Non-Confluent NLC Graph Grammar Inference by Compressing Disjoint Subgraphs

TL;DR

This paper explores the inference of non-confluent NLC graph grammar rules from disjoint isomorphic subgraphs, extending previous work by relaxing the non-touching condition and addressing more complex rule structures.

Contribution

It characterizes conditions for inferring NLC graph grammar rules from disjoint isomorphic subgraphs, advancing understanding of graph grammar inference.

Findings

Provides a characterization for rule inference from disjoint subgraphs

Extends previous results to non-confluent graph grammar rules

Addresses more complex graph structures and inference conditions

Abstract

Grammar inference deals with determining (preferable simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly little known on grammar inference for graph grammars. In this paper we take a further step in this direction and work within the framework of node label controlled (NLC) graph grammars. Specifically, we characterize, given a set of disjoint and isomorphic subgraphs of a graph $G$, whether or not there is a NLC graph grammar rule which can generate these subgraphs to obtain $G$. This generalizes previous results by assuming that the set of isomorphic subgraphs is disjoint instead of non-touching. This leads naturally to consider the more involved ``non-confluent'' graph grammar rules.