Automata in the Category of Glued Vector Spaces

TL;DR

This paper introduces a category-theoretic framework for automata that inherently support minimization, presenting a new hybrid class combining deterministic and weighted automata over a field.

Contribution

It develops a novel categorical approach to automata with built-in minimization, and defines a new hybrid automata class bridging deterministic and weighted automata.

Findings

New categorical automata class with minimization by design

Hybrid automata combining deterministic and weighted features

Framework applicable to automata over fields

Abstract

In this paper we adopt a category-theoretic approach to the conception of automata classes enjoying minimization by design. The main instantiation of our construction is a new class of automata that are hybrid between deterministic automata and automata weighted over a field.