COMP 2805: DISCRETE MATH II
(Introduction to Theory of Computation)

Instructor:  Professor Anil Maheshwari
Office:  School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6, Room 5364,  Herzberg Physics Building,
Phone: (613) 520-4333, Fax: (613) 520-4334,

OFFICE HOURS:  Tuesday 0915 to 1159. (On Sept. 13th/20th it is from 1030).
                  

E-mail: anil@scs.carleton.ca, WWW:http://www.scs.carleton.ca/~maheshwa.


Term: FALL 2005
Class Hours: Tuesday and Thursday: 1435 to 1555
Venue: SA 502

Course-TAs: 
Ghada Badr Wednesdays from  0830 to 1030 in 1175 HP. She will change her office hour on Oct. 26th and will have it on Oct. 27th the same time.
This is just for that particular date.
Mohammad Nikseresht Friday's from 1000 to 1200 in 1175 HP

Course Objectives: A second course in theoretical aspects of computer science. Topics will include
Formal languages and automata theory (regular languages, finite automata, context-free languages, pushdown automata), computability theory (Turing machines, Church-Turing Thesis, decidability, Halting Problem).

Courses Prerequisites:  COMP 1805
Please revise this course quickly - especially  proof by induction, proof by contradiction, cantor's proof
to show why real numbers are uncountable, and general graph theory - paths, cycles, connectedness.

COURSE NOTES:
Here are course notes for the entire course. 
Please note that these notes are ever changing and they will positively be modified
during the term.  Please let me know if you find errors or typos, or if some parts of the notes "need improvement". Besides reading the course notes,  look at  some of the excellent reference text books.

Reference Books:

Course Evaluation

Final Examination : 55%
Mid-Term Exam :  25%
Assignments (4 Assignments):  20%


Important Dates: Late assignments will not be accepted. Assignments have to be given to me in the class on the due date (before the lecture starts).  Please write neatly, and in case you think that your handwriting
is not that great, then please submit a typed copy (although this will take significant amount of time).
 

Posted Due Date
Assignment 1

Sept 22
Oct 6
Assignment 2

Oct 6
Oct 20
Assignment 3

Nov 1
Nov 15
Assignment 4

Nov 16
Dec 1
Mid-Term
Oct 27

Last Date to Withdraw : November 7
Final Exam:  Please check which date and what time it is!
Final exam includes all the material covered in the class, corresponding sections in the notes, and all the material covered in the assignments and mid-term. This material includes numerous theorems, proofs, definitions, and exercises. Expect proving theorems, stating definitions, solving problems, in the Final Exam. I will mark the final exam in a fairly strict and straighforward manner and will not apply any exception to this. If you have concern on this, please let me know before the classes end.
A wrong proof is worth 0 marks.
A wrong definition is worth 0 marks.
A wrong use of a theorem is worth 0 marks.
A wrong formulation of a problem is worth 0 marks.
Missing states, or transitions, or rules, in a DFA, NFA, RE, CFG, PDAs and Turing Machines may cost huge deduction of marks.



Sept 8: Overview and motivation.

Sept 13/15: Basic Terminology- functions,  alphabets, strings and Languages. Countability - Set of Integers are Countable. Cantor's Diagonalization and Introduction to Finite Automata.

Sept 19/21: Deterministic finite automata: definition and examples,  What does M accepts/rejects w mean?
What is a regular language? How to show that a language is regular. Examples of  Regular Languages. Why Union of two regular sets is regular. Union of two regular sets is regular and Introduction to non-determinism.

Sept 26/28: More examples of NFA's, Definitions of NFA, acceptance and the language.
Equivalence of NFA and DFA.
Equivalence of NFA-DFA examples,  Closure of Regular Languages.
Closure of Regular Languages: union, concatenation, star, intersection, complement

Oct 4/6: Regular Expressions: From Regular Expressions to NFA
From DFA to Regular Expressions

OCt 11/13: From DFA to Regular Expressions and Pumping Lemma
Examples of Pumping Lemma.

Oct. 18/20 Introduction to Context Free Grammars.
Context Free Grammars.
Context Free Grammers, Context Free Languages and Examples.
Chomsky Normal Form.

Oct. 25 : Review, Problems from Assignment/Other Examples

Oct 27 MID-TERM

Nov 1/3: Push Down Automata's
PDA, NPDA and CFG-->NPDA
Pumping Lemma for CFG, Examples of non-context free languages.

Nov 8/10 Pumping Lemma for CFG.
         Turing machines +  Palindrome Example;
        
Nov. 15/17: Multi-tape Turing machines; equivalence with single-tape Turing machines. 
What is an algorithm. Church-Turing Thesis;

Novemner 22/24: Definitions of Turing-decidable;  
                Turing-recognizable languages. 
                Some decidable languages; Every Regular Language and context-free language is decidable;
There are languages that are not recognizable; The language A_TM is recognizable; The language A_TM is undecidable;
A language A is decidable if and only if A and its complement are both recognizable;
The complement of the language A_TM is not recognizable.  Halt is undecidable but recognizable.

Nov. 29/Dec. 1: P v/s NP and meaning of NP-completeness, Review + Problems + Course Evaluation.

HERE ARE SOME SAMPLE SOLUTIONS

SEE YOU IN EXAM



Important Notes:

I do not read e-mails sent from yahoo - and other such domains. They goto my Trash folders. Please send e-mails from Carleton.Ca accounts only and I promise you that I will respond! 


Accommodation of special needs students: Students with disabilities requiring academic accommodations in this course are encouraged to contact a coordinator at the Paul Menton Centre for Students with Disabilities to complete the necessary letters of accommodation. After registering with the PMC, make an appointment to meet and discuss your needs with me at least two weeks prior to the midterm exam. This is necessary in order to ensure sufficient time to make the necessary arrangements. Please check the
deadline for submitting completed forms to the Paul Menton Centre for formally scheduled exam accommodations with the Paul Menton Centre.


http://www.scs.carleton.ca/~maheshwa