Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2019
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 will be based on existing recordings provided by Diego Tipaldi combined with regular weekly meetings with a tutor.
Schedule
The exercise lessons will take place on Mondays from 12:15 to 14:00 in room 015 on the ground floor of building 106.
Exam
There will be an oral exam. The date of the exam will be announced accordingly.
Course Material
Slides and Recordings
| Topic | Slides | Recordings |
| Introduction | n/a | 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, 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 Mohamad Ahmadi by the given deadlines.
| Week | Topic(s) | Assigned Date | Problem Set | Sample Solution | ||
| 1 | Mathematical Preliminaries | 29.04.2019 | Exercise 01 | Solution 01 | ||
| 2 | DFA, NFA, Regular Languages |
06.05.2019 | Exercise 02 | Solution 02 | ||
| 3 | Regular Expressions Non-regular Languages |
13.05.2019 | Exercise 03 | Solution 03 | ||
| 4 | Context-Free Grammars Pushdown Automata |
20.05.2019 | Exercise 04 | Solution 04 | ||
| 5 | Turing Machines | 27.05.2019 | Exercise 05 | Solution 05 | ||
| 6 | Decidability and Undecidability Halting Problem |
03.06.2019 | Exercise 06 | Solution 06 | ||
| 7 | Decidability Landau Notation |
17.06.2019 | Exercise 07 | Solution 07 | ||
| 8 | Complexity | 24.06.2019 | Exercise 08 | Solution 08 | ||
| 9 | Propositional Logic | 02.07.2019 | Exercise 09 | Solution 09 | ||
| 10 | Resolution Calculus First Order Logic |
03.07.2018 | Exercise 10 | Solution 10 | ||
Additional Material
-
Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.