# The equivalence of boundary and confluent graph grammars on graph languages of bounded degree

## Abstract

Let B-edNCE and C-edNCE denote the families of graph languages generated by boundary and by confluent edNCE graph grammars, respectively. Boundary means that two nonterminals are never adjacent, and confluent means that rewriting steps are order independent. By definition, boundary graph grammars are confluent, so that B-edNCE \(\subseteq\) C-edNCE. Engelfriet et. al. [8] have shown that this inclusion is proper, in general, using certain graph languages of unbounded degree as a witness. We prove that equality holds on graph languages of bounded degree, i.e., B-edNCE_{deg}=C-edNCE_{deg}, where the subscript “deg” refers to graph languages of bounded degree. Thus, for bounded degree, boundary graph grammars are the operator normal form of confluent graph grammars and e.g., the characterization results obtained independently for B-edNCE and C-edNCE can be merged. Our result confirms boundary and confluent graph grammars as notions for context-free graph grammars.

## Keywords

graph grammars boundary and confluent graph grammars operator normal form graph languages of bounded degree## Preview

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