ND-HYPERSUBSTITUTIONS OF MANY-SORTED ALGEBRAS
Klaus Denecke, Somsak Lekkoksung · Demonstratio Mathematica · 2010
A non-deterministic hypersubstitution maps any operation symbol of type r 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 hypersubstitution 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]).