Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2021/22
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. Every week, the assigned lecture recording(s) will be uploaded here on the site. This and combined with weekly interactive online exercise lessons will hopefully prepare the participants for the final exam.

Final Exam

  • Type of exam: The exam will be oral.
  • Date: 25.02.2022 and 28.02.2022
  • Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
  • Duration: Approx. 30 minutes.
  • Place: Probably some seminar room in building 106. We will clarify that soon.
  • Measures due to Corona: Tentative information (might be updated later): You have to bring a proof of vaccination (COVID App). Everyone has to wear a surgical mask or FFP2 mask (or equivalent) during the whole exam.


There will be an introductory session in the first week of the semester on Monday, 18.10.2021, 10:15 - 11:00. The session will take place online via the conference system Zoom. The link on how to access the Zoom meetings is available here.


There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Monday at 10:15 - 12:00 via the video conference system Zoom. The link on how to access the Zoom meetings is available here.

Instant Messanger: 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 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).

Slides and Recordings

The course is based on existing recordings provided by Diego Tipaldi

Topic Slides Recordings
Introduction+Warm up PDF n/a
Mathematical Preliminaries PDF MP4 (44:30)
DFA, NFA, Regular Languages PDF MP4 (1:14:04)
Regular Languages and closure wrt elementary operations
Regular expressions MP4 (1:37:55)
Non-regular languages MP4 (22:12)
Context Free Grammars I PDF 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 PDF MP4 (52:31)
Turing Machines II MP4 (1:23:03)
Decidability and decidable languages. PDF 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 PDF 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. PDF 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. Refutation-completeness and Resolution. MP4 (04:16)
First Order Logic. Derivations. PDF MP4 (46:47)
First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms. MP4 (1:39:04)

  • Lecture notes of a previous edition of this course.
    Covers everything except the parts on propositional and first order logic.
  • Theoretical Computer Science - Bridging Course Exam Summer 2017 Exam
  • Theoretical Computer Science - Bridging Course Exam Winter 2017 Exam
  • Theoretical Computer Science - Bridging Course Exam Summer 2018 Exam
  • Theoretical Computer Science - Bridging Course Exam Winter 2018 Exam
  • Exercises from a previous year of the course
  • Text Books

    [sipser] Introduction to the Theory of Computation
    Michael Sipser
    PWS Publishing, 1997, ISBN 0-534-95097-3
    [HMU] Introduction to Automata Theory, Languages, and Computation
    John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman
    Addison-Wesley, 3rd edition, 2006, ISBN 81-7808-347-7
    [mendelson] Introduction to Mathematical Logic
    Elliott Mendelson
    CRC Press, 6th edition, 2015, ISBN-13: 978-1482237726
    [enderton] A Mathematical Introduction to Logic
    Herbert B. Enderton
    Academic Press, 2nd edition, 2001, ISBN-13: 978-0122384523