Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2018
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 13:45 in building 101 room 101-01-016.
Exam
The exam will take place on 7th of September 2018 at 10:00 am, in room 101-01-009/13 (the rooms are next to each other). The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment is not allowed!
We recommend you to write a summary of the topics covered in the lecture. This has two advantages: First, you will see the big picture and also learn the details (if your summary is well crafted and if you do it by yourself). Second you can bring it to the exam in case you can't rememeber some definition (this is way more handy than a book which you have never worked with before).
Course Material
Slides and Recordings
| Topic | Slides | Recordings |
| Introduction | 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
Responsible for the exercises is Mohamad Ahmadi.
| Week | Topic(s) | Assigned Date | Problem Set | Sample Solution | ||
| 1 | Mathematical Preliminaries | 23.04.2018 | Exercise 01 | Solution 01 | ||
| 2 | DFA, NFA, Regular Languages |
30.04.2018 | Exercise 02 | Solution 02 | ||
| 3 | Regular Expressions Non-regular Languages |
07.05.2018 | Exercise 03 | Solution 03 | ||
| 4 | Context-Free Grammars Pushdown Automata |
18.05.2018 | Exercise 04 | Solution 04 | ||
| 5 | Turing Machines | 25.05.2018 | Exercise 05 | Solution 05 | ||
| 6 | Decidability and Undecidability Halting Problem |
04.06.2018 | Exercise 06 | Solution 06 | ||
| 7 | Decidability Landau Notation |
11.06.2018 | Exercise 07 | Solution 07 | ||
| 8 | Complexity | 18.06.2018 | Exercise 08 | Solution 08 | ||
| 9 | Propositional Logic | 25.06.2018 | 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.