Descriptive Combinatorics, Computable Combinatorics, and ASI Algorithms

Abstract

We introduce new types of local algorithms, which we call "ASI Algorithms", and use them to demonstrate a link between descriptive and computable combinatorics. This allows us to unify arguments from the two fields, and also sometimes to port arguments from one field to the other. As an example, we generalize a computable combinatorics result of Kierstead and use it to get within one color of the Baire measurable analogue of Vizing's Theorem. We also improve Kierstead's result for multigraphs along the way.