce two functions fb and gb such that fb:N -> NxN 
and gb:NxN -> N are the bijections based on the functions f and g given in 
this problem. Submit the source code and some sample output for your 
program.