Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2021/22
Fabian Kuhn
Course description
The aim of the course is to provide basic knowledge of theoretical computer science to computer science M.Sc. students who do not yet have this necessary background (e.g., because of a different major during their undergraduate studies). The course introduces the (mathematical) foundations of theoretical computer science. We will see what can be computed and how efficiently, as well as what cannot. More specifically, the following topics will be included:
- Automata
- Formal languages
- Formal grammars
- Turing machines
- Decidability
- Complexity theory
- Logic
Course Format
The course is based on existing recordings provided by Diego Tipaldi. Every week, the assigned lecture recording(s) will be uploaded here on the site. This and combined with weekly interactive online exercise lessons will hopefully prepare the participants for the final exam.
Final Exam
- Type of exam: The exam will be oral.
- Date: 25.02.2022 and 28.02.2022
- Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
- Duration: Approx. 30 minutes.
- Place: Probably some seminar room in building 106. We will clarify that soon.
- Measures due to Corona: Tentative information (might be updated later): You have to bring a proof of vaccination (COVID App). Everyone has to wear a surgical mask or FFP2 mask (or equivalent) during the whole exam.
Announcements
There will be an introductory session in the first week of the semester on Monday, 18.10.2021, 10:15 - 11:00. The session will take place online via the conference system Zoom. The link on how to access the Zoom meetings is available here.
Schedule
There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Monday at 10:15 - 12:00 via the video conference system Zoom. The link on how to access the Zoom meetings is available here.
Instant Messanger: An instant messaging platform (Zulip) is offered for all students to discuss any issues related to the course whether among themselves or with the tutor. To join Zulip, click on the invitation link which is also given here.
Important note: The link on how to access Zoom or join Zulip can only be accessed from within the university network (i.e., use VPN to access the page from home or access the internet via the university eduroam).
Slides and Recordings
The course is based on existing recordings provided by Diego Tipaldi
Topic | Slides | Recordings |
Introduction+Warm up | n/a | |
Mathematical Preliminaries | MP4 (44:30) | |
DFA, NFA, Regular Languages | MP4 (1:14:04) | |
Regular Languages and closure wrt elementary operations | ||
Regular expressions | MP4 (1:37:55) | |
Non-regular languages | MP4 (22:12) | |
Context Free Grammars I | MP4 (1:34:09) | |
Context Free Grammars II | MP4 (42:00) | |
Pushdown Automata | MP4 (1:11:18) | |
Pumping Lemma for Context Free Grammars | MP4 (1:29:51) | |
Turing Machines I | MP4 (52:31) | |
Turing Machines II | MP4 (1:23:03) | |
Decidability and decidable languages. | MP4 (52:54) | |
Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument | MP4 (1:15:40) | |
Decidability and the halting problems. | MP4 (12:50) | |
Complexity I | MP4 (1:28:51) | |
Complexity II | MP4 (1:34:27) | |
Complexity III | MP4 (1:28:08) | |
Propositional Logic and basic definitions, CNF/DNF, logical entailment. | MP4 (37:11) | |
Propositional Logic. Deduction/Contraposition/Contradiction Theorems and Derivations. | MP4 (1:00:14) | |
Propositional Logic. Derivations, Soundness and Completeness of calculi. | MP4 (53:16) | |
Propositional Logic. Refutation-completeness and Resolution. | MP4 (04:16) | |
First Order Logic. Derivations. | MP4 (46:47) | |
First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms. | MP4 (1:39:04) |
Exercises
You will be provided with an exercise sheet every week here on the website, which you should work on at home after watching the according lecture(s), and the solutions will be discussed in the exercise lessons.
It is not mandatory to submit solutions but it is recommended. In case you wish to get feedback on your written solutions (whether using Latex, Word, or handwritten scans), send your solutions via email to Salwa Faour by the given deadlines.
Week | Topic(s) | Assigned Date | Due (midnight) | Exercises | Sample Solution | |
1 | Mathematical Preliminaries | 18.10.2021 | 24.10.2021 | Exercise 01 | Solution 01 | |
2 | DFA, NFA, Regular Languages |
25.10.2021 | 07.11.2021 | Exercise 02 | Solution 02 | |
3 | Regular Expressions, Pumping Lemma |
08.11.2021 | 14.11.2021 | Exercise 03 | Solution 03 | |
4 | Context-Free Grammars Pushdown Automata |
15.11.2021 | 21.11.2021 | Exercise 04 | Solution 04 | |
5 | Turing Machines |
22.11.2021 | 28.11.2021 | Exercise 05 | Solution 05 | |
6 | Decidability |
29.11.2021 | 05.12.2021 | Exercise 06 | Solution 06 | |
7 | Landau Notation and Polynomial Time Decidability | 06.12.2021 | 19.12.2021 | Exercise 07 | Solution 07 | |
8 | Classes P, NP, and NP complete | 20.12.2021 | 09.01.2022 | Exercise 08 | Solution 08 | |
9 | Propositional Logic | 10.01.2022 | 23.01.2022 | Exercise 09 | Solution 09 | |
10 | Predicate Logic | 24.01.2022 | 30.01.2022 | Exercise 10 | Solution 10 | |
11 | Revision Sheet | 31.01.2021 | 06.02.2021 | Exercise 11 | Solution 11 | |
Additional Material
- Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic. - Theoretical Computer Science - Bridging Course Exam Summer 2017 Exam
- Theoretical Computer Science - Bridging Course Exam Winter 2017 Exam
- Theoretical Computer Science - Bridging Course Exam Summer 2018 Exam
- Theoretical Computer Science - Bridging Course Exam Winter 2018 Exam
- Exercises from a previous year of the course