R70-27 Tree Generating Regular Systems

This paper concerns itself with rooted trees which have labeled nodes. The labels are taken from a stratified alphabet (each label is associated with a nonnegative number, the number of branches descending from it). The alphabet is divided into terminal and nonterminal labels. Tree generating grammars called regular systems are introduced. A set of trees serve as "axioms" and production rules of the form Φ→Ψ, where Φ and Φ are trees, allow successive replacement of subtrees Φ by Ψ. The "language" generated by such a system is the set of trees generable from the axioms containing terminal labels only. Such languages, when trees are written linearly (prefix or postfix form) are context free.