Theoretical Computer Science  Bridging Course
Graduate Course  Summer Term 2018
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 will be based on existing recordings provided by Diego Tipaldi combined with regular weekly meetings with a tutor.
Schedule
The exercise lessons will take place on Mondays from 12:15 to 13:45 in building 101 room 10101016.
Exam
The exam will take place on 7th of September 2018 at 10:00 am, in room 10101009/13 (the rooms are next to each other). 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).
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)  
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
Responsible for the exercises is Mohamad Ahmadi.
Week  Topic(s)  Assigned Date  Problem Set  Sample Solution  
1  Mathematical Preliminaries  23.04.2018  Exercise 01  Solution 01  
2  DFA, NFA, Regular Languages 
30.04.2018  Exercise 02  Solution 02  
3  Regular Expressions Nonregular Languages 
07.05.2018  Exercise 03  Solution 03  
4  ContextFree Grammars Pushdown Automata 
18.05.2018  Exercise 04  Solution 04  
5  Turing Machines  25.05.2018  Exercise 05  Solution 05  
6  Decidability and Undecidability Halting Problem 
04.06.2018  Exercise 06  Solution 06  
7  Decidability Landau Notation 
11.06.2018  Exercise 07  Solution 07  
8  Complexity  18.06.2018  Exercise 08  Solution 08  
9  Propositional Logic  25.06.2018  Exercise 09  Solution 09  
10  Resolution Calculus First Order Logic 
03.07.2018  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.