Graph Surfing in Reaction Systems from a Categorial Perspective

TL;DR

This paper introduces a categorical framework for graph-based reaction systems, enabling the use of diverse data structures like graphs and hypergraphs for modeling reactions.

Contribution

It extends reaction systems to a categorical setting, broadening their applicability to various graph-like structures beyond simple graphs.

Findings

Categorical approach unifies various graph structures in reaction systems

Enables modeling of complex reactions on hypergraphs and similar structures

Provides a foundation for future research in graph-based reaction modeling

Abstract

Graph-based reaction systems were recently introduced as a generalization of the intensely studied set-based reaction systems. They deal with simple edge-labeled directed graphs, and dynamic semantics of graph-based reaction systems is defined by graph surfing as a novel kind of graph transformation where, in a single surf step, reactions are applied to a subgraph of a given background graph yielding a successor subgraph. In this paper, we propose a categorical approach to reaction systems so that a wider spectrum of data structures becomes available on which reaction systems can be based. In this way, many types of graphs, hypergraphs, and graph-like structures are covered.