Simon Fraser University
Engaging the World

Course Outlines

Fall 2020 - CMPT 308 D100

Computability and Complexity (3)

Class Number: 6605

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 9 – Dec 8, 2020: Mon, Wed, Fri, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 13, 2020
    Sun, 3:30–6:30 p.m.
    Burnaby

  • Prerequisites:

    MACM 201.

Description

CALENDAR DESCRIPTION:

This course introduces students to formal models of computations such as Turing machines and RAMs. Notions of tractability and intractability are discusses both with respect to computability and resource requirements. The relationship of these concepts to logic is also covered.

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

  • Preliminaries (if needed) - sets, functions, relations, alphabets, strings, asymptotics.
  • 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:

  • 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 2020

Teaching at SFU in fall 2020 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges 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. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).