Theoretical Computer Science  Bridging Course
Graduate Course  Winter Term 2018/19
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.
Schedule
The exercise lessons will take place each Monday from 12:15 to 1:45 pm in building 101 room SR 01 016 (GeorgesKoehlerAllee 101).
There will be no tutorial on 28th January. On 4th February, there will be a session for questions regarding the complete material of the course.
Exam
The exam will take place on 4th of March 2019 at 2 pm in room 10101009/13 (the rooms are next to each other). It will take 90 min. The exam will be an openbook 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).
Slides and Recordings
The course is based on existing recordings provided by Diego Tipaldi.
Topic  Slides  Recordings 
Mathematical Preliminaries  MP4 (44:30)  
DFA, NFA, Regular Languages  MP4 (1:14:04)  
Regular Languages and closure wrt elementary operations  
Regular expressions  MP4 (1:37:55)  
Nonregular languages  MP4 (22:12)  
Context Free Grammars I  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  MP4 (52:31)  
Turing Machines II  MP4 (1:23:03)  
Decidability and decidable languages.  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  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.  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. Refutationcompleteness and Resolution.  MP4 (04:16)  
First Order Logic. Derivations.  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 Email to philipp.bamberger(at)cs.unifreiburg.de or bring your solution as hard copy to the exercise lessons.
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Week  Topic(s)  Assigned Date  Due Date  Exercises  Sample Solution  
1  Mathematical Preliminaries  22.10.2018  29.10.2018  Exercise 01  Solution 01  
2  Automata, Regular Languages  29.10.2018  05.11.2018  Exercise 02  Solution 02  
3  Regular Expressions, Pumping Lemma, ContextFree Grammar  05.11.2018  12.11.2018  Exercise 03  Solution 03  
4  PDA, Chomsky Normal Form, Context Free Grammar  12.11.2017  19.11.2017  Exercise 04  Solution 04  
5  Turing Machines  19.11.2018  26.11.2018  Exercise 05  Solution 05  
6  Decidability  26.11.2018  03.12.2018  Exercise 06  Solution 06  
7  Decidability, Landau Notation  03.12.2018  10.12.2018  Exercise 07  Solution 07  
8  Decidability, P, NP  10.12.2018  17.12.2018  Exercise 08  Solution 08  
9  P vs. NP  17.12.2017  07.01.2018  Exercise 09  Solution 09  
10  Propositional Logic, CNF, DNF, Calculi  07.01.2019  14.01.2019  Exercise 10  Solution 10  
11  FO Logic, Resolution Calculus  14.01.2019  21.01.2019  Exercise 11  Solution 11  
Additional Material

Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.
Previous Exams (no sample solutions are provided)
Text Books
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).