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 (GeorgesKoehlerAllee 101).
Exam
The exam will take place on 13th of March 2018 at 10:00 am, 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.
Week  Topic(s)  Assigned Date  Due Date  Exercises  Sample Solution  
1  Mathematical Preliminaries  23.10.2017  30.10.2017  Exercise 01  
2  Automata, Regular Languages  30.10.2017  06.11.2017  Exercise 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  Turing Machines  20.11.2017  27.11.2017  Exercise 05  
6  Decidability  27.11.2017  04.12.2017  Exercise 06  
7  Decidability, Landau Notation  05.12.2017  11.12.2017  Exercise 07  
8  Decidability, P, NP  11.12.2017  18.12.2017  Exercise 08  
9  P vs. NP  18.12.2017  15.01.2018  Exercise 09  
10  Propositional Logic, CNF, DNF, Calculi  15.01.2018  22.01.2018  Exercise 10  
11  FO Logic, Resolution Calculus  22.01.2018  29.01.2018  Exercise 11  
Additional Material
 Material from previous lectures

Lecture notes of a previous edition of this course.
Covers everything except the parts on propositional and first order logic.
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).