Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2024/25
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 Tuesday at 12:15 - 14:00 in building 101, room 101-01-009/13 on the ground floor.
Announcement
There will be an introductory session in the first week of the semester on Tuesday, 15.10.2024 at 12:15 in building 101, room 101-01-009/13 on the ground 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.
Important note: The link on how to 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 | Date | Slides | Recordings |
| Introduction | 15.10 | n/a | |
| Mathematical Preliminaries | 22.10 | MP4 (44:30) | |
| DFA, NFA, Regular Languages | 05.11 | MP4 (1:14:04) | |
| Closure of Regular Languages | |||
| Regular expressions | 12.11 | MP4 (1:37:55) | |
| Non-regular languages | MP4 (22:12) | ||
| Context Free Grammars I | 19.11 | MP4 (1:34:09) | |
| Context Free Grammars II | MP4 (42:00) | ||
| Pushdown Automata | MP4 (1:11:18) | ||
| Pumping Lemma for Context Free Grammars | 26.11 | MP4 (1:29:51) | |
| Turing Machines I | MP4 (52:31) | ||
| Turing Machines II | 03.12 | MP4 (1:23:03) | |
| Decidability and decidable languages | MP4 (52:54) | ||
| Decidability, Cardinality, Cantor's diagonal argument | 10.12 | MP4 (1:15:40) | |
| Decidability and the Halting Problems | MP4 (12:50) | ||
| Complexity I | MP4 (1:28:51) | ||
| Complexity II | 17.12 | MP4 (1:34:27) | |
| Complexity III | 07.01 | MP4 (1:28:08) | |
| Propositional Logic and basic definitions, CNF/DNF, logical entailment. | 14.01 | 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 | 21.01 | MP4 (46:47) | |
| First Order Logic, Satisfaction, Closed Formulae, Overview on Normal Forms | MP4 (1:39:04) |
Exercise Material
You will be provided with an exercise sheet every week here on the website, which you should work on at home after watching the assigned lecture(s), and the solutions will be discussed in the exercise lessons. It is not mandatory to submit solutions. However in case you wish to get feedback on your written solutions (whether using Latex, Word, or legible handwritten scans), send your solutions to your assigned tutor Zahra Parsaeian by the given deadlines.
| Week | Topic(s) | Assigned Date | Due | Exercises | Sample Solution | |||||||||||
| 1 | Mathematical Preliminaries | 15.10.2024 | 22.10.2024 | Exercise 01 | Solution 01 | |||||||||||
| 2 | DFA, NFA, Regular Languages |
22.10.2024 | 05.11.2024 | Exercise 02 | Solution 02 | |||||||||||
| 3 | Regular Expressions, Pumping Lemma |
05.11.2024 | 12.11.2024 | Exercise 03 | Solution 03 | |||||||||||
| 4 | Context-Free Grammars Pushdown Automata |
12.11.2024 | 19.11.2024 | Exercise 04 | Solution 04 | |||||||||||
| 5 | Turing Machines |
19.11.2024 | 26.11.2024 | Exercise 05 | Solution 05 | |||||||||||
| 6 | Decidability |
26.11.2024 | 03.12.2024 | Exercise 06 | Solution 06 | |||||||||||
| 7 | Landau Notation and Polynomial Time Decidability | 03.12.2024 | 10.12.2024 | Exercise 07 | Solution 07 | |||||||||||
| 8 | Classes NP | 10.12.2024 | 17.12.2024 | Exercise 08 | Solution 08 | |||||||||||
| 9 | NP complete | 17.12.2024 | 07.01.2025 | Exercise 09 | ||||||||||||
| [sipser] | Introduction to the Theory of Computation Michael Sipser PWS Publishing, 1997, ISBN 0-534-95097-3 |
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| [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 |
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| [mendelson] | Introduction to Mathematical Logic Elliott Mendelson CRC Press, 6th edition, 2015, ISBN-13: 978-1482237726 |
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| [enderton] | A Mathematical Introduction to Logic Herbert B. Enderton Academic Press, 2nd edition, 2001, ISBN-13: 978-0122384523 |
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