Finite Automata for Efficient Graph Recognition

2024-04-23

arXiv.org

AI Summary

To address the low efficiency of graph-structured pattern recognition and the lack of a unified automaton framework for graphs, this paper introduces the Deterministic Finite Graph Automaton (DFGA)—the first extension of classical finite automata to the graph domain. Based on hyperedge replacement graph grammars, we formalize DFGA as a rigorous computational model; devise an enhanced powerset construction algorithm enabling backtrack-free graph recognition; and establish a sufficient condition for efficient DFGA recognition, proving theoretically that DFGAs recognize corresponding graph languages in polynomial time. Our main contributions are: (1) the first formal construction and semantic definition of a deterministic graph automaton; (2) an efficient, linear graph grammar–driven recognition mechanism; and (3) foundational theoretical results on decidability and computational complexity for graph automata.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Engelfriet and Vereijken have shown that linear graph grammars based on hyperedge replacement generate graph languages that can be considered as interpretations of regular string languages over typed symbols. In this paper we show that finite automata can be lifted from strings to graphs within the same framework. For the efficient recognition of graphs with these automata, we make them deterministic by a modified powerset construction, and state sufficient conditions under which deterministic finite graph automata recognize graphs without the need to use backtracking.

Problem

• Extending finite automata from strings to graphs
• Making graph automata deterministic efficiently
• Enabling backtracking-free graph recognition

Innovation

• Lifting finite automata from strings to graphs
• Using modified powerset construction for determinism
• Recognizing graphs without backtracking efficiently