The main goals for Week 6 are to:
Synthesize what we have learned about finite computation in the first 5 weeks, and start exploring unbounded computation.
Appreciate the connection between functions and languages, and the different ways of talking about computation.
Understand and be able to formally define a Finite State Automaton, and to reason about the language accepted (or function computed) by a Deterministic Finite Automaton.
Be able to reason about the power of a DFA and understand deeply the proof that DFAs are strictly more powerful than Boolean circuits.
Understand how to interpret Regular Expressions, define them formally, and reason about their capabilities.
The schedule is identical to previous weeks, and repeated here (with updated dates).
|Day||"Tuesday" Cohort||"Wednesday" Cohort||"Thursday" Cohort||"Friday" Cohort||"Sunday" Cohort||"Monday" Cohort|
|Wed 30 Sep||Preparation||(Week 5)||(Week 5)||(Week 5)||(Week 5)||(Week 5)|
|Thu 1 Oct||Preparation||Preparation||(Week 5)||(Week 5)||(Week 5)||(Week 5)|
|Fri 2 Oct||Preparation||Preparation||Preparation||(Week 5)||(Week 5)||(Week 5)|
|Sat/Sun 3/4 Oct||Cohort Meeting||Preparation||Preparation||Preparation||(Week 5)||(Week 5)|
|Mon 5 Oct||Preparation||Cohort Meeting||Preparation||Preparation||Preparation||(Week 5)|
|Tue 6 Oct||Assessed Cohort Meeting||Preparation||Cohort Meeting||Preparation||Preparation||Preparation|
|Wed 7 Oct||Write-up Due||Assessed Cohort Meeting||Preparation||Cohort Meeting||Preparation||Preparation|
|Thu 8 Oct||Week 7||Write-up Due||Assessed Cohort Meeting||Preparation||Cohort Meeting||Preparation|
|Fri 9 Oct||Week 7||Week 7||Write-up Due||Assessed Cohort Meeting||Preparation||Cohort Meeting|
|Sat/Sun 10/11 Oct||Week 7||Week 7||Week 7||Write-up Due||Assessed Cohort Meeting||Preparation|
|Mon 12 Oct||Week 7||Week 7||Week 7||Week 7||Write-up Due||Assessed Cohort Meeting|
|Tue 13 Oct||Week 7||Week 7||Week 7||Week 7||Week 7||Write-up Due|
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.
After the Assessed Cohort Meeting, your Cohort Leader will select one problem that your cohort needs to write-up and submit. The write-up is due by 11:59pm on the day after your assessed cohort meeting (see the schedule above).
This week focuses on material in Chapter 6: Functions with Infinite domains, Automata, and Regular expressions. Our presentation in the videos differs from how things are presented in the textbook (our way of defining a DFA is closer to the Alternate Definition mentioned in Remark 6.3 than the way Definition 6.2 defines a DFA; the book’s presentation on regular expressions is similar to ours, but not identical). Astute readers and viewers are encouraged to look for places where the differences matter, or if they are only cosmetic.
You can play all the videos using this playlist, but don’t forget to take breaks: Week 6 Playlist
These videos are edited from these cs3102 classes (we don't generally recommend watching the unedited versions, but they are available if you want to):
- (Spring 2020) Automata - Full Video, Slides
- (Spring 2020) Regular Expressions and Closure - Full Video, Slides
Warm-up: Questions about Strings (4:01)
Functions and Languages (11:16)
Beyond Finite Functions (8:23)
Finite Automaton for XOR (6:28)
Formalizing Finite State Automata (3:29)
Power of Deterministic Finite Automata (8:15)
Regular Expressions (17:27)