Theoretical Computer Science  Bridging Course
Graduate Course  Summer Term 2016
Fabian Kuhn
Exam: Wednesday, 17.8.2016, 10:00  12:00, 10100010/14
The exam will be 120 minutes. You are allowed to bring any printed or written material to the exam. No electronic equipment will be allowed!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 regular weekly meetings with a tutor. In the first week (on Mon, 18.4.2016, 12:15, 10100010/14), there will be a meeting where we will briefly discuss the content and the format of the course. More details will also be provided here soon.
Course Material
Slides and Recordings
Topic  Slides  Recordings 
Introduction  n/a  
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
Responsible for the exercises are Anisur Rahaman Molla and Chaodong Zheng. Hand in your solutions (electronically preferred) by sending an Email to anisur.rahaman@cs.unifreiburg.de and chaodong@cs.unifreiburg.de in due date. If you want to submit the solutions in hard copy, drop it in room no 10600005 (office of Chaodong Zheng).
Additional Material

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