6 research outputs found
Eilenberg theorems for many-sorted formations
A theorem of Eilenberg establishes that there exists a bijection between the
set of all varieties of regular languages and the set of all varieties of
finite monoids. In this article after defining, for a fixed set of sorts
and a fixed -sorted signature , the concepts of formation of
congruences with respect to and of formation of -algebras, we
prove that the algebraic lattices of all -congruence formations and of
all -algebra formations are isomorphic, which is an Eilenberg's type
theorem. Moreover, under a suitable condition on the free -algebras and
after defining the concepts of formation of congruences of finite index with
respect to , of formation of finite -algebras, and of formation
of regular languages with respect to , we prove that the algebraic
lattices of all -finite index congruence formations, of all
-finite algebra formations, and of all -regular language
formations are isomorphic, which is also an Eilenberg's type theorem.Comment: 46 page
Quantifier Variance without Collapse
The thesis of quantifier variance is consistent and cannot be refuted via a collapse argument
Congruence based proofs of the recognizability theorems for free many-sorted algebras
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