Theoretical Computer Science  Bridging Course
Graduate Course  Summer Term 2020
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 interactive online exercise lessons. This will prepare the participants for the final exam.
Exam
 Type of exam: The exam will be oral.
 Date: 8th September.
 Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
 Duration: 30 Minutes.
 Place: Probably some seminar room in building 106. We will clarify that soon.
 Measures due to Corona: We might offer to do the exam online via a online conference system (we will clarify that later). If the exam takes place physically, we will have a large, well ventilated room and distancing measures. Also you should bring a mask when entering the building and the seminar room (you can remove it during the exam).
Schedule
There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Tuesday at 12:15  14:00 via the conference system Zoom. The link on how to access the zoom meetings is available on the lecture online access information page, which is only visible from within the university network (i.e., use VPN to access the page from home).
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 Salwa Faour by the given deadlines.
Week  Topic(s)  Assigned Date  Due Date  Exercises  Sample Solution  
1  Mathematical Preliminaries  12.05.2020  19.05.2020  Exercise 01  Solution 01  
2  DFA, NFA, Regular Languages 
19.05.2020  26.05.2020  Exercise 02  Solution 02  
3  Regular Expressions, Pumping Lemma 
26.05.2020  02.06.2020  Exercise 03  Solution 03  
4  ContextFree Grammars Pushdown Automata 
02.06.2020  09.06.2020  Exercise 04  Solution 04  
5  Turing Machines 
09.06.2020  16.06.2020  Exercise 05  Solution 05  
6  Decidability 
16.06.2020  23.06.2020  Exercise 06  Solution 06  
7  Decidability Landau Notation  23.06.2020  30.06.2020  Exercise 07  Solution 07  
8  Complexity  30.06.2020  07.07.2020  Exercise 08  Solution 08  
9  Propositional Logic  07.07.2020  14.07.2020  Exercise 09  Solution 09  
10  Propositional Logic, CNF, DNF, Calculi  14.07.2020  21.07.2020  Exercise 10  Solution10  
11  Revision Sheet  21.07.2020  28.07.2020  Exercise 11  Solution11  
Additional Material

Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.