Context-free grammars on trees

Abstract

In this paper we discuss still another version of indexed grammars 1 and macro grammars3,gaining some geometric intuition about the structure of these systems. An ordinary context-free grammar is a rewriting system for strings; we find that a macro grammar is a rewriting system for trees. CF grammars on strings form a special case since strings can be thought of as trees without branching nodes. We consider the special case of finite-state grammars in this report. We define the tree analogue of a non deterministic generalized sequential machine and obtain results about the domain and range of such a mapping. We relate these results to the theory of generalized finite automata6.