Finite and algorithmic model theory
Finite and algorithmic model theory
Lehrveranstaltung mit SWS 2/2/0 (Vorlesung/Übung/Praktikum) in SS 2021
Dozent
Tutor
Umfang (SWS)
- 2/2/0
Module
Leistungskontrolle
- Mündliche Prüfung
Finite and algorithmic model theory (summer semester 2020/21)
Course Description
The goal of the lecture is to present a basic mathematical toolkit useful for studying expressivity&complexity of first-order logic and its fragments. It is motivated by applications of logics in computer science (e.g. in formal verification, databases or knowledge representation). The course is recommended to students enjoying theoretical computer science or/and pure mathematics.
Prerequisites
Undergraduate-level knowledge of predicate and first-order logic (syntax&semantics of FO), as well as a little from computational complexity (Turing machines, standard (non)deterministic complexity classes and basic knowledge about undecidable problems), is required. Don't worry if you are not fluent with the mentioned material from computational complexity -- it will be possible to organize some extra lessons to cover the essentials.
Schedule and Location
Because of the ongoing COVID-19 pandemic, all lectures and tutorials will be online, via Zoom, respectively on Tuesdays (14:50 - 16:20) and Wednesdays (11:10 - 12:40). The lecturer and the tutor for the course will be Bartosz Bednarczyk, teaching under the supervision of Sebastian Rudolph.
Lecture plan
The expected content of the lecture will be as follows:
1. Inexpressivity via compactness theorem and why it is not appropriate for finite models.
2. Zero-one laws of FO.
3. Ehrenfeucht-Fraïssé games - a basic tool for showing FO-inexpressivity.
4. FO can express only local properties: Hanf locality with applications to fixed parameter tractability of FO model-checking on graphs of bounded degree.
5. On the complexity of fixed-variable fragments of FO, undecidability of FO.
6. NP-completeness of FO1 and solving finite satisfiability for FO1 with counting quantifiers via integer programming.
7. NExpTime upper bounds for FO2 and exponential model property of FO2.
8. ExpTime upper bound for GF2 and its tree-model property.
9. AExpSpapce=2ExpTime upper bounds for full GF.
Opportunities
B. Bednarczyk is happy to provide research-level master's or bachelor's projects ideas (of different difficulty levels) and to supervise them.
Contact
Please, feel free to contact B. Bednarczyk if you have any further questions.- Erich Grädel et al, Finite Model Theory and Its Applications
- Leonid Libkin, Elements of Finite Model Theory
- Martin Otto, Finite Model Theory — Lecture Notes
- Erich Grädel, Algorithmic Model Theory — Lecture Notes
- Erich Gradel, Egon Börger, Yuri Gurevich, The Classical Decision Problem
Veranstaltungskalender abonnieren (icalendar)
| Vorlesung | Introduction & Compactness method | DS5, 13. April 2021 in Videokonferenz | Datei |
| Übung | Q&A | DS3, 14. April 2021 in Videokonferenz | |
| Vorlesung | Zero-One Laws of FO | DS5, 20. April 2021 in Videokonferenz | Datei |
| Übung | Exercises on Compactness | DS3, 21. April 2021 in Videokonferenz | Datei |
| Vorlesung | The missing proofs on 0-1 law + Intro to EF Games | DS5, 27. April 2021 in Videokonferenz | Datei |
| Übung | Exercises on Zero-One Laws | DS3, 28. April 2021 in APB E005 | Datei |
| Vorlesung | E-F Games | DS5, 4. Mai 2021 in APB E005 | Datei |
| Entfällt | NO EXERCISES | DS3, 5. Mai 2021 in APB E005 | |
| Vorlesung | Proving E-F Games | DS5, 11. Mai 2021 in APB E005 | Datei |
| Übung | Exercises on EF games | DS3, 12. Mai 2021 in APB E005 | Datei |
| Vorlesung | Locality | DS5, 18. Mai 2021 in APB E005 | Datei |
| Übung | Exercises on E-F games and locality | DS3, 19. Mai 2021 in APB E005 | Datei |
| Entfällt | No lecture | DS5, 25. Mai 2021 in APB E005 | |
| Entfällt | No exercises | DS3, 26. Mai 2021 in APB E005 | |
| Vorlesung | Tilings and undecidability of FO | DS5, 1. Juni 2021 in APB E005 | Datei |
| Übung | Exercises on pebble games, Hanf locality and MSO | DS3, 2. Juni 2021 in APB E005 | Datei |
| Vorlesung | Model checking on graphs with bounded degree and NP-completeness of FO1 and C1 | DS5, 8. Juni 2021 in APB E005 | Datei |
| Vorlesung | Decidable fragment of first-order logic, C1 and introduction to FO2 | DS5, 15. Juni 2021 in APB E005 | Datei |
| Übung | Exercises on decidability/undecidability | DS3, 16. Juni 2021 in APB E005 | Datei |
| Vorlesung | The last lecture [recap] | DS5, 20. Juni 2021 in APB E005 | |
| Vorlesung | Finite model property for FO2 | DS5, 22. Juni 2021 in APB E005 | Datei |
| Übung | Exercises on C1 and related logics | DS3, 23. Juni 2021 in APB E005 | Datei |
| Vorlesung | Guarded Fragment: Part 1 | DS5, 29. Juni 2021 in APB E005 | Datei |
| Übung | Exercises on FO2 and related logics | DS3, 30. Juni 2021 in APB E005 | |
| Übung | Exercises on FO2 and related logics: Part II | DS3, 7. Juli 2021 in APB E005 | Datei |
| Vorlesung | Guarded Fragment: Part 2 | DS5, 13. Juli 2021 in APB E005 | Datei |
Kalender
