Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2022
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.


In conjunction with the the recorded lecture we offer weekly exercise lessons. The exercise lessons will in principle take place hybrid every Tuesday at 12:15 - 14:00 in building 051 room 00-031 and via the video conference system Zoom. The link on how to access the Zoom meetings is available in the data access section below.


There will be an introductory session in the first week of the semester on Tuesday, 26.04.2022 at 12:15 in building 051 room 00-031. Alternatively we will enable participation via Zoom. The link on how to access the Zoom meeting is available in the data access section below.

Final Exam

Type of exam : oral
Date : Friday 26.08.2022
Time: Each Student will be assigned a time slot. You can check your time slot on HisInOnE.
Duration: Approx. 30 minutes.
Place: In the 1st floor seminar room of building 106.

Data Access

Zoom: The link on how to access the weekly Zoom meetings is available here.

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 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 Watch for
Introduction PDF n/a
Mathematical Preliminaries PDF MP4 (44:30) Exercise 1
DFA, NFA, Regular Languages PDF MP4 (1:14:04) Exercise 2
Closure of Regular Languages
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, 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 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, Overview on Normal Forms MP4 (1:39:04)