Goals

This week, we introduce the most important and widely used model of computation, the Turing machine, and start to address the big question of what can and cannot be computed by any machine with a finite description.

The main goals for Week 9 are to:

Understand what cannot be computed by a finite automaton and why.
Use and understand Turing Machines as a model of computing.
Study a definition of computability.
Explore the powers and limitations of Turing Machines.
Understand why some numbers are uncomputable, and what this means.
Learn different variations on Turing Machines and how they can be transformed.

Schedule

Day	“Monday” Cohort	“Tuesday” Cohort	“Wednesday” Cohort	“Thursday” Cohort	“Friday” Cohort
Wed 20 Oct	Preparation	(Week 8)	(Week 8)	(Week 8)	(Week 8)
Thurs 21 Oct	Preparation	Preparation	(Week 8)	(Week 8)	(Week 8)
Fri 22 Oct	Preparation	Preparation	Preparation	(Week 8)	(Week 8)
Sat 23 Oct	Prep Cohort Meeting	Preparation	Preparation	Preparation	(Week 8)
Sun 24 Oct	Revision	Prep Cohort Meeting	Preparation	Preparation	Preparation
Mon 25 Oct	Assessed Meeting	Revision	Prep Cohort Meeting	Preparation	Preparation
Tues 26 Oct	Writeup Due	Assessed Meeting	Revision	Prep Cohort Meeting	Preparation
Wed 27 Oct	(Week 10)	Writeup Due	Assessed Meeting	Revision	Prep Cohort Meeting
Thurs 28 Oct	(Week 10)	(Week 10)	Writeup Due	Assessed Meeting	Revision
Fri 29 Oct	(Week 10)	(Week 10)	(Week 10)	Writeup Due	Assessed Meeting
Sat 30 Oct	(Week 10)	(Week 10)	(Week 10)	(Week 10)	Writeup Due

Cohort Problems

These are the problems you should discuss in your Cohort Meeting, and everyone in your cohort should be prepared to present and discuss solutions to at the Assessed Cohort Meeting:

The problems are posted here and we think its a good idea to look at them early, but you’re not expected to be able to solve them until after doing the readings and watching the videos below.

There is no programming portion for this week.

Peer Evaluation

Your second peer evalution is due with your week 9 writeup. Please complete it following these instructions: Peer Eval.

Reading

This week we discuss the material contained in Chapter 7: Loops and Infinity.

Turing Machines and other similar models of computing are taught in many different ways in many different places. In addition to the course materials, you’ll find plenty of other presentations of this material available on youtube, other textbooks, lecture slides from other universities, blog posts, etc. Please be advised that there are many subtly different presentations of Turing machines, and so what you see elsewhere may differ from what we covered, but the key ideas are universal and should be the same in any good presentation. Typically minor changes are made to the model either for convenience of the context, or so real-world running times are more similar to the running time of the model (more on this in future weeks).

You can read Turing’s paper here: Alan M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem. 1936.

Videos

You can play all the videos using this playlist, but don’t forget to take breaks: Week 9 Playlist (note that in previous semesters this content was covered in week 8).

Some videos are edited from these cs3102 classes (we don’t generally recommend watching the unedited versions, but they are available if you want to):