Weak Greibach Normal Form for Hyperedge Replacement Grammars

TL;DR

This paper introduces a weak Greibach normal form for hyperedge replacement grammars, enabling the generation of a broad class of hypergraph languages, including star graphs, and generalizes existing proofs from string grammars.

Contribution

It presents a new weak Greibach normal form for hyperedge replacement grammars that covers more hypergraph languages than previous normal forms.

Findings

Every context-free hypergraph language can be generated by a grammar in this normal form.

The proof generalizes the string grammar case with additional technical considerations.

Includes a normal form corresponding to lexicalized string grammar forms.

Abstract

It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they do not cover a large class of hypergraph languages (e.g. languages consisting of star graphs). In this paper, we introduce a weak Greibach normal form, whose definition corresponds to the lexicalized normal form for string grammars, and prove that every context-free hypergraph language (with nonsubstantial exceptions) can be generated by a grammar in this normal form. The proof presented in this paper generalizes a corresponding one for string grammars with a few more technicalities.