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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course - Winter Term 2017/18
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 exercise lessons. This will prepare the participants for the exercise sheets that have to submitted weekly and for the final exam. The exercise sheets are graded and an average score of 50% is required to be admitted to the exam.


Schedule

The exercise lessons will take place each Monday from 12:15 to 1:45 pm in building 101 room SR 01 016 (Georges-Koehler-Allee 101).


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

Submit your solutions by sending an E-mail to philipp.bamberger(at)cs.uni-freiburg.de or bring your solution as hard copy to the exercise lessons.


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

1 Mathematical Preliminaries 23.10.2017 30.10.2017 Exercise 01 Solution 01
2 Automata, Regular Languages 30.10.2017 06.11.2017 Exercise 02 Solution 02
3 Regular Expressions, Pumping Lemma, ContextFree Grammar 09.11.2017: Fixed important typo in Exercise 1. 06.11.2017 13.11.2017 Exercise 03
4 PDA, Chomsky Normal Form, Context Free Grammar 13.11.2017 20.11.2017 Exercise 04
5 20.11.2017 27.11.2017
6 27.11.2017 04.12.2017
7 05.12.2017 11.12.2017
8 11.12.2017 18.12.2017
9 18.12.2017 15.01.2018
10 15.01.2018 22.01.2018
11 22.01.2018 29.01.2018


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

Errata

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).