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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course -Summer Term 2024
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.

Schedule

In conjunction with the the recorded lecture we offer weekly exercise lessons. The exercise lessons will take place in person every Tuesday at 12:05 - 13:50 in building 51, seminar room 51-00-031.

Announcement

There will be an introductory session in the first week of the semester on Tuesday, 16.04.2024 at 12:15 in building 51, seminar room 51-00-031.


Data Access

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 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 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) Exercise 3
Non-regular languages MP4 (22:12)
Context Free Grammars I PDF MP4 (1:34:09) Exercise 4
Context Free Grammars II MP4 (42:00)
Pushdown Automata MP4 (1:11:18)
Pumping Lemma for Context Free Grammars MP4 (1:29:51) Exercise 5
Turing Machines I PDF MP4 (52:31)
Turing Machines II MP4 (1:23:03) Exercise 6
Decidability and decidable languages PDF MP4 (52:54)
Decidability, Cardinality, Cantor's diagonal argument MP4 (1:15:40) Exercise 7
Decidability and the Halting Problems MP4 (12:50)
Complexity I PDF MP4 (1:28:51)
Complexity II MP4 (1:34:27) Exercise 8
Complexity III MP4 (1:28:08) Exercise 9
Propositional Logic and basic definitions, CNF/DNF, logical entailment. PDF MP4 (37:11) Exercise 10
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) Exercise 11
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 here on the website, which you should work on at home after watching the assigned lecture(s), and the solutions will be discussed in the exercise lessons. It is not mandatory to submit solutions. However in case you wish to get feedback on your written solutions (whether using Latex, Word, or legible handwritten scans), send your solutions to your assigned tutor Zahra Parsaeian by the given deadlines.


Week Topic(s) Assigned Date Due Exercises Sample Solution

1 Mathematical Preliminaries 16.04.2024 23.04.2024 Exercise 01 Solution 01
2 DFA, NFA, Regular Languages
23.04.2024 30.04.2024 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma
30.04.2024 07.05.2024 Exercise 03 Solution 03
4 Context-Free Grammars
Pushdown Automata
07.05.2024 14.05.2024 Exercise 04 Solution 04
5 Pumping Lemma (CFL), Turing Machines
14.05.2024 28.05.2024 Exercise 05


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