# Introduction to Automatic Structures

# Introduction to Automatic Structures

##### Course with SWS 2/1/0 (lecture/exercise/practical) in SS 2016

**Lecturer**

**Tutor**

**SWS**

- 2/1/0

**Modules**

- INF-B-510
- INF-B-520
- INF-BAS6
- INF-VERT6
- MCL-TCSL
- MCL-PI
- Theorie der Programmierung Fachgebiet Theorie der Programmierung
- EMCL-A-PI
- EMCL-A-TCSL

**Examination method**

- Oral exam

### Course Description

An automatic structure is one whose domain and atomic relations are computable by finite-state automata. The type of automata considered are those that operate synchronously on their inputs, which can be finite or infinite words or trees. The fundamental property of every automatic structure is that the first order definable relations are computable by automata.

The course will be devoted to the study of (mathematical) structures that can be described by finite state machines such as finite automata, tree automata and omega automata. In particular, we study

- mathematical and algorithmic properties of automata,
- algorithmic and logical properties of automatic structures, and
- typical mathematical structures that are described by automata, e.g. linear orders, Boolean algebras, graphs, and groups.

### Organisation

The lecture takes place weekly on **Mondays 13:00-14:30** (DS 4) in APB E005. All the material necessary for successfully approving the course will be presented during the lecture. Students are strongly recommended to copy the material written on the blackboard during lecture time.

The lecture is accompanied by exercise sessions given every second week on **Tuesdays 09:20-10:50** (DS 2) in APB E005**Mondays 14:50-16:20** (DS 5) in APB 3027. All students are encouraged to present their solutions to the exercises, as they are useful for better understanding of the lecture material. Exercise sheets will be available online about a week before the session.

### Prerequisites

- The course will use notions of automata theory, e.g. basic automata models.
- Solid knowledge of propositional and ideally also first order logic is helpful.

The lecture will be based on the following course material:

Subscribe to events of this course (icalendar)

Lecture | Lecture | DS4, April 4, 2016 in APB E005 | |

Lecture | Lecture | DS4, April 11, 2016 in APB E005 | |

Exercise | Tutorial 1 | DS5, April 11, 2016 in APB 3027 | File |

Lecture | Lecture | DS4, April 18, 2016 in APB E005 | |

Lecture | Lecture | DS4, April 25, 2016 in APB E005 | |

Exercise | Tutorial 2 | DS5, April 25, 2016 in APB 3027 | File |

Lecture | Lecture | DS4, May 2, 2016 in APB E005 | |

Lecture | Lecture | DS4, May 9, 2016 in APB E005 | |

Exercise | Tutorial 3 | DS5, May 9, 2016 in APB 3027 | File |

Lecture | Lecture | DS4, May 23, 2016 in APB E005 | |

Exercise | Tutorial 4 | DS5, May 23, 2016 in APB 3027 | File |

Lecture | Lecture | DS4, May 30, 2016 in APB E005 | |

Lecture | Lecture | DS4, June 6, 2016 in APB E005 | |

Exercise | Tutorial 5 | DS5, June 6, 2016 in APB 3027 | File |

Lecture | Lecture | DS4, June 13, 2016 in APB E005 | |

Exercise | Tutorial 5 (continued) | DS5, June 13, 2016 in APB 3027 | |

Lecture | Lecture | DS4, June 20, 2016 in APB E005 | |

Lecture | Lecture | DS4, June 27, 2016 in APB E005 | |

Exercise | Tutorial 6 | DS5, June 27, 2016 in APB 3027 | |

Lecture | Lecture | DS4, July 4, 2016 in APB E005 | |

Lecture | Lecture | DS4, July 11, 2016 in APB E005 | |

Exercise | Tutorial 7 | DS5, July 11, 2016 in APB 3027 |

### Calendar