A Unified Framework for Reaction Systems Based on Interval Structures

2026-07-14

AI Summary

Existing reaction system models lack a unified semantic foundation in handling multiplicity, resource management, concurrency, and state evolution. This work proposes a unified framework based on interval structures and interval transformation systems, decoupling operational semantics into four orthogonal components: resources, generation, update, and execution strategies, thereby enabling flexible instantiation of diverse reaction system variants. The approach is the first to uniformly characterize multiple classes of reaction systems using interval structures and naturally extends to computational models such as Petri nets. By incorporating a preprocessing mechanism, it further supports quantitative reaction systems. Experimental results reproduce classical models and their variants, demonstrating the framework’s superior expressiveness and generality.

Abstract

Reaction systems have evolved into a rich family of computational models differing in their treatment of multiplicities, resource management, concurrency, and state evolution. We introduce a unified semantic framework based on interval structures and interval-based transformation systems. The framework decomposes operational semantics into independent resource, production, update, and execution strategies, providing a common basis for describing, comparing, and constructing reaction-system variants. We show that classical reaction systems, restricted reaction systems, multiset reaction systems, reaction systems with concentration, and resource-preserving multiset reaction systems are all recovered as instantiations of the framework. Quantitative reaction systems are accommodated through an additional preprocessing stage. We further demonstrate that the framework naturally extends beyond reaction systems to other computational models, including Petri nets. The proposed framework provides a common semantic foundation for existing models and a flexible basis for developing and analysing new computational formalisms.

Problem

• reaction systems
• unified framework
• interval structures
• semantic foundation
• computational models

Innovation

• interval structures
• reaction systems
• unified semantic framework
• interval-based transformation
• computational models