The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue). If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.

The seminar is open to public and does not require any form of registration.

Visit website for this news | Export event in iCalendar format

- Date
- Tuesday, October 03 2017 at 11:00AM
- Place
- Salle de Conférence (Pavillon des Jardins)
- Speaker
- Dietrich Kuske (TU Ilmenau)

We introduce the logic FOCN(ℙ) which extends first-order logic by counting and by numerical predicates from a set ℙ, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature.

We obtain a locality result showing that every FOCN(ℙ)-formula can be
transformed into a formula in Hanf normal form that is equivalent on all finite
structures of degree at most *d*.
A formula is in Hanf normal form if it is a Boolean
combination of formulas describing the neighbourhood around its tuple of free
variables and arithmetic sentences with predicates from ℙ over atomic statements
describing the number of realisations of a type with a single centre. The
transformation into Hanf normal form can be achieved in time elementary in
*d* and the size of the input formula.
From this locality result, we infer the following applications:

- The Hanf-locality rank of first-order formulas of bounded quantifier alternation depth only grows polynomially with the formula size.
- The model checking problem for the fragment FOC(ℙ) of FOCN(ℙ) on structures of bounded degree is fixed-parameter tractable (with elementary parameter dependence).
- The query evaluation problem for fixed queries from FOC(ℙ) over fully
dynamic databases of degree at most
*d*can be solved efficiently: there is a dynamic algorithm that can enumerate the tuples in the query result with constant delay, and that allows to compute the size of the query result and to test if a given tuple belongs to the query result within constant time after every database update.

- [1] Dietrich Kuske and Nicole Schweikardt. First-order logic with counting. In
*32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, Reykjavik, Iceland, June 20-23, 2017*, pages 1–12. IEEE Computer Society, 2017.

- Private Pages
- RSS
- Page maintained by Stéphane Le Roux and Matthias Fuegger.
- English
- Français