Theoretical Computer Science  Bridging Course
Graduate Course  Winter Term 2022/23
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 Monday at 10:15  12:00 in building 106, seminar room 10604007 on the 4th floor. We will also enable participation via Zoom for the the students who cannot join us physically. The link on how to access the Zoom meeting is available in the data access section below
Announcement
There will be an introductory session in the first week of the semester on Monday, 17.10.2022 at 10:15 in building 106, seminar room 10604007 on the 4th 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.
Zoom: The link on how to access the weekly Zoom meetings is available here.
Important note: The link on how to access Zoom or 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  Slides  Recordings 
Introduction  n/a  
Mathematical Preliminaries  MP4 (44:30)  
DFA, NFA, Regular Languages  MP4 (1:14:04)  
Closure of Regular Languages  
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, 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  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, Overview on Normal Forms  MP4 (1:39:04) 
Text Books:
[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 