Fall 2022 - CMPT 308 D100
Computability and Complexity (3)
Class Number: 5237
Delivery Method: In Person
Course Times + Location:
Mo 12:30 PM – 1:20 PM
SSCK 9500, Burnaby
Th 12:30 PM – 2:20 PM
SSCK 9500, Burnaby
Exam Times + Location:
Dec 17, 2022
12:00 PM – 3:00 PM
SSCC 9000, Burnaby
1 778 782-6912
Prerequisites:(MACM 201 or CMPT 210) with a minimum grade of C-.
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.
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.
- 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.
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 + SUPPLIES:
- Introduction to Automata Theory, Languages and Computation - 3rd Edition, J.E. Hopcroft , Rajeev Motwani, J.D. Ullman, , Addison Wesley, 2006, 9780321455369
Introduction to the Theory of Computation 3rd Edition
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
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