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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2021/22
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: 25.02.2022 and 28.02.2022
  • Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
  • Duration: Approx. 30 minutes.
  • Place: Probably some seminar room in building 106. We will clarify that soon.
  • Measures due to Corona: Tentative information (might be updated later): You have to bring a proof of vaccination (COVID App). Everyone has to wear a surgical mask or FFP2 mask (or equivalent) during the whole exam.

Announcements

There will be an introductory session in the first week of the semester on Monday, 18.10.2021, 10:15 - 11:00. The session will take place online via the conference system Zoom. The link on how to access the Zoom meetings is available here.

Schedule

There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Monday at 10:15 - 12:00 via the video conference system Zoom. The link on how to access the Zoom meetings is available here.

Instant Messanger: 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 access Zoom or 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).

Slides and Recordings

The course is based on existing recordings provided by Diego Tipaldi

Topic Slides Recordings
Introduction+Warm up 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.


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

1 Mathematical Preliminaries 18.10.2021 24.10.2021 Exercise 01 Solution 01
2 DFA, NFA, Regular Languages
25.10.2021 07.11.2021 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma
08.11.2021 14.11.2021 Exercise 03 Solution 03
4 Context-Free Grammars
Pushdown Automata
15.11.2021 21.11.2021 Exercise 04 Solution 04
5 Turing Machines
22.11.2021 28.11.2021 Exercise 05 Solution 05
6 Decidability
29.11.2021 05.12.2021 Exercise 06 Solution 06
7 Landau Notation and Polynomial Time Decidability
06.12.2021 19.12.2021 Exercise 07 Solution 07
8 Classes P, NP, and NP complete 20.12.2021 09.01.2022 Exercise 08 Solution 08
9 Propositional Logic 10.01.2022 23.01.2022 Exercise 09 Solution 09
10 Predicate Logic 24.01.2022 30.01.2022 Exercise 10 Solution 10
11 Revision Sheet 31.01.2021 06.02.2021 Exercise 11 Solution 11

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