CS 360 Assignment 5
For all problems, you should justify any statement you make.
1. For each of the following, give a one tape TM that accepts the language or computes the
function. Include a transition diagram of your TM and also an informal description
CS 360 nal exam questions from Spring 2007
The following questions appeared on the CS 360 nal exam for Spring 2007. (The usual exam cover sheet, formatting, and point values have been removed.) 1. Dene a language A cfw_0, 1 as follows: A = cfw_w cfw_0, 1
CS 360 Fall 2011
Assignment 5
Due at 4:00 PM on Friday, December 2nd
1. (10 marks) Let L = cfw_an bn cn | n 1. Design a Turing machine that accepts L.
SOLUTION:
We create a non-deterministic Turing machine with three tapeheads. The tapeheads all start
out
CS 360 Introduction to the Theory of Computing
Spring 2008
Assignment 1 Solutions
Let us x the alphabet = cfw_0, 1 for all of this assignment. 1. [3 points] Give a DFA that recognizes the language L1 = cfw_x : 1110 is not a prex of x. Solution: To maintai
Module 9
Undecidability
What computers cant do.
CS 360: Introduction to the Theory of Computing
Daniel G. Brown, University of Waterloo
9.1
Topics for this module
A language that is not decidable
Other undecidable languages
Reduction: how to prove languag
Lecture 10
Proving languages to be
non-context-free
In this lecture we will study a method through which certain languages can be
proved to be non-context-free. The method will appear to be quite familiar, because
it closely resembles the one we discussed
Lecture 4
Regular operations and regular
expressions
In this lecture we will discuss the regular operations, as well as regular expressions
and their relationship to regular languages.
4.1 Regular operations
The regular operations are three operations on
Lecture 14
Decidable languages
In the previous lecture we discussed some examples of encoding schemes, through
which various objects can be represented by strings over a given alphabet. We will
begin this lecture by considering a few more encoding schemes
Lecture 17
Further discussion of Turing
machines
In this lecture we will discuss various aspects of decidable and Turing-recognizable
languages that were not mentioned in previous lectures. In particular, we will discuss closure properties of these classe
Lecture 15
Undecidable languages
In the previous lecture we discussed several examples of decidable languages relating to finite automata and context-free grammars. In this lecture we will discuss
analogous languages relating to Turing machines, and we wi
Lecture 7
Context-free grammars and languages
The next class of languages we will study in the course is the class of context-free
languages. They are defined by the notion of a context-free grammar, or a CFG for
short, which you will have encountered pre
Lecture 21
The CookLevin theorem
The purpose of this lecture is to state and prove the CookLevin theorem, which
gives us a primordial NP-complete language, from which many other languages
can be proved NP-complete. There are thousands of interesting NP-co
Lecture 3
Nondeterministic finite automata
This lecture is focused on the nondeterministic finite automata (NFA) model and its
relationship to the DFA model.
Nondeterminism is an important concept in the theory of computing. It refers
to the possibility o
Lecture 12
The Turing machine model of
computation
For most of the remainder of the course we will study the Turing machine model
of computation, named after Alan Turing (19121954) who proposed the model in
1936. Turing machines are intended to provide a
Lecture 13
Variants of Turing machines and
encoding objects as strings
In this lecture we will continue to discuss the Turing machine model, beginning
with some ways in which the model can be changed without affecting its power.
We will also start discuss
SOLUTIONS
Introduction to Automata Theory,
Languages, and Computation
Collected & Prepared By
rontdu@gmail.com
13th Batch (06-07) Dept. of Computer Science & Engineering University of Dhaka
Copyright: No copyright
1
TABLE OF CONTENTS
SOLUTIONS FOR CHAPTER
CS 360 Assignment 5
Due Wednesday, July 30, 4:00 PM
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; se
CS 360 Assignment 4
Due on Friday, July 18, 4:00 PM
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; se
CS 360 Assignment 1
Solutions
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; see the course outline f
CS 360 Assignment 4
Solutions
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; see the course outline f
CS 360 Assignment 5
Solutions
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; see the course outline f
FINAL EXAMINATION
WINTER TERM 2014
Student Name (Print Legibly)
SOLUTIONS
(family name)
(given name)
Signature
Waterloo Student ID Number
COURSE NUMBER
CS 360
COURSE TITLE
Introduction to the Theory of Computing
COURSE SECTION
001
DATE OF EXAM
Tuesday, Ap
CS 360 Assignment 3
Solutions
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; see the course outline f
CS 360 Assignment 2
Solutions
You should start as early as possible, and contact course staff if you get stuck.
This assignment is worth between 0% and 4% of your mark in the course, depending on how many
points you receive on it; see the course outline f
Lecture 2
Countability for languages and
deterministic finite automata
The main goal of this lecture is to introduce the finite automata model, but first
we will finish our introductory discussion of alphabets, strings, and languages by
connecting them wi
Lecture 16
Computable functions and mapping
reductions
In this lecture we will discuss the notion of a reduction, which is useful for proving
that certain languages are undecidable (or that they are non-Turing-recognizable).
16.1 Computable functions and
Lecture 20
Boolean circuits
In this lecture we will discuss the Boolean circuit model of computation and its
connection to the Turing machine model. Although the Boolean circuit model is
fundamentally important in theoretical computer science, we will not
CS 360 - Mid Term Examination 2 - Winter 2014
Solutions
Instructions:
This examination is closed book.
You have 80 minutes to complete the examination.
The problems you need to solve are on the back of this sheet.
Please wait to begin the examination
FINAL EXAMINATION
WINTER TERM 2014
Student Name (Print Legibly)
(family name)
(given name)
Signature
Waterloo Student ID Number
COURSE NUMBER
CS 360
COURSE TITLE
Introduction to the Theory of Computing
COURSE SECTION
001
DATE OF EXAM
Tuesday, April 15, 20