hmwk_2 - • the set of all integers • all finite...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Discrete Structures Aug 30 2011 Assignment 2: Due at beginning of class Mon, Sept 12 Prof. Hopcroft *******Note: this is the first homework that will be subject to the style guide on the website. Points will be deducted for homeworks not following the guidelines.******** 1 Regular Expressions Write a regular expression for the set of all strings of 0’s and 1’s that have two blocks of 1’s. A sample string your regular expression should represent: 000000111111000111000 2 Recurrence Relation Find a close form solution for the following recurrence equations: (Also, show that you checked the first four values of your solution) 1. f ( n ) = 5 f ( n - 1) - 6 f ( n - 2) with boundary conditions f (0) = 0 and f (1) = 1. 2. f ( n ) = 6 f ( n - 1) - 12 f ( n - 2)+8 f ( n - 3) with boundary conditions f (0) = 1, f (1) = 6, and f (2) = 32. 3 Induction Prove by induction that 2 n 4 + 2 n 2 + 4 is divisible by 4 for all n 1. 4 Countably Infinite OR NOT!?! For each set say whether or not the set is countably infinite:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • the set of all integers • all finite subsets of integers • all subsets of integers • the set of all reals • all finite subsets of reals • all subsets of reals • the set of all finite length strings • all finite subsets of the set of all finite length strings • all subsets of the set of all finite length strings • all computer programs 1 • functions mapping integers to the set { , 1 } • fuctions mapping integers to integers 5 Countable Concept In a concise way, write an explaination of countably infinite a high school student could understand. And, give an example of a set that is not countably infinite or finite and explain why. 6 Countable Triplets Sketch a algorithm to list all triples of a countably infinite set. 2...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

hmwk_2 - • the set of all integers • all finite...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online