RNDr. Tomáš Jakl, Ph.D.

Projekty

Algorithms and Game Comonads

Program
Horizon Europe
Poskytovatel
Evropská komise
Kód
101111373
Období
2024 - 2026
Popis
The emerging theory of game comonads establishes a fruitful interplay between category theory, mathematical logic, and algorithms. This theory has shown its power when obtaining new Lovasz-type theorems, preservation theorems and decomposition theorems in finite model theory. In our recent work we show that the theory of game comonads can be leveraged to obtain the two traditional Courcelle theorems, stating FPT decidability of monadic second order logic on classes of bounded tree-width and clique-width. This result is only a first step in concrete algorithmic applications of the theory. The abstract setting of game comonads is a good candidate for a systematic treatment of algorithmic problems. The first objective of the project is to formulate a general theory of FPT decidability in terms of game comonads. To start with, we describe some of the important model-theoretic algorithms.