##
Theoretical Computer Science - Bridging Course

Graduate Course -Summer Term 2024

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 interactive exercise lessons. This will prepare the participants for the final exam.

**Schedule**

In conjunction with the the recorded lecture we offer weekly exercise lessons.
The exercise lessons will take place *in person* every **Tuesday** at **12:05 - 13:50** in building 51, seminar room 51-00-031.

**Announcement**

There will be an introductory session in the first week of the semester on Tuesday, 16.04.2024 at 12:15 in building 51, seminar room 51-00-031.

## Data Access

**Zulip**: An instant messaging platform (Zulip) is offered for all students to discuss any issues related to the course whether among themselves or with the tutor. To join Zulip, click on the invitation link which is also given here.

** Important note: **
The link on how to join Zulip can only be accessed from within the university network (i.e., use VPN to access the page from home or access the internet via the university eduroam).

## Course Material

The course is based on existing recordings provided by Diego Tipaldi

Topic | Slides | Recordings | Watch for |

Introduction | n/a | n/a | |

Mathematical Preliminaries | MP4 (44:30) | Exercise 1 | |

DFA, NFA, Regular Languages | MP4 (1:14:04) | Exercise 2 | |

Closure of Regular Languages | |||

Regular expressions | MP4 (1:37:55) | Exercise 3 | |

Non-regular languages | MP4 (22:12) | ||

Context Free Grammars I | MP4 (1:34:09) | Exercise 4 | |

Context Free Grammars II | MP4 (42:00) | ||

Pushdown Automata | MP4 (1:11:18) | ||

Pumping Lemma for Context Free Grammars | MP4 (1:29:51) | Exercise 5 | |

Turing Machines I | MP4 (52:31) | ||

Turing Machines II | MP4 (1:23:03) | Exercise 6 | |

Decidability and decidable languages | MP4 (52:54) | ||

Decidability, Cardinality, Cantor's diagonal argument | MP4 (1:15:40) | Exercise 7 | |

Decidability and the Halting Problems | MP4 (12:50) | ||

Complexity I | MP4 (1:28:51) | ||

Complexity II | MP4 (1:34:27) | Exercise 8 | |

Complexity III | MP4 (1:28:08) | Exercise 9 | |

Propositional Logic and basic definitions, CNF/DNF, logical entailment. | MP4 (37:11) | Exercise 10 | |

Propositional Logic, Deduction/Contraposition/Contradiction Theorems | MP4 (1:00:14) | ||

Propositional Logic, Derivations, Soundness and Completeness of calculi | MP4 (53:16) | ||

Propositional Logic, Refutation-completeness and Resolution | MP4 (04:16) | ||

First Order Logic, Derivations | MP4 (46:47) | Exercise 11 | |

First Order Logic, Satisfaction, Closed Formulae, Overview on Normal Forms | MP4 (1:39:04) |