Introduction to Theory of Computation (COMP 3803)
Fall 2024
Instructor:
Michiel Smid
Office: Herzberg Building 5125C
E-mail: michiel@scs.carleton.ca
Plagiarism, integrity, university policies:
Lectures:
- Wednesday and Friday, 11:35-12:55, check Carleton Central for the
classroom.
- Lectures, midterm, and final exam will be in-person.
- In the section "What was done in class", you will find links to
video lectures from winter 2021.
Fall term:
- First lecture: Wednesday September 4.
- October 21-25: Fall break, no classes.
- Last lecture: Wednesday December 4.
- No lecture on Friday December 6 (classes follow a Monday schedule).
Office hours:
- Office hours will start in the week of September 9 and will be
in-person only.
- Michiel Smid: Tuesday, 10-11, Herzberg 5125C.
- Alma Arevalo Loyola: Monday, 11-noon, Herzberg 4115.
- Ajay Sandhu: Tuesday 11-noon, Herzberg 4125.
Course calendar description:
Theoretical aspects of computer science. Topics include: formal
languages and automata theory, computability theory.
Prerequisite: COMP 2804.
Precludes additional credit for COMP 2805 (no longer offered).
Lectures three hours a week.
List of topics:
Formal languages and automata theory: regular languages, finite
automata, context-free languages, pushdown automata.
Computability theory: Turing machines, Church-Turing Thesis,
decidability, Halting Problem.
Textbook:
Important dates:
- Assignment 1: posted September 13, due September 27.
- Assignment 2: posted October 4, due October 20.
- Midterm: October 30, in class (and in-person only).
- Assignment 3: posted November 1, due November 17.
- Assignment 4: posted November 15, due December 1.
- Final exam: TBA.
Grading scheme:
- Assignments: 25%
- Midterm: 25%
- Final exam: 50%
Assignments:
- Late assignments will not be accepted.
- You are encouraged to use
LaTeX to type
your solutions. In case you want to learn LaTeX,
here is a tutorial.
- You can use the freely available
Ipe
drawing editor to make figures.
- Each assignment must be submitted as one single PDF file through
Brightspace.
- You can type your solutions, or write them by hand and scan them
(for example, using a scan app on your phone or using a real
scanner).
- Assignment 1 is due Friday September 27, before 23:59.
- Here is Assignment 1 as a
pdf file.
- Here is the LaTeX file.
- Here and
here are the figures.
- Here are the solutions
for Assignment 1.
- Assignment 2 is due Sunday October 20, before 23:59.
- Here is Assignment 2 as a
pdf file.
- Here is the LaTeX file.
- Here are the solutions
for Assignment 2.
- Assignment 3 is due Sunday November 17, before 23:59.
- Here is Assignment 3 as a
pdf file.
- Here is the LaTeX file.
- Here are the solutions
for Assignment 3.
- Assignment 4 is due Sunday December 1, before 23:59.
- Here is Assignment 4 as a
pdf file.
- Here is the LaTeX file.
Assignments from the fall term of 2022:
Midterm:
- The midterm will be on Wednesday October 30, 11:30-12:55,
in-person, in our regular classroom.
- It will be a multiple-choice exam with 18 questions. There will only
be questions about regular languages. Thus, you are supposed to know
everything that was done in class up to, and including, the pumping
lemma, as well as the first two assignments.
- Here is the midterm
from Fall 2022.
- Here is the midterm
from Fall 2023.
- Here is the midterm
from this term.
Final exam:
- Information will be posted here.
What was done in class (all links to video lectures are from previous
terms):
- September 4:
- September 6:
- September 11:
- Union/intersection/complement of regular languages is regular;
regular operations: union, concatenation, and star (Section 2.3).
- Introduction to nondeterministic finite automata
(Section 2.4.1).
- Video
lecture 3.
- September 13:
- Introduction to nondeterministic finite automata
(Sections 2.4.2 and 2.4.3), definition of nondeterministic
finite automaton (Section 2.4.4).
- Converting an NFA without epsilon-transitions to a DFA
(Section 2.5).
- Video
lecture 4.
- September 18:
- Converting an arbitrary NFA to a DFA (Section 2.5).
- Closure under the regular operations (Section 2.6);
Exercise 2.18.
- Video
lecture 5.
- Video
lecture 6.
- September 20:
- Regular expressions (Section 2.7).
- How to convert a regular expression to an NFA (Section 2.8.1).
- Video
lecture 7.
- September 25:
- How to convert a DFA to a regular expression (Section 2.8.2).
- Video
lecture 8.
- September 27:
- October 2:
- Pumping Lemma, more examples (Section 2.9); introduction to
context-free grammars (Section 3.1).
- Video
lecture 10.
- October 4:
- Context-free grammars (Section 3.1); examples of context-free
grammars (Section 3.2).
- Video
lecture 11.
- October 9:
- Converting a DFA to a CFG, every regular language is context-free
(Section 3.3); Chomsky Normal Form (Section 3.4; definition of
CNF, sketch how to convert CFG to CNF).
- Video
lecture 12.
- October 11:
- Deterministic pushdown automata; a^n b^n (Sections 3.5, 3.6.2).
- Video
lecture 13.
- October 16:
- No lecture. Watch the video.
- Deterministic pushdown automata; properly nested parentheses
(Sections 3.5, 3.6.1).
- Nondeterministic pushdown automata (Section 3.6.3).
- Video
lecture 14.
- October 18:
- No lecture. Watch the video.
- Converting a context-free grammar to a nondeterministic pushdown
automaton (Section 3.7); statement of the pumping lemma for
context-free languages (Section 3.8); first example in
Section 3.8.2.
- Video
lecture 15.
- October 21-25: Fall break.
- October 30: Midterm.
- November 1:
- Statement of the pumping lemma (Section 3.8); examples in
Section 3.8.2.
- Video
lecture 16.
- November 6:
- Proof of the pumping lemma (Section 3.8.1).
-
Turing machines
(Section 4.1); accepting palindromes using a one-tape Turing
machine (Section 4.2.1).
- Video
lecture 17.
- November 8:
- Accepting palindromes using a two-tape Turing machine
(Section 4.2.2).
- More examples of Turing machines (Sections 4.2.3, 4.2.4, 4.2.5).
- Equivalence of multi-tape Turing machines and single-tape Turing
machines (Section 4.3).
- Video
lecture 18.
- November 13:
- What is an algorithm? Church-Turing Thesis (Section 4.4);
definition of a language being decidable (Section 5.1);
the languages A_DFA, A_NFA, and A_CFG are decidable; every
context-free language is decidable (Sections 5.1.1, 5.1.2,
5.1.3).
- The Halting
Problem is undecidable (Section 5.1.5).
- Video
lecture 19.
- November 15:
- November 20:
Tentative schedule, based on the last time I taught this course.
IGNORE ALL DATES BELOW; THEY ARE FROM LAST YEAR!!!!!!!!!!!
- November 29:
- December 4:
- Language A is decidable if and only if both A and its complement
are enumerable (Section 5.7); Halt is enumerable, but its
complement is not enumerable (Section 5.7); both EQ_TM and its
complement are not enumerable (Section 5.8); the set of all
enumerable languages is countable (Section 5.6.1); the set of
all languages is not countable (Section 5.6.2).
- Video
lecture 23.
- December 6: