Algorithms and Game Comonads

Our modern society is driven by computers, digital services, and algorithms. Understanding their weaknesses and limitations is one of the main subjects of study of theoretical computer science.

Probably the most studied aspect of algorithms is their efficiency of use of computational resources, embodied as the running time of an algorithm.

Parameterised complexity is a branch of theoretical computer science interested in determining whether there exists an efficient algorithm that solves a given computational problem.

The efficiency is determined based on the structure of the input data.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.

This project bring together expertise in category theory, in the form of the applicant and expertise in parameterised complexity, in the form of the host institution and the supervisor who will devote their efforts into bridging the gap between the two thus-far mostly disjoint disciplines of computer science and mathematics.