Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2020
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 online exercise lessons. This will prepare the participants for the final exam.
Exam
- Type of exam: The exam will be oral.
- Date: 8th September.
- Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
- Duration: 30 Minutes.
- Place: Probably some seminar room in building 106. We will clarify that soon.
- Measures due to Corona: We might offer to do the exam online via a online conference system (we will clarify that later). If the exam takes place physically, we will have a large, well ventilated room and distancing measures. Also you should bring a mask when entering the building and the seminar room (you can remove it during the exam).
Schedule
There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Tuesday at 12:15 - 14:00 via the conference system Zoom. The link on how to access the zoom meetings is available on the lecture online access information page, which is only visible from within the university network (i.e., use VPN to access the page from home).
Slides and Recordings
The course is based on existing recordings provided by Diego Tipaldi
| Topic | Slides | Recordings |
| 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, 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, send your solutions to Salwa Faour by the given deadlines.
| Week | Topic(s) | Assigned Date | Due Date | Exercises | Sample Solution | ||||||||
| 1 | Mathematical Preliminaries | 12.05.2020 | 19.05.2020 | Exercise 01 | Solution 01 | ||||||||
| 2 | DFA, NFA, Regular Languages |
19.05.2020 | 26.05.2020 | Exercise 02 | Solution 02 | ||||||||
| 3 | Regular Expressions, Pumping Lemma |
26.05.2020 | 02.06.2020 | Exercise 03 | Solution 03 | ||||||||
| 4 | Context-Free Grammars Pushdown Automata |
02.06.2020 | 09.06.2020 | Exercise 04 | Solution 04 | ||||||||
| 5 | Turing Machines |
09.06.2020 | 16.06.2020 | Exercise 05 | Solution 05 | ||||||||
| 6 | Decidability |
16.06.2020 | 23.06.2020 | Exercise 06 | Solution 06 | ||||||||
| 7 | Decidability Landau Notation | 23.06.2020 | 30.06.2020 | Exercise 07 | Solution 07 | ||||||||
| 8 | Complexity | 30.06.2020 | 07.07.2020 | Exercise 08 | Solution 08 | ||||||||
| 9 | Propositional Logic | 07.07.2020 | 14.07.2020 | Exercise 09 | Solution 09 | ||||||||
| 10 | Propositional Logic, CNF, DNF, Calculi | 14.07.2020 | 21.07.2020 | Exercise 10 | Solution10 | ||||||||
| 11 | Revision Sheet | 21.07.2020 | 28.07.2020 | Exercise 11 | Solution11 | ||||||||
Additional Material
-
Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.