Congruence based proofs of the recognizability theorems for free many-sorted algebras

TL;DR

This paper extends recognizability theorems from single-sorted to many-sorted free algebras, offering algebraic proofs based on congruence without relying on automata or grammars.

Contribution

It introduces a uniform algebraic approach to recognizability theorems for many-sorted algebras, avoiding traditional automata-based methods.

Findings

Generalized recognizability theorems to many-sorted algebras

Provided algebraic proofs using congruence concepts

Eliminated the need for automata or grammars in proofs

Abstract

We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of them based on the concept of congruence.