# Theoretical Computer Science (Bridging Course) - WS 2014/15

## Aims of the lecture

The participants should get a foundational knowledge of the theoretical aspects of computer science.## Contents of the lecture

This course will address theoretical aspects of computer science. It comprises the fundamental mathematical properties of computer hard- and software. 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

## People

- Lecturer: Gian Diego Tipaldi
- Tutor: Federico Boniardi

## Rooms and Times

There will be no classical face to face lectures. Instead, the participants are supposed to follow the video recordings themselves. We provide exercise sheets and tutorials every week, to make sure the material is understood properly.- Lecture:
- Mon 20 April 2015, 10-12 in building 52, SR 02-017: Introduction

- Tutorials:
- Mon, 10-12 in building 52, SR 02-017: By appointment

- Final Exam:
- Mon 31st August 2015, 10-12 in building 101, SR 01-016

## Language

Lectures are held in English, course material and exercise sheets are in English. Students may ask questions and submit exercise sheets in English.## Credit Points

6 ECTS points## Course Book

Michael Sipser. "Introduction to the theory of computation". PWS Publishing Co., Boston, MA, 1996## Additional Information

- There is a QnA forum from the last semester for questions.
- Teaching is done in English.

## Material

Topic | Slides | Videos | Homework Assignment | Solutions |

Introduction | 00.pdf | n/a | --- | --- |

Mathematical Preliminiaries | 02.pdf | MP4 | Sheet0 | Sheet0 |

DFA, NFA, Regular Languages | 03.pdf | MP4 | Sheet1 | Sheet1 |

Regular Languages and closure wrt elementary operations | --- | --- | ||

Regular expressions | MP4 | Sheet2 | Sheet2 | |

Non-regular languages | MP4 | --- | --- | |

Context Free Grammars | 04.pdf | MP4 | Sheet3 | Sheet3 |

Context Free Grammars | MP4 | --- | --- | |

Pushdown Automata | MP4 | Sheet4 | Sheet4 | |

Pumping Lemma for Context Free Grammars | MP4 | Sheet5 | Sheet5 | |

Turing Machines | 05.pdf | MP4 | --- | --- |

Turing Machines | MP4 | Sheet6 | Sheet6 | |

Decidability and decidable languages. | 06.pdf | MP4 | --- | --- |

Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument | MP4 | Sheet7 | Sheet7 | |

Decidability and the halting problems. | MP4 | --- | --- | |

Complexity | 07.pdf | MP4 | Sheet8 | Sheet8 |

Complexity | MP4 | --- | --- | |

Complexity | MP4 | Sheet9 | Sheet9 | |

Complexity | MP4 | Sheet10 | Sheet10 | |

Propositional Logic and basic definitions, CNF/DNF, logical entailment. | 08.pdf | MP4 | --- | --- |

Propositional Logic. Deduction/Contraposition/Contradiction Theorems and Derivations. | MP4 | Sheet11 | Sheet11 | |

Propositional Logic. Derivations, Soundness and Completeness of calculi. | MP4 | --- | --- | |

Propositional Logic. Refutation-completeness and Resolution. | MP4 | Sheet12 | Sheet12 | |

First Order Logic. Derivations. | 09.pdf | MP4 | --- | --- |

First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms. | MP4 | --- | --- | |

Review of some old exam questions. QnA. | Revision Sheet | n/a | --- | Solutions |