Fall 2020 - CMPT 308 D100
Computability and Complexity (3)
Class Number: 6605
Delivery Method: In Person
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.
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.
- 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.
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
- Michael Sipser
- Cengage Learning
- 3rd Edition
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
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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 (firstname.lastname@example.org or 778-782-3112).