Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2021
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. The online lectures are given in the table further below.


In conjunction with the the recorded lecture we offer weekly online exercise lessons. The exercise lessons will take place online every Wednesday at 12:15 - 14:00 (date was moved) via the conference system Zoom. The link on how to access the Zoom meeting is found in the access data section below. Also a forum will be set up on Zulip for questions about the lecture and the exercises. Further details will be given shortly.


It was requested to move the date of the exercise lesson to Wednesday 12:15 pm - 2 pm. So we will move the exercise session unless there is a objection by someone (so far no one objected on Zulip). Please notify us in case this changed date does not work for you. Otherwise we will meet on Wednesday.

Data Access

The link on how to access the Zoom meetings is available here, which is only visible 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
Mathematical Preliminaries PDF MP4 (44:30)
DFA, NFA, Regular Languages PDF MP4 (1:14:04)
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)

Exercise Material

You will be provided with an exercise sheet every week to practice the lecture material in this section. The solutions will be discussed in the exercise lessons the week after. It is not mandatory to submit solutions. However, in case you wish to get feedback on your written solutions, you have to hand them in by the given deadlines. All submissions must be in, or converted to pdf format.

We recommend to prepare your solutions with Latex for best readability. Solutions prepared with Word or similar text editors or scans or photos of handwritten solutions in pdf format are ok, but must be well readable. Send your solutions via email to salwa.faour@cs.uni-freiburg.de (even exercise numbers) or philipp.schneider@cs.uni-freiburg.de (odd exercise numbers) by the given deadlines.

Exercise Topic Assigned Due (12 pm) Solution

Exercise 01 Mathematical Preliminaries 20.04.2021 27.04.2021 Solution 01
Exercise 02 DFA, NFA, Regular Languages 28.04.2021 05.05.2021 Solution 02
Exercise 03 Regular Expressions, Pumping Lemma 05.05.2021 12.05.2021 Solution 03
Exercise 04 Context-Free Grammars, Pushdown Automata 12.05.2021 19.05.2021 Solution 04
Exercise 05 Turing Machines 19.05.2021 02.06.2021 Solution 05
Exercise 06 Decidability 02.06.2021 09.06.2021 Solution 06
Exercise 07 Polynomial Time Decidability 09.06.2021 16.06.2021 Solution 07
Exercise 08 Class NP & Intro to NP-completeness 16.06.2021 23.06.2021 Solution 08
Exercise 09 More NP-complete Problems & Overview 23.06.2021 30.06.2021 Solution 09
Exercise 10 Propositional Logic, CNF, DNF 30.06.2021 07.07.2021 Solution 10
Exercise 11 Correct & Complete Calculi, Resolution 07.07.2021 14.07.2021 Solution 11
Exercise 12 Predicate Logic 14.07.2021 21.07.2021 Solution 12

Additional Material

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

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