Automata in the Category of Glued Vector Spaces

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

Automata Minimization: a Functorial Approach

In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: A) We provide sufficient conditions on the output category so that minimization of the corresponding automata is guaranteed. B) We show how to lift adjunctions between the categories for output values to adjunctions between categories of automata. C) We show how this framework can be instantiated to unify several phenomena in automata theory, starting with determinization, minimization and syntactic algebras. We provide explanations of Choffrut's minimization algorithm for subsequential transducers and of Brzozowski's minimization algorithm in this setting.Comment: journal version of the CALCO 2017 paper arXiv:1711.0306

On Structure and Organization: An Organizing Principle

We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding example is the hyperstructure of higher order Brunnian rings and similarly structured many-body systems.Comment: Minor revision of section