Simon Fraser University
Engaging the World

Course Outlines

Fall 2021 - CMPT 308 D100

Computability and Complexity (3)

Class Number: 4565

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 8 – Dec 7, 2021: Mon, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 8 – Dec 7, 2021: Wed, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Dec 14, 2021
    Tue, 8:30–11:30 a.m.
    Burnaby

  • Prerequisites:

    MACM 201 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. NP-completeness.

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.

COURSE-LEVEL EDUCATIONAL GOALS:

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: Non-determinism, 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, Michael Sipser, Cengage Learning, 2012,3rd Edition

ISBN: 9781133187790

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site 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/s10-01.html

TEACHING AT SFU IN FALL 2021

Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place.  Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.