Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2017
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 exercise lessons. This will prepare the participants for the exercise sheets that have to submitted weekly and for the final exam. The exercise sheets are graded and an average score of 50% is required to be admitted to the exam.
Schedule
The first meeting will be in the third week of the semester on Monday 08.05. from 12:00 - 14:00 in building 101 room 01-016, where we will briefly discuss the content and the format of the course and after that get started with the first lesson.
In the following weeks the exercise lessons will take place, where we will discuss the next exercise sheet and hand out your results of the previous exercise sheet.
The question and answer meetings take place every Thursday from 16:15 to 18:00 in building 106 room 00-015.
Exam
The exam will take place on 17th of August at 10:00 am, in room 101-01-016. It will take 120 min. 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).
For future reference we provide the sample solution for this exam: Exam Solution.
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
Submit your solutions (electronically preferred) by sending an E-mail to (Email address to be announced) in due date. If you want to submit the solutions in hard copy, drop it in room 106-00-004 or 106-00-005 .
| Week | Topic(s) | Assigned Date | Due Date (23:59) | Exercises | Sample Solution | |
| 1 | Mathematical Preliminaries | 08.05.2017 | 15.05.2017 | Exercise 01 | Solution 01 | |
| 2 | DFA, NFA, Regular Languages | 15.05.2017 | 22.05.2017 | Exercise 02 | Solution 02 | |
| 3 | Regular expressions Non-regular languages |
22.05.2017 | 29.05.2017 | Exercise 03 | Solution 03 | |
| 4 | Context Free Grammars |
29.05.2017 | 12.06.2017 | Exercise 04 | Solution 04 | |
| 5 | Turing Machines I Turing Machines II |
12.06.2017 | 19.06.2017 | Exercise 05 | Solution 05 | |
| 6 | Decidability and decidable languages Decidability and the halting problem |
19.06.2017 | 26.06.2017 | Exercise 06 | Solution 06 | |
| 7 | Complexity I Complexity II |
26.06.2017 | 03.07.2017 | Exercise 07 | Solution 07 | |
| 8 | Complexity III | 03.07.2017 | 10.07.2017 | Exercise 08 | Solution 08 | |
| 9 | Propositional Logic. Deduction/ Contraposition/Contradiction Theorems and Derivations | 10.07.2017 | 17.07.2017 | Exercise 09 | Solution 09 | |
| 10 |
Derivations, Soundness and Completeness of calculi. Refutation-completeness and Resolution. First Order Logic. | 17.07.2017 | 24.07.2017 | Exercise 10 | Solution 10 | |
Tutorial Slides
Starting from the 5th tutorial we used slides which we provide here for future reference.
Additional Material
- Material from previous lectures
-
Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.
Text Books
Errata
There is an error on page 35 of the second set of the lecture slides on which the pumping lemma is stated. The statement should be made about strings s of length at least p from the language A (instead of any string s of length at least p).