Regular Tree Grammar - Derivation of Trees

Derivation of Trees

The grammar implicitly defines a set of trees: any tree that can be derived from using the rule set is said to be described by . This set of trees is known as the language of . To express this more formally, we define the relation on the set as follows:

Wwe say that can be derived in a single step into a tree (in short: ), if there is a context and a production such that:

• , and
• .

Here, a context means a tree with exactly one hole in it; if is such a context, we denote by the result of filling the tree into the hole of .

The tree language generated by is the language .

Here, denotes the set of all trees composed from symbols of, while denotes successive applications of .

A language generated by some regular tree grammar is called a regular tree language.