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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2020
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 online exercise lessons. This will prepare the participants for the final exam.

Exam

  • Type of exam: The exam will be oral.
  • Date: 8th September.
  • Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
  • Duration: 30 Minutes.
  • Place: Probably some seminar room in building 106. We will clarify that soon.
  • Measures due to Corona: We might offer to do the exam online via a online conference system (we will clarify that later). If the exam takes place physically, we will have a large, well ventilated room and distancing measures. Also you should bring a mask when entering the building and the seminar room (you can remove it during the exam).

Schedule

There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Tuesday at 12:15 - 14:00 via the conference system Zoom. The link on how to access the zoom meetings is available on the lecture online access information page, which is only visible from within the university network (i.e., use VPN to access the page from home).

Slides and Recordings

The course is based on existing recordings provided by Diego Tipaldi

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)


Exercises

You will be provided with an exercise sheet every week, 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, send your solutions to Salwa Faour by the given deadlines.


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

1 Mathematical Preliminaries 12.05.2020 19.05.2020 Exercise 01 Solution 01
2 DFA, NFA, Regular Languages
19.05.2020 26.05.2020 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma
26.05.2020 02.06.2020 Exercise 03 Solution 03
4 Context-Free Grammars
Pushdown Automata
02.06.2020 09.06.2020 Exercise 04 Solution 04
5 Turing Machines
09.06.2020 16.06.2020 Exercise 05 Solution 05
6 Decidability
16.06.2020 23.06.2020 Exercise 06 Solution 06
7 Decidability
Landau Notation
23.06.2020 30.06.2020 Exercise 07 Solution 07
8 Complexity 30.06.2020 07.07.2020 Exercise 08 Solution 08
9 Propositional Logic 07.07.2020 14.07.2020 Exercise 09 Solution 09
10 Propositional Logic, CNF, DNF, Calculi 14.07.2020 21.07.2020 Exercise 10 Solution10
11 Revision Sheet 21.07.2020 28.07.2020 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