Simon Fraser University
Engaging the World

Course Outlines

Spring 2020 - CMPT 409 D100

Special Topics in Theoretical Computing Science (3)

Computability + Logic

Class Number: 6751

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2020: Mon, Wed, Fri, 12:30–1:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 19, 2020
    Sun, 12:00–3:00 p.m.
    Burnaby

  • Prerequisites:

    CMPT 307.

Description

CALENDAR DESCRIPTION:

Current topics in theoretical computing science depending on faculty and student interest.

COURSE DETAILS:

Cross-listed with CMPT 701 This course is on theoretical foundations of Computer Science. It provides insights into the nature and limitations of computation and logical reasoning. The first part deals with fundamental theoretical results in logic. It includes first-order logic (syntax and semantics), the completeness theorem for first-order logic, undecidability of first-order logic, Peano Arithmetic, compactness, and Lowenheim-Skolem theorems. We will take a pick into how complexity classes can be characterized in logic, on the example of Fagin's theorem for NP. The second part starts with Register machines as a model of computation and proceeds to the theory of primitive recursive, and then recursive, functions and relations. We use the technique of diagonalization several times in the course, in particular to show the existence of non-enumerable sets. We study the existence of algorithms (effective computational procedures) for solving decision problems. In particular, we learn about the halting problem, for which we prove that no algorithm can solve it. We show that non-computability of many problems follows from a single result, Rice's theorem. We consider Universal functions, Decidability theorem and several result illustrating incompleteness phenomena in mathematics and theory of computation including Tarski's theorem and Godel's Incompleteness Theorems. There is no required textbook. A list of recommended references will be provided. As the main reference, we will use the lecture notes of Stephen A. Cook which will be posted on the course website.

  • Syntax and semantics of propositional and predicate calculus
  • Completeness of Gentzen proof systems
  • Formal theories, nonstandard models
  • Recursive and primitive recursive functions, Computability
  • Church-Turing thesis
  • Computationally unsolvable problems
  • Recursively enumerable sets
  • Godel Incompleteness Theorems

Grading

NOTES:

To be announced in the first week of classes.

Materials

MATERIALS + SUPPLIES:

  • A Mathematical Introduction to Logic, 2nd Edition., Herbert B. Enderton, Elsevier Science, 2001, 9780122384523
  • Introduction to the Theory of Computation, Michael Sipser, Cengage, 2012, 9781133187790

RECOMMENDED READING:

  • A Mathematical Introduction to Logic, 2nd Edition., Herbert B. Enderton, Elsevier Science, 2001, 9780122384523
  • Introduction to the Theory of Computation, Michael Sipser, Cengage, 2012, 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