Finite Automata for Efficient Graph Recognition

TL;DR

This paper extends finite automata to graph recognition within a hyperedge replacement framework, enabling efficient, deterministic graph recognition without backtracking under certain conditions.

Contribution

It introduces a method to lift finite automata from strings to graphs and makes them deterministic for efficient recognition.

Findings

Finite automata can be adapted for graph recognition.

Deterministic automata recognize graphs efficiently without backtracking.

Sufficient conditions for backtracking-free recognition are provided.

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.