Algorithms and Complexity

Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2016/17
Fabian Kuhn


Exam Notification

The exam will take place on Tuesday, February 21st from 9:00 am to 10:30 in room 082-00-006 (Kinohoersaal). It will take 90 minutes. The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment will not be 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 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 exercise sheets and weekly meetings with a tutor. In the following weeks the tutorials will take place, somewhat flexibly at the beginning of each week, taking into account the time schedules of the participants.

Course Material

Additional material

A tutorial on how to use the resolution calculus.
The exercise sheet from the question and answer lesson with solutions for selected parts.

Slides and Recordings

Topic Slides Recordings
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)


Submit your solutions (electronically preferred) by sending an E-mail to Philipp Schneider and Chaodong Zheng in due date. If you want to submit the solutions in hard copy, drop it in room 106-00-004 or 106-00-005 (offices of Philipp Schneider and Chaodong Zheng).

Week Topic(s) Assigned Date Due Date (23:59) Problem Set Sample Solution

1 Mathematical Preliminaries 20.10.2016 02.11.2016 Exercise 01 Solution 01

2 DFA, NFA, Regular Languages 28.10.2016 09.11.2016 Exercise 02 Solution 02

3 Regular expressions
Non-regular languages
02.11.2016 16.11.2016 Exercise 03 Solution 03

4 Context Free Grammars I
Context Free Grammars II
11.11.2016 23.11.2016 Exercise 04 Solution 04

5 Pushdown Automata
Pumping Lemma for Context Free Grammars
21.11.2016 30.11.2016 Exercise 05 Solution 05

6 Turing Machines I
Turing Machines II
28.11.2016 07.12.2016 Exercise 06 Solution 06

7 Decidability and decidable languages
Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument
Decidability and the halting problems
02.12.2016 14.12.2016 Exercise 07 Solution 07

8 Complexity I
Complexity II
09.12.2016 21.12.2016 Exercise 08 Solution 08

9 Complexity III 19.12.2016 11.01.2017 Exercise 09 Solution 09

10 Propositional Logic. Deduction/ Contraposition/Contradiction Theorems and Derivations 08.01.2017 18.01.2017 Exercise 10 Solution 10

11 Propositional Logic. Derivations, Soundness and Completeness of calculi
Propositional Logic. Refutation-completeness and Resolution
16.01.2017 25.01.2017 Exercise 11 Solution 11

12 First Order Logic. Derivations
First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms
23.01.2017 01.02.2017 Exercise 12 Solution 12

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


There is an error on page 35 of the second set of the lecture slides on which the pumping lemma is stated. The statement should be made about strings s of length at least p from the language A (instead of any string s of length at least p).