Abstrakt
Parameterised complexity is a branch of theoretical computer science interested in determining whether there exists an efficient algorithm that solves a given computational problem based on structural constraints for its input. The main limitation of parameterised complexity is that these analyses of computational problems are done on a case-by-case basis. This means that if somebody changes the problem or its parameterisation ever so slightly, the whole analysis has to be redone from scratch.
To tackle this problem we propose to use game comonads, a novel structural approach to logic in computer science. The theory of game comonads draws its strength from category theory, a well-established discipline of mathematics which specialises on compositionality, reusability of its tools and high-level of abstraction. Game comonads, despite being relatively new, have already shown to be a useful tool in the study of finite model theory, which is an adjacent area of study of parameterised complexity.
The primary goal of this project is to bring compositional tools of category theory into the setting of algorithms, with game comonads acting as the connecting glue.