Simon Fraser University
Engaging the World

Course Outlines

Summer 2023 - CMPT 407 D100

Computational Complexity (3)

Class Number: 4006

Delivery Method: In Person

Overview

  • Course Times + Location:

    We 11:30 AM – 12:20 PM
    SSCK 9500, Burnaby

    Fr 10:30 AM – 12:20 PM
    SSCC 9002, Burnaby

  • Exam Times + Location:

    Aug 15, 2023
    8:30 AM – 11:30 AM
    AQ 3005, Burnaby

  • Prerequisites:

    CMPT 307 with a minimum grade of C-. CMPT 308 is recommended.

Description

CALENDAR DESCRIPTION:

Study of what is, and is not, efficiently computable with limited resources (time, space, randomness, parallelism, nondeterminism, interaction, and quantum). Complexity classes and connections among them. Interplay between complexity and algorithm design.

COURSE DETAILS:

Please note this course is cross-listed with CMPT 710

The main goal of Complexity Theory is to answer the question: What can be efficiently computed given limited resources? This is a more "practical" version of the main question of Computability Theory: What can be computed? In this course, we will see a rich landscape of complexity classes that are used to characterize problems according to the required resources (such as time, space, randomness, parallelism). We will discuss some known and conjectured relationships among these classes, obtaining a detailed map of the complexity world. Proving the correctness of this map would involve solving some of the deepest open problems in computer science, including the famous "P vs NP" question.

Topics

  • Time and Space Complexity Classes, Nondeterminism
  • Nonuniformity and Circuit Complexity
  • Randomness
  • Alternation and the Polynomial-Time Hierarchy
  • Interactive Proofs
  • Counting Classes
  • Relativization and Natural Proofs
  • Probabilistically Checkable Proofs
  • Current frontiers in Complexity Theory
  • Quantum Computing

Grading

NOTES:

To be discussed in the first week of classes.

Materials

MATERIALS + SUPPLIES:

Reference Books

  • Computational Complexity, Christos H. Papadimitriou, Addison Wesley, 1995, 9780201530827

REQUIRED READING:

Computational Complexity: A Modern Approach
S. Arora and B. Barak
Cambridge
ISBN: 9780521424264

RECOMMENDED READING:

Introduction to the Theory of Computation
Mike Sipser
Cengage Learning, 2012, 3rd Edition
ISBN: 9781133187790

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/s10-01.html