Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2018
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 will be based on existing recordings provided by Diego Tipaldi combined with regular weekly meetings with a tutor.


The exercise lessons will take place on Mondays from 12:15 to 13:45 in building 101 room 101-01-016.


The exam will take place on 7th of September 2018 at 10:00 am, in room 101-01-009/13 (the rooms are next to each other). The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment is not allowed!

We recommend you to write a summary of the topics covered in the lecture. This has two advantages: First, you will see the big picture and also learn the details (if your summary is well crafted and if you do it by yourself). Second you can bring it to the exam in case you can't rememeber some definition (this is way more handy than a book which you have never worked with before).

Course Material

Slides and Recordings

Topic Slides Recordings
Introduction 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)


Responsible for the exercises is Mohamad Ahmadi.

Week Topic(s) Assigned Date Problem Set Sample Solution

1 Mathematical Preliminaries 23.04.2018 Exercise 01 Solution 01

2 DFA, NFA, Regular Languages
30.04.2018 Exercise 02 Solution 02

3 Regular Expressions
Non-regular Languages
07.05.2018 Exercise 03 Solution 03

4 Context-Free Grammars
Pushdown Automata
18.05.2018 Exercise 04 Solution 04

5 Turing Machines 25.05.2018 Exercise 05 Solution 05

6 Decidability and Undecidability
Halting Problem
04.06.2018 Exercise 06 Solution 06

7 Decidability
Landau Notation
11.06.2018 Exercise 07 Solution 07

8 Complexity 18.06.2018 Exercise 08 Solution 08

9 Propositional Logic 25.06.2018 Exercise 09 Solution 09

10 Resolution Calculus
First Order Logic
03.07.2018 Exercise 10 Solution 10

Additional Material

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