Theoretical Computer Science  Bridging Course
Graduate Course  Winter Term 2016/17
Fabian Kuhn
Exam Notification
The exam will take place on Tuesday, February 21st from 9:00 am to 10:30 in room 08200006 (Kinohoersaal). It will take 90 minutes. The exam will be an openbook exam, which means you are allowed to bring any printed or written material. Electronic equipment will not be 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 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 will be based on existing recordings provided by Diego Tipaldi combined with exercise sheets and weekly meetings with a tutor. In the following weeks the tutorials will take place, somewhat flexibly at the beginning of each week, taking into account the time schedules of the participants.
Course Material
Additional material
A tutorial on how to use the resolution calculus.
The exercise sheet from the question and answer lesson with solutions for selected parts.
Slides and Recordings
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 (electronically preferred) by sending an Email to Philipp Schneider and Chaodong Zheng in due date. If you want to submit the solutions in hard copy, drop it in room 10600004 or 10600005 (offices of Philipp Schneider and Chaodong Zheng).
Week  Topic(s)  Assigned Date  Due Date (23:59)  Problem Set  Sample Solution  
1  Mathematical Preliminaries  20.10.2016  02.11.2016  Exercise 01  Solution 01  
2  DFA, NFA, Regular Languages  28.10.2016  09.11.2016  Exercise 02  Solution 02  
3  Regular expressions Nonregular languages 
02.11.2016  16.11.2016  Exercise 03  Solution 03  
4  Context Free Grammars I Context Free Grammars II 
11.11.2016  23.11.2016  Exercise 04  Solution 04  
5  Pushdown Automata Pumping Lemma for Context Free Grammars 
21.11.2016  30.11.2016  Exercise 05  Solution 05  
6  Turing Machines I Turing Machines II 
28.11.2016  07.12.2016  Exercise 06  Solution 06  
7  Decidability and decidable languages Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument Decidability and the halting problems 
02.12.2016  14.12.2016  Exercise 07  Solution 07  
8  Complexity I Complexity II 
09.12.2016  21.12.2016  Exercise 08  Solution 08  
9  Complexity III  19.12.2016  11.01.2017  Exercise 09  Solution 09  
10  Propositional Logic. Deduction/ Contraposition/Contradiction Theorems and Derivations  08.01.2017  18.01.2017  Exercise 10  Solution 10  
11 
Propositional Logic. Derivations, Soundness and Completeness of calculi Propositional Logic. Refutationcompleteness and Resolution  16.01.2017  25.01.2017  Exercise 11  Solution 11  
12 
First Order Logic. Derivations First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms 
23.01.2017  01.02.2017  Exercise 12  Solution 12  
Additional Material

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).