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Encoding Reaction Systems in Petri Nets

Lookup NU author(s): Emeritus Professor Maciej KoutnyORCiD, Dr Lukasz Mikulski

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

Reaction systems are rooted in processes inspired by the functioning of the living cell.The key idea behind the resulting formal model is that suchprocesses are determined by the interactions of biochemical reactions.Moreover,such interactions are based on the fundamental mechanisms of facilitation and inhibition.Since their inception, reaction systems have developed into an extensively investigated model of computation with unique characteristics and a wide range of potential applications.The semantical model of reaction systems is based on the concept of system states consisting of sets of entities, and state transformations enacted by sets of reactions. Another important behavioural property is the non-permanency ofthe entities, and so data persistence has to be consciously implemented.Issues like this need to be taken into account in all simulationsof reaction systems by means of other existing models and tools,such as Petri nets. In this paper, we provide four different Petri net encodings of basic reaction systems operating without interacting with external environment.We start from a naive encoding that is based on the behaviour of a reaction system $\RS$ only, transforming the transition system of $\RS$ into a Petri netin the form of a marked graph.Such a solution introduces exponentially many places and transitions.In the subsequent encodings, we cope with this exponentiality ending up with a solution that is polynomial in the size of the original reaction system. We then show how this polynomial encoding can be adapted to provide a polynomial encoding for reaction systems operating with contexts provided by context automata. The encoding method proposed in this paper is modular and can provide a basis for compositional construction of reaction systems.

Publication metadata

Author(s): Koutny M, Mikulski L

Publication type: Article

Publication status: Published

Journal: Natural Computing

Year: 2026

Volume: 25

Online publication date: 14/02/2026

Acceptance date: 07/10/2025

Date deposited: 02/03/2026

ISSN (print): 1567-7818

ISSN (electronic): 1572-9796

Publisher: Springer Nature

URL: https://doi.org/10.1007/s11047-025-10060-7

DOI: 10.1007/s11047-025-10060-7

Data Access Statement: No datasets were generated or analysed during the current study.

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