Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2016
Fabian Kuhn
Exam: Wednesday, 17.8.2016, 10:00 - 12:00, 101-00-010/14
The exam will be 120 minutes. You are allowed to bring any printed or written material to the exam. No electronic equipment will be allowed!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. In the first week (on Mon, 18.4.2016, 12:15, 101-00-010/14), there will be a meeting where we will briefly discuss the content and the format of the course. More details will also be provided here soon.
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 are Anisur Rahaman Molla and Chaodong Zheng. Hand in your solutions (electronically preferred) by sending an E-mail to anisur.rahaman@cs.uni-freiburg.de and chaodong@cs.uni-freiburg.de in due date. If you want to submit the solutions in hard copy, drop it in room no 106-00-005 (office of Chaodong Zheng).
Additional Material
-
Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.