This course focuses on three areas central to the theory of computation: automata, computability and complexity, to investigate the question: What are the fundamental capabilities and limitations of computers? We study automata (models of computation) e.g., finite state machines, pushdown automata and Turing machines and the languages recognized by them. We investigate complexity theory, to classify problems as easy or hard and computability theory to classify problems as solvable or not.
See the course outline for more information.
Tuesday, 8:15am–9:05am; Wednesday, 10:15am–11:05am; Friday, 9:15am–10:05am
All lectures are held in Mulroney Hall, room 4032.
M. Sipser, Introduction to the Theory of Computation. Cengage, 3rd edition, 2012.
The textbook is available for sale at the campus bookstore. Course notes will also be provided for each lecture.
- Two assignments (15% each, total 30%)
- Two quizzes (12.5% each, total 25%)
- Written report (total 40%): topic proposal (10%) and report (30%)
- Participation in lectures (5%)
You must complete both the topic proposal and the written report in order to pass the course, even if the weighted sum of your other submissions is at least 50%.
- Sep. 15: The first assignment has been posted. It is due by Oct. 15 at 9:15am.
- Sep. 10: The second set of lecture notes has been posted.
- Sep. 7: The first set of lecture notes has been posted.
- Sep. 1: Welcome to the course! The first lecture is on Sep. 7.
|1||Introduction, mathematical preliminaries||Sipser, 0.1–0.2|
|2||Regular languages: finite automata, nondeterminism, nonregularity||Sipser, 1.1–1.4|
|3||Context-free languages: pushdown automata, grammars, unary CFLs||Sipser, 2.1–2.2|
|4||Context-free languages: ambiguous grammars, non-context-freeness||Sipser, 2.1, 2.3|
|5||Deterministic CFLs, parsing||Sipser, 2.4|
|6||Parsing, state complexity||Sipser, 2.4|
|7||Beyond context-free: Turing machines, variants||Sipser, 3.1–3.2|
|8||Decidability, undecidability, reducibility||Sipser, 4.1–4.2, 5.1–5.3|
|9||Reducibility, Kolmogorov complexity||Sipser, 5.3, 6.3–6.4|
|—||Fall study break||—|
|10||Complexity theory: algorithm analysis, P, NP||Sipser, 7.1–7.3|
|11||NP-completeness, reducibility, space complexity||Sipser, 7.4–7.5, 8.1–8.2|
|12||PSPACE, L, NL, completeness, course review||Sipser, 8.2–8.5|
- Assignment 1, due Oct. 15
- Topic Proposal, due Oct. 29
- Assignment 2, due Nov. 26
- Report, due Dec. 7
Assignments are due at the beginning of class on the due date. Late assignments will be accepted up to the beginning of the first class following the due date. Late assignments are subject to a penalty of 10% deducted from the earned mark.
The topic proposal and report must be submitted on the due date. Late submissions will not be accepted.
Taylor J. Smith
Email: tjsmith [at] stfx [dot] ca
Office: Annex, Room 9A
Student hours: Monday, 2:15pm–3:15pm; Tuesday, 9:15am–10:15am