Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2017/18
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 exercise lessons will take place each Monday from 12:15 to 1:45 pm in building 101 room SR 01 016 (Georges-Koehler-Allee 101).
Exam
The exam will take place on 13th of March 2018 at 10:00 am, in room 101-01-009/13 (the rooms are next to each other). It will take 90 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).
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 by sending an E-mail to philipp.bamberger(at)cs.uni-freiburg.de or bring your solution as hard copy to the exercise lessons.
| Week | Topic(s) | Assigned Date | Due Date | Exercises | Sample Solution | |
| 1 | Mathematical Preliminaries | 23.10.2017 | 30.10.2017 | Exercise 01 | Solution 01 | |
| 2 | Automata, Regular Languages | 30.10.2017 | 06.11.2017 | Exercise 02 | Solution 02 | |
| 3 | Regular Expressions, Pumping Lemma, ContextFree Grammar 09.11.2017: Fixed important typo in Exercise 1. | 06.11.2017 | 13.11.2017 | Exercise 03 | Solution 03 | |
| 4 | PDA, Chomsky Normal Form, Context Free Grammar | 13.11.2017 | 20.11.2017 | Exercise 04 | Solution 04 | |
| 5 | Turing Machines | 20.11.2017 | 27.11.2017 | Exercise 05 | Solution 05 | |
| 6 | Decidability | 27.11.2017 | 04.12.2017 | Exercise 06 | Solution 06 | |
| 7 | Decidability, Landau Notation | 05.12.2017 | 11.12.2017 | Exercise 07 | Solution 07 | |
| 8 | Decidability, P, NP | 11.12.2017 | 18.12.2017 | Exercise 08 | Solution 08 | |
| 9 | P vs. NP | 18.12.2017 | 15.01.2018 | Exercise 09 | Solution 09 | |
| 10 | Propositional Logic, CNF, DNF, Calculi | 15.01.2018 | 22.01.2018 | Exercise 10 | Solution 10 | |
| 11 | FO Logic, Resolution Calculus | 22.01.2018 | 29.01.2018 | Exercise 11 | Solution 11 | |
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).