Introduction to Theory of Computation (COMP 3803)
Fall 2025
Instructor:
Michiel Smid
Office: Herzberg Building 5125C
E-mail: michiel@scs.carleton.ca
Course outline:
Lectures:
- Tuesday and Thursday, 2:35-3:55, check Carleton Central for the
classroom.
- Lectures, tests, and final exam will be in-person.
- You are strongly encouraged to come to class. In the section "What
was done in class", you will find links to video lectures from winter
2021. These videos can be useful if, for some reason, you miss
some classes.
Fall term:
- First lecture: Thursday September 4.
- October 20-24: Fall break, no classes.
- Last lecture: Thursday December 4.
Office hours:
- Office hours will start in the week of September 8 and will be
in-person only.
- Michiel: TBA, Herzberg 5125C.
- TA: TBA.
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:
- Test 1, in class: Thursday October 9.
- Test 2, in class: Thursday October 30.
- Test 3, in class: Thursday November 20.
Grading scheme:
- Test 1: 16%
- Test 2: 17%
- Test 3: 17%
- Final exam: 50%
Problem sets:
- There will be four Problem sets. You do not hand them in and they
will not be marked. They are meant to prepare you for the tests and
final exam. Solutions will be posted.
- Problem set 1: posted on TBA, solutions posted on TBA.
- Problem set 2: posted on TBA, solutions posted on TBA.
- Problem set 3: posted on TBA, solutions posted on TBA.
- Problem set 4: posted on TBA, solutions posted on TBA.
Assignments from the fall term of 2022:
What was done in class (all links to video lectures are from previous
terms):
Tentative schedule, based on the last time I taught this course.
Ignore the dates, they are from last year.
- 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:
- 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:
- November 22:
- November 27:
- 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.
- November 29: