cos2601 - wikistudent, unisa

24/01/2012 COS2601 - WikiStudent, Unisa

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This is an example of a machine that will be created in thismodule

COS2601

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Contents

1 Theoretical computer science 2

1.1 Introduction

1.2 The Unisa syllabus

2 The COS2601 textbook

2.1 Prescribed textbook

2.2 Quotes from the textbook2.3 Recommended reading

3 The COS2601 exam

3.1 Past exam papers

4 How to pass COS2601

4.1 Study tips

4.2 Useful links

5 Study notes

5.1 Download notes

5.2 Create notes online

6 Student opinions

6.1 Student survey

6.2 Pros of COS26016.3 Cons of COS2601

Theoretical computer science 2

Introduction

Theoretical Computer Science 2 is a module that allows you to study a class of theoretical machines known asFinite Automata (FA). These FA's can be used to recognize symbol patterns like binary sequences eg.'10101011100111' or character strings eg. 'abcdefgh'. These sequences or strings are called languages which arefed to these machines and either accepted or rejected.

There are various applications for such theoretical machines in Computer Science. Typical applications are thedevelopment of Communications protocols and Cryptography.

The prerequisites for this module are either COS1501 or MAT2612.COS101S provides a natural introduction to the topics presented here. There are also similarities with MAT2612in a few significant areas.



The Unisa syllabus

1. Background

2. Languages

3. Recursive Definitions

4. Regular Expressions

5. Finite Automata

6. Transition Graphs

7. Kleene's Theorem

8. Finite Automata with Output

9. Regular Languages

10. Nonregular Languages

11. Decidability

The COS2601 textbook

Prescribed textbook

ISBN 9780471137726

Title: Introduction to Computer Theory (http://www.loot.co.za/refer.html?

referrer=8113849355&/shop/main.jsp?page=detail&id=978-0-471-13772-6)

Author: Daniel I. A. Cohen

Edition: 2nd

Publisher: John Wiley and Sons

Year published: 1996

Year prescribed: 2010

Quotes from the textbook

" . . . b u t w h a t i s f a r l e s s c l e a r i s e x a c t l y w h a t ࠗ * s h o u l d m e a n .

W e s h a l l a v o i d t h i s p h i l o s o p h i c a l c r i s i s b y n e v e r u s i n g t h i s s y m b o l i s m a n d a v o i d i n g t h o s e w h o d o . "

- - C o h e n p . 3 7 , C h a p t e r 4 ( R e g u l a r e x p r e s s i o n s )

Recommended reading

The COS2601 exam

Past exam papers

The Exam in May 2011

Question 1

Fairly Simple, Set theory. If you went over your MCQ of Tutorial letter 101, you would've been fine.



Question 2:

Given the alphabet

a) Give the universal set,

b) the generator(s),

c) a function on the universal set,

d) write the definition of the language EVENAB where the words are of even length and which do not

contain the substring ab.

Question 3:

a) Give the recursive definition of of all positive integers greater than 2,

b) formulate the induction principle,

c) apply the induction principle to prove a given equation.

Question 4:

You had to decide whether two regular expressions are similar or equivalent, if not you had to supply a

counter example.

Question 5:

Build an FA that meets certain criteria.

Question 6:

Use Kleene's theorem to convert a Transition Graph into a regular expression.

Question 7:

Build an FA which is the concatenation of and ( )

Question 8:

Simplify a given FA with a largish number of states so that it only has 4 states.

Question 9:

Use the Pumping Lemma with length to prove that the language is notregular.

Question 10:

I've noticed in these questions, they ask you to explain an algorithm or method of proof and then apply it. Inthis question, it was to decide whether an accepted language was finite or infinite. They are getting clever

now, students are just memorising without understanding, thats why they are asking to explain your answer.

The questions closely resembled the supplied example paper from the 2011 and 2009 exam tutorial letters. NoMealy's or Moore's!

The Exam in May 2010

This exam was relatively straightforward. The questions closely resembled the supplied example paper.



Question 1:

Use the Pumping Lemma with length to prove that the language is not regular.

Question 2:

Given the alphabet

a) Give the universal set,b) the generator(s),

c) a function on the universal set,d) write the definition of the language EVENnotAB where the words are of even length and which do not

contain the substring ab.

Question 3:

a) Give the recursive definition of of all positive integers greater than 3,

b) formulate the induction principle,c) apply the induction principle to prove a given equation.

Question 4:

You had to devise two regular expressions according to certain criteria.

Question 5:

Build an FA that meets certain criteria.

Question 6:

Use Kleene's theorem to convert a Transition Graph into a regular expression.

Question 7:

Build an FA which is the concatenation of and ( )

Question 8:

Simplify a given FA with a largish number of states so that it only has 4 states.

Question 9:

Some questions (mostly theory) about decidability.

Question 10:

Given a word and some languages over the alphabet , say whether or not you think it ispossible for the word to be in one of the languages.

The exam in Oct/Nov 2009

The 2009 exam was definitely easier than the 2008 exam. The following 10 questions were asked:

Question 1:



a) Give the set over the alphabet that do not end on .

b) Give the set and where

Question 2:

Very similar to the assignment question and it was exactly the same as the one in the sample paper that was

given.

Given the alphabet

a) Give the universal set,b) the generator(s),

c) a function on the universal set,d) write the definition of the language ODDAB where the words are of odd length which do not contain the

substring ab.

Question 3:

Very similar to the assignment question and it was exactly the same as the one in the sample paper that wasgiven.

a) Give the recursive definition of of all positive integers greater than or equal to 5,

b) formulate the induction principle,

c) apply the induction principle to prove that

Question 4:

a) Give a regular expression which defines the language which generate all words with the total amount of

divisible by 3.

b) Give a regular expression which defines the language which generate all words ending on .

Question 5:

Build an FA that does not accept the substring anywhere in it.

Question 6:

Use Kleene's theorem to find a regular expression. Had to convert a TG to a regular expression.

Question 7:

and had to be used to find the union of these two FA's.

Question 8:

The input and output on a Moore machine was given and the Moore machine was to be drawn using onlythree states.

Question 9:

Had to use the Pumping Lemma with length to prove that is non regular.

Question 10:



Explain briefly the method of finding if a language is accepted by two FA's, and .


The exam was very similar to those of previous years. The inductive proof required you to show that is a

divisor of for all positive integers .


The exam this year covered most of the syllabus, and the format has not changed over the years. There wereenough simpler questions to push 40% and above.


The exam was very nice - and predictable. (The questions were nowhere near as difficult as some of the textbookones). It seems they keep the format the same every year, and this exam was incredibly similar to the one from 2years back. At least 25% of the questions came straight from that past paper.

How to pass COS2601

Study tips

There are 20 exercises at the end of each chapter of the prescribed textbook by Cohen - unfortunately allwithout solutions. But it doesn't hurt to try them all out anyway. We could buy a (very handy) disk from

Unisa with interactive exercises on the pumping lemma. It's well worth buying, even if you don't have any

problems. The exercises were well chosen and written to catch you out!

Useful links

Jflap software (http://jflap.org/jflaptmp/) - This is a link to excellent software for helping you studying themodule and expecially useful for drawing the diagrams. Just double click on the jar file to run the program.

With it you can do machines, grammars, lemmas and more (and it's free).

An outline of outcomes of the subject (http://geekswithblogs.net/MarkPearl/archive/2011/05/18/unisa-

theoretical-computer-sciencendashoutline-of-things-you-should-know.aspx) - Things you should know forthe exam.

Study notes

Download notes

AuthorDownload

linkYear

createdDescription

BronwenSolutions to

chapter 42003

A student's (correct) worked-out solutions to the first 11 problems in

chapter 4 of the textbook by Cohen.

BronwenSolutions to

chapter 22003

A student's (correct) worked-out solutions to all 20 problems in chapter 2

of the textbook by Cohen.

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Student opinions

Student survey

How challenging did you

find COS2601?

How useful is COS2601 in

your field of work?

What did you get for the

COS2601 exam?

Pros of COS2601

If you work very hard at this module you'll find COS3701 a breeze. The extra hours spent in second year

will definitely pay off in final year as the concepts are exactly the same.

Cons of COS2601

This is a very abstract module which will require a lot of dedicated studying.

The textbook is almost like a very long piece of cryptic notes the author made while he was busy with his

PhD or something. It is difficult to follow and the Unisa study guide is in some instances necessary to decrypt

the textbook, but it doesn't succeed in doing that every time.

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Categories: Unisa Modules | Completed Modules | Computer Science

This page was last modified 10:04, 26 May 2011 by Bronwen. Based on work by Ahmed Vahed , Zelna

Ellis, Andreas Pauley and Gert Yes.

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