Theoretical Computer Science  Bridging Course
Graduate Course  Winter Term 2019/20
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 final exam.
Schedule
The exercise lessons will take place every Monday from 12:15 to 14:00 in building 101 room SR 01 016 (GeorgesKoehlerAllee 101).
Exam
The exam will take place on 25.02.2020 at 15:00 in room 10101009/13 . The exam will be an openbook 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).
You can see an example of the previous exams here.
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)  
Nonregular 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. Refutationcompleteness 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
You will be provided with an exercise sheet every week, and the solutions will be discussed in the exercise lessons. It is not mandatory to submit solutions. However, in case you wish to get feedback on your written solutions, send your solutions to Mohamad Ahmadi by the given deadlines.
Week  Topic(s)  Assigned Date  Due Date  Exercises  Sample Solution  
1  Mathematical Preliminaries  21.10.2019  28.10.2019  Exercise 01  Solution 01  
2  Automata, Regular Languages  25.10.2019  04.11.2019  Exercise 02  Solution 02  
3  Regular Expressions, Pumping Lemma, ContextFree Grammar  04.11.2019  11.11.2019  Exercise 03  Solution 03  
4  PDA, Chomsky Normal Form, Context Free Grammar  11.11.2019  18.11.2019  Exercise 04  Solution 04  
5  Turing Machines  18.11.2019  25.11.2019  Exercise 05  Solution 05  
6  Decidability  25.11.2019  02.12.2019  Exercise 06  Solution 06  
7  Decidability, Landau Notation  02.12.2019  09.12.2019  Exercise 07  Solution 07  
8  Complexity  09.12.2019  16.12.2019  Exercise 08  Solution 08  
9  Propositional Logic  17.12.2019  13.01.2020  Exercise 09  Solution 09  
10  Propositional Logic, CNF, DNF, Calculi  13.01.2020  20.01.2020  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.
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).