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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2020/21
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. Every week, the assigned lecture recording(s) will be uploaded here on the site. This and combined with weekly interactive online exercise lessons will hopefully prepare the participants for the final exam.

Final Exam

  • Type of exam: The exam will be oral.
  • Date: March 10
  • Place: Whether the exam can be done physical is yet to be determined.

Schedule

There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Monday at 11:45 - 13:30 via the conference system Zoom. 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).

Slides and Recordings

The course is based on existing recordings provided by Diego Tipaldi

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)

Exercises

You will be provided with an exercise sheet every week here on the website, which you should work on at home after watching the according lecture(s), and the solutions will be discussed in the exercise lessons.
It is not mandatory to submit solutions but it is recommended. In case you wish to get feedback on your written solutions (whether using Latex, Word, or handwritten scans), send your solutions via email to Salwa Faour by the given deadlines.

Instant Messanger: An instant messaging platform (Zulip) will be offered soon for all students to discuss any issues related to the course whether among themselves or with the tutor. Please send an email to your tutor saying which email you want to use for Zulip.


Week Topic(s) Assigned Date Due Date Exercises Sample Solution

1 Mathematical Preliminaries 2.11.2020 9.11.2020 Exercise 01 Solution 01
2 DFA, NFA, Regular Languages
9.11.2020 16.11.2020 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma
16.11.2020 23.11.2020 Exercise 03 Solution 03
4 Context-Free Grammars
Pushdown Automata
23.11.2020 30.11.2020 Exercise 04 Solution 04
5 Turing Machines
30.11.2020 07.12.2020 Exercise 05 Solution 05
6 Decidability
07.12.2020 14.12.2020 Exercise 06 Solution 06
7 Decidability
Landau Notation
14.12.2020 21.12.2020 Exercise 07 Solution 07
8 Complexity 23.12.2020 11.01.2021 Exercise 08 Solution 08
9 Propositional Logic 11.01.2021 18.01.2021 Exercise 09 Solution 09
10 Propositional Logic, CNF, DNF, Calculi, First Order Logic 18.01.2021 25.01.2021 Exercise 10 Solution10
11 Revision Sheet 25.01.2021 01.02.2021 Exercise 11 Solution11


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