Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2022/23
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 combined with weekly interactive exercise lessons. This will prepare the participants for the final exam.
Schedule
In conjunction with the the recorded lecture we offer weekly exercise lessons. The exercise lessons will take place in person every Monday at 10:15 - 12:00 in building 106, seminar room 106-04-007 on the 4th floor. We will also enable participation via Zoom for the the students who cannot join us physically. The link on how to access the Zoom meeting is available in the data access section below
Announcement
There will be an introductory session in the first week of the semester on Monday, 17.10.2022 at 10:15 in building 106, seminar room 106-04-007 on the 4th floor.
Data Access
Zulip: 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.
Zoom: The link on how to access the weekly Zoom meetings is available 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).
Course Material
The course is based on existing recordings provided by Diego Tipaldi
| Topic | Slides | Recordings |
| Introduction | n/a | |
| Mathematical Preliminaries | MP4 (44:30) | |
| DFA, NFA, Regular Languages | MP4 (1:14:04) | |
| Closure of Regular Languages | ||
| 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, 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 | 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, Overview on Normal Forms | MP4 (1:39:04) |
Text Books:
| [sipser] | Introduction to the Theory of Computation Michael Sipser PWS Publishing, 1997, ISBN 0-534-95097-3 |
|
| [HMU] | Introduction to Automata Theory, Languages, and Computation John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman Addison-Wesley, 3rd edition, 2006, ISBN 81-7808-347-7 |
|
| [mendelson] | Introduction to Mathematical Logic Elliott Mendelson CRC Press, 6th edition, 2015, ISBN-13: 978-1482237726 |
|
| [enderton] | A Mathematical Introduction to Logic Herbert B. Enderton Academic Press, 2nd edition, 2001, ISBN-13: 978-0122384523 |
|