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A Kleene theorem for free many-sorted algebras

2026/06/29 by Lü Gong, Raúl Ruiz Mora, Nofre Sanmartín Vich +1 · 1 voice
Computer Science · #cs.LO #cs.FL

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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.

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