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:
- Introduction
to the Theory of Computation, by Michael Sipser, PWS Publishing
Company, Boston, 1997.
- Elements
of the Theory of Computation (second edition), by Harry
Lewis and Christos Papadimitriou, Prentice-Hall, 1998.
- Introduction
to Languages and the Theory of Computation (third edition),
by John Martin, McGraw-Hill, 2003.
- Introduction
to Automata Theory, Languages, and Computation (second
edition), by John Hopcroft, Rajeev Motwani, Jeffrey Ullman, Addison
Wesley, 2001.
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).
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!
- Assignment 4 is marked and can be picked from my office.
- Please collect all your assignments etc. from my office by
December 15th (After that they may disappear!)
- Mid-Terms were handed out on Thursday Nov. 3
- Assignment 2 was handed out on Tuesday Nov. 2.
- Mid-Term is in Steacie 310 on Thursday Oct. 27th from 1430 till
1600.
- Assignment 1 is posted at 10AM on Sept. 22. Its on this web-page.
- All assignments and Mid-term are compulsory.
Missed/late assignments and mid-term exams are worth 0%.
- In case a student misses the mid-term due to medical reasons
(doctor's
note required), then her/his marks will be added to the
final exam.
- In order to pass the course, you need to pass in each of the
components,
(a) Sum total of 4 Assignments, (b) Mid-term and (c) Finals,
individually.
- All marked assignments and Mid-term should be retained by
students
as proof of completion. Sometimes assignments are marked and handed
back
but the mark fails to get recorded.
- Students are encouraged to collaborate on assignments, but at the
level of discussion only. When writing down the solutions, they must do
so in their own words.
- Past experience has shown that those who do not put adequate
effort into the assignments do not learn the material and have
extremely high chances of failing the exams.
- Copying of assignments is not tolerated. Such cases will be
referred
to the Director of School of Computer Science and the Dean of Science
for
proper action. THIS POLICY
IS STRICTLY ENFORCED.
- The assignments will be normally marked in one weeks time and
they will brought to the class for pickup. After that they will be
available from the (unattended) bin placed outside my office
door.
- This
explains why I am a bad teacher !
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