Fall 2022  CMPT 308 D100
Computability and Complexity (3)
Class Number: 5237
Delivery Method: In Person
Overview

Course Times + Location:
Sep 7 – Dec 6, 2022: Mon, 12:30–1:20 p.m.
BurnabySep 7 – Dec 6, 2022: Thu, 12:30–2:20 p.m.
Burnaby 
Exam Times + Location:
Dec 17, 2022
Sat, 12:00–3:00 p.m.
Burnaby

Instructor:
Valentine Kabanets
kabanets@sfu.ca
1 778 7826912

Prerequisites:
(MACM 201 or CMPT 210) with a minimum grade of C.
Description
CALENDAR DESCRIPTION:
Formal models of computation such as automata and Turing machines. Decidability and undecidability. Recursion Theorem. Connections between computability and logic (Gödel’s Incompleteness). Time and space complexity classes. NPcompleteness.
COURSE DETAILS:
This course focuses on the inherent "complexity" of solving problems using a computer. The goal is to understand why some seemingly simple problems cannot be solved on computers and others have no efficient (ie fast) solution. In the course, we will see the formal notions of computers, computability and complexity. At the successful completion of this course students will understand why, for example, computer viruses are so pervasive and why no one will ever write a perfect virus checker. We will see how these concepts are related to logic, in particular, the famous Incompleteness Theorem of Godel. Finally, we will see a few surprising results from modern complexity, in particular, the results making use of randomness in computation.
Topics
 Turing Machines as a formalization of the intuitive notion of an algorithm.
 Computability (Does a program exist?): basic computability (checking if a program is in an infinite loop), reducibilities and oracles, the Recursion Theorem (existence of computer viruses).
 Review of Logic and Godel's Incompleteness Theorem.
 Complexity Theory: Nondeterminism, the class NP, reductions.
 Randomness in Computation: Interactive Proofs.
 Approximation algorithms and hardness of approximation: Probabilistically Checkable Proofs and the PCP Theorem.
Grading
NOTES:
There will be 4 assignments, 2 midterms and a final examination. The exact grade distribution will be announced at the start of classes.
Students must attain an overall passing grade on the weighted average of exams in the course in order to obtain a clear pass (C or better).
Materials
MATERIALS + SUPPLIES:
Reference Books
 Introduction to Automata Theory, Languages and Computation  3rd Edition, J.E. Hopcroft , Rajeev Motwani, J.D. Ullman, , Addison Wesley, 2006, 9780321455369
REQUIRED READING:
Introduction to the Theory of Computation 3rd Edition
Michael Sipser,
Cengage Learning,
2012
ISBN: 9781133187790
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/coursematerials/mypersonalizedcoursematerials.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s1001.html