A Kleene theorem for free many-sorted algebras

Lü Gong; Raúl Ruiz Mora; Nofre Sanmartín Vich; Enric Cosme Llópez

A Kleene theorem for free many-sorted algebras

Logic in Computer Science 2026-06-29 v1 Formal Languages and Automata Theory

Authors: Lü Gong , Raúl Ruiz Mora , Nofre Sanmartín Vich , Enric Cosme Llópez

Abstract

In this work, we generalize Kleene's theorem from free single-sorted algebras to free many-sorted algebras. Our main result establishes that, under appropriate finitary assumptions, a language of a given sort in a free many-sorted algebra is recognizable if and only if it is regular.

Cite

@article{arxiv.2606.29939,
  title  = {A Kleene theorem for free many-sorted algebras},
  author = {Lü Gong and Raúl Ruiz Mora and Nofre Sanmartín Vich and Enric Cosme Llópez},
  journal= {arXiv preprint arXiv:2606.29939},
  year   = {2026}
}

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35 pages