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Nd-hypersubstitutions of many-sorted algebras

Denecke K., Lekkoksung S.

Demonstratio Mathematica

2010

Vol. 43, nr 3

519-537

A non-deterministic hypersubstitution maps any operation symbol of type ? to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities ([2]). We can extend those hypersubstitutions to many-sorted non-deterministic hypersubstitutions which map any operation symbol to a tree language of the corresponding sort ([5]). The aim of this paper is to show that the extension of a many-sorted non-deterministic hyper-substitution is an endomorphism of some clone and that the set of all non-deterministic hypersubstitutions of each sort forms a semigroup. These results can be applied to study M-solid many-sorted varieties of tree languages (see [4]).