Summer 2019 - CMPT 308 D100

Computability and Complexity (3)

Class Number: 4796

Delivery Method: In Person

Overview

  • Course Times + Location:

    Mo, We, Fr 1:30 PM – 2:20 PM
    WMC 3260, Burnaby

  • Exam Times + Location:

    Aug 8, 2019
    3:30 PM – 6:30 PM
    AQ 3159, 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, 1-2 midterms and a final examination. The exact grade distribution will be announced at the start of classes.

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:

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

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS