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<p>Reaction systems are rooted in processes inspired by the functioning of the living cell. The key idea behind the resulting formal model is that such processes 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 of the entities, and so data persistence has to be consciously implemented. Issues like this need to be taken into account in all simulations of 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathscr {R}\)</EquationSource> </InlineEquation> only, transforming the transition system of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathscr {R}\)</EquationSource> </InlineEquation> into a Petri net in 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.</p>

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Encoding reaction systems in Petri nets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月14日

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  • Maciej Koutny,
  • Łukasz Mikulski

摘要

Reaction systems are rooted in processes inspired by the functioning of the living cell. The key idea behind the resulting formal model is that such processes 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 of the entities, and so data persistence has to be consciously implemented. Issues like this need to be taken into account in all simulations of 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 \(\mathscr {R}\) only, transforming the transition system of \(\mathscr {R}\) into a Petri net in 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.