Module 5 Worksheet
In Class Questions
1) (S5) Express the problem {/\, aa} as a LRP in the Input,Yes/No Question format.
Input:
Yes/No Question:
2) (S5) Express the problem {a
n
 n is a perfect square} as a LRP in the Input,Yes/No
Question format.
Input:
Yes/No Question:
3) (S8) Give the shortest possible string that represents a legal program for solving a
language recognition problem.
4) (S16) Prove that the set of natural numbers that are a multiple of 5 is countably
infinite.
5) (S16) Consider the following listing of the set of integers.
0, 1, 2,
…, 1, 2, …
Does every integer appear at a finite position?
What does this imply about whether or not the set of integers is countably infinite?
6) (S17) What do we need to do to prove that a set is uncountably infinite?
7) (S21) Write a program that takes as input a nonnegative number and outputs the
corresponding string over {a,b}.
0 maps to /\, 1 maps to a, 2 maps to b, 3 maps to aa,
…
8) (S21) Suppose we list all the strings in {a,b}* in alphabetical order.
Does every string
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 TORNG
 Natural number, Countable set, Input,Yes/No Question format

Click to edit the document details