A Unified Framework for Reaction Systems Based on Interval Structures
arXiv:2607.13097
The paper proposes a unified semantic framework based on interval structures that can represent and compare various reaction-system models and related computational formalisms such as Petri nets.
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.