Context-free grammars on trees

  • Authors:
  • William C. Rounds

  • Affiliations:
  • Case Western Reserve University, Cleveland, Ohio

  • Venue:
  • STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
  • Year:
  • 1969

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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.