Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2016/17
Fabian Kuhn
Exam Notification
The exam will take place on Tuesday, February 21st from 9:00 am to 10:30 in room 082-00-006 (Kinohoersaal). It will take 90 minutes. The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment will not be 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 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 exercise sheets and weekly meetings with a tutor. In the following weeks the tutorials will take place, somewhat flexibly at the beginning of each week, taking into account the time schedules of the participants.
Course Material
Additional material
A tutorial on how to use the resolution calculus.
The exercise sheet from the question and answer lesson with solutions for selected parts.
Slides and Recordings
| 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 Philipp Schneider and Chaodong Zheng in due date. If you want to submit the solutions in hard copy, drop it in room 106-00-004 or 106-00-005 (offices of Philipp Schneider and Chaodong Zheng).
| Week | Topic(s) | Assigned Date | Due Date (23:59) | Problem Set | Sample Solution | |
| 1 | Mathematical Preliminaries | 20.10.2016 | 02.11.2016 | Exercise 01 | Solution 01 | |
| 2 | DFA, NFA, Regular Languages | 28.10.2016 | 09.11.2016 | Exercise 02 | Solution 02 | |
| 3 | Regular expressions Non-regular languages |
02.11.2016 | 16.11.2016 | Exercise 03 | Solution 03 | |
| 4 | Context Free Grammars I Context Free Grammars II |
11.11.2016 | 23.11.2016 | Exercise 04 | Solution 04 | |
| 5 | Pushdown Automata Pumping Lemma for Context Free Grammars |
21.11.2016 | 30.11.2016 | Exercise 05 | Solution 05 | |
| 6 | Turing Machines I Turing Machines II |
28.11.2016 | 07.12.2016 | Exercise 06 | Solution 06 | |
| 7 | Decidability and decidable languages Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument Decidability and the halting problems |
02.12.2016 | 14.12.2016 | Exercise 07 | Solution 07 | |
| 8 | Complexity I Complexity II |
09.12.2016 | 21.12.2016 | Exercise 08 | Solution 08 | |
| 9 | Complexity III | 19.12.2016 | 11.01.2017 | Exercise 09 | Solution 09 | |
| 10 | Propositional Logic. Deduction/ Contraposition/Contradiction Theorems and Derivations | 08.01.2017 | 18.01.2017 | Exercise 10 | Solution 10 | |
| 11 |
Propositional Logic. Derivations, Soundness and Completeness of calculi Propositional Logic. Refutation-completeness and Resolution | 16.01.2017 | 25.01.2017 | Exercise 11 | Solution 11 | |
| 12 |
First Order Logic. Derivations First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms |
23.01.2017 | 01.02.2017 | Exercise 12 | Solution 12 | |
Additional Material
-
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).