On the solidity of general varieties of tree languages

Abstract

For a class of hypersubstitutions K, we dene the K-solidity of general varieties of tree languages (GVTLs) that contain tree languages over all alphabets, general varieties ofnite algebras (GVFAs), and general varieties ofnite congruences (GVFCs). We show that if K is a so-called category of substitutions, a GVTL is K-solid exactly in case the corresponding GVFA, or the corresponding GVFC, is K-solid. We establish the solidity status of several known GVTLs with respect to certain categories of substitutions derived from some important classes of tree homomorphisms.