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Algorithms and Complexity
 


Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2017
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 first meeting will be in the third week of the semester on Monday 08.05. from 12:00 - 14:00 in building 101 room 01-016, where we will briefly discuss the content and the format of the course and after that get started with the first lesson. In the following weeks the exercise lessons will take place, where we will discuss the next exercise sheet and hand out your results of the previous exercise sheet.
The question and answer meetings take place every Thursday from 16:15 to 18:00 in building 106 room 00-015.


Exam

The exam will take place on the 17th of August at 10:00 am. It will take 120 min. The exam will be an open-book exam, which means you are allowed to bring any printed or written material. Electronic equipment is not allowed!

We recommend you to write a summary of the topics covered in the lecture. This has two advantages: First, you will see the big picture and also learn the details (if your summary is well crafted and if you do it by yourself). Second you can bring it to the exam in case you can't rememeber some definition (this is way more handy than a book which you have never worked with before).


Course Material

Slides and Recordings

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 (electronically preferred) by sending an E-mail to (Email address to be announced) in due date. If you want to submit the solutions in hard copy, drop it in room 106-00-004 or 106-00-005 .


Week Topic(s) Assigned Date Due Date (23:59) Exercises Sample Solution

1 Mathematical Preliminaries 08.05.2017 15.05.2017 Exercise 01 Solution 01

2 DFA, NFA, Regular Languages 15.05.2017 22.05.2017 Exercise 02 Solution 02

3 Regular expressions
Non-regular languages
22.05.2017 29.05.2017 Exercise 03 Solution 03

4 Context Free Grammars
29.05.2017 12.06.2017 Exercise 04 Solution 04

5 Turing Machines I
Turing Machines II
12.06.2017 19.06.2017 Exercise 05 Solution 05

6 Decidability and decidable languages
Decidability and the halting problem
19.06.2017 26.06.2017 Exercise 06 Solution 06

7 Complexity I
Complexity II
26.06.2017 03.07.2017 Exercise 07 Solution 07

8 Complexity III 03.07.2017 10.07.2017 Exercise 08 Solution 08

9 Propositional Logic. Deduction/ Contraposition/Contradiction Theorems and Derivations 10.07.2017 17.07.2017 Exercise 09 Solution 09

10 Derivations, Soundness and Completeness of calculi.
Refutation-completeness and Resolution.
First Order Logic.
17.07.2017 24.07.2017 Exercise 10


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).