A generalized superposition of linear tree languages and products of linear tree languages

Abstract

A linear tree language of type [Formula: see text] is a set of linear terms, terms containing no multiple occurrences of the same variable, of that type. Instead of the usual generalized superposition of tree languages, we define the generalized linear superposition to deal with linear tree languages and study its properties. Using this superposition, we define the product of linear tree languages. This product is not associative on the collection of all linear tree languages, but it is associative on some subsets of this collection whose products of any element in the subsets are nonempty. We classify such subsets and study properties of the obtained semigroup especially idempotent elements, regular elements, and Green’s relations [Formula: see text] and [Formula: see text].