Theoretical Computer Science  Bridging Course
Graduate Course  Winter Term 2024/25
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 exercise lessons. This will prepare the participants for the final exam.
Schedule
In conjunction with the the recorded lecture we offer weekly exercise lessons. The exercise lessons will take place in person every Tuesday at 12:15  14:00 in building 101, room 10101009/13 on the ground floor.
Announcement
There will be an introductory session in the first week of the semester on Tuesday, 15.10.2024 at 12:15 in building 101, room 10101009/13 on the ground floor.
Data Access
Zulip: An instant messaging platform (Zulip) is offered for all students to discuss any issues related to the course whether among themselves or with the tutor. To join Zulip, click on the invitation link which is also given here.
Important note: The link on how to join Zulip can only be accessed from within the university network (i.e., use VPN to access the page from home or access the internet via the university eduroam).
Course Material
The course is based on existing recordings provided by Diego Tipaldi
Topic  Date  Slides  Recordings 
Introduction  15.10  n/a  
Mathematical Preliminaries  22.10  MP4 (44:30)  
DFA, NFA, Regular Languages  05.11  MP4 (1:14:04)  
Closure of Regular Languages  
Regular expressions  12.11  MP4 (1:37:55)  
Nonregular languages  MP4 (22:12)  
Context Free Grammars I  19.11  MP4 (1:34:09)  
Context Free Grammars II  MP4 (42:00)  
Pushdown Automata  MP4 (1:11:18)  
Pumping Lemma for Context Free Grammars  26.11  MP4 (1:29:51)  
Turing Machines I  MP4 (52:31)  
Turing Machines II  03.12  MP4 (1:23:03)  
Decidability and decidable languages  MP4 (52:54)  
Decidability, Cardinality, Cantor's diagonal argument  10.12  MP4 (1:15:40)  
Decidability and the Halting Problems  MP4 (12:50)  
Complexity I  MP4 (1:28:51)  
Complexity II  17.12  MP4 (1:34:27)  
Complexity III  07.01  MP4 (1:28:08)  
Propositional Logic and basic definitions, CNF/DNF, logical entailment.  14.01  MP4 (37:11)  
Propositional Logic, Deduction/Contraposition/Contradiction Theorems  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  21.01  MP4 (46:47)  
First Order Logic, Satisfaction, Closed Formulae, Overview on Normal Forms  MP4 (1:39:04) 
Exercise Material
You will be provided with an exercise sheet every week here on the website, which you should work on at home after watching the assigned lecture(s), 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 (whether using Latex, Word, or legible handwritten scans), send your solutions to your assigned tutor Zahra Parsaeian by the given deadlines.
Text Books:
Week  Topic(s)  Assigned Date  Due  Exercises  Sample Solution  
1  Mathematical Preliminaries  15.10.2024  22.10.2024  Exercise 01  Solution 01  
2  DFA, NFA, Regular Languages 
22.10.2024  05.11.2024  Exercise 02  Solution 02  
3  Regular Expressions, Pumping Lemma 
05.11.2024  12.11.2024  Exercise 03 
[sipser]  Introduction to the Theory of Computation Michael Sipser PWS Publishing, 1997, ISBN 0534950973 

[HMU]  Introduction to Automata Theory, Languages, and Computation John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman AddisonWesley, 3rd edition, 2006, ISBN 8178083477 

[mendelson]  Introduction to Mathematical Logic Elliott Mendelson CRC Press, 6th edition, 2015, ISBN13: 9781482237726 

[enderton]  A Mathematical Introduction to Logic Herbert B. Enderton Academic Press, 2nd edition, 2001, ISBN13: 9780122384523 