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 01016, 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 00015.
Exam
The exam will take place on 17th of August at 10:00 am, in room 10101016. It will take 120 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).
For future reference we provide the sample solution for this exam: Exam Solution.
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 (electronically preferred) by sending an Email to (Email address to be announced) in due date. If you want to submit the solutions in hard copy, drop it in room 10600004 or 10600005 .
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 Nonregular 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. Refutationcompleteness and Resolution. First Order Logic.  17.07.2017  24.07.2017  Exercise 10  Solution 10 
Tutorial Slides
Starting from the 5th tutorial we used slides which we provide here for future reference.
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).