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SOS Rules for Equivalences of Reaction Systems

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Functional and Constraint Logic Programming (WFLP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12560))

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Abstract

Reaction Systems (RSs) are a successful computational framework inspired by biological systems. A RS combines a set of entities with a set of reactions over them. Entities can be provided by an external context, used to enable or inhibit each reaction, and also produced by reactions. RS semantics is defined in terms of an (unlabelled) rewrite system: given the current set of entities, a rewrite step consists of the application of all and only the enabled reactions. In this paper we define, for the first time, a compositional labelled transition system for RSs with recursive and nondeterministic contexts, in the structural operational semantics (SOS) style. This is achieved by distilling a signature whose operators directly correspond to the ingredients of RSs and by defining some simple SOS inference rules for any such operator. The rich information recorded in the labels allows us to define an assertion language to tailor behavioural equivalences on some specific properties or entities. The SOS approach is suited to drive additional enhancements of RSs along features such as quantitative measurements of entities and communication between RSs. The SOS rules have been also exploited to design a prototype implementation in logic programming.

Research supported by MIUR PRIN 201784YSZ5 ASPRA, by U. of Pisa PRA_2018_66 DECLWARE, by U. of Sassari: Fondo di Ateneo per la ricerca 2020.

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Notes

  1. 1.

    Conceptually, one could extend labels to record J and Q in separate positions from R and I, respectively, like in \(\langle W\vartriangleright R,J,I,Q,P\rangle \). However, one would then need to rewrite the side conditions of all the rules by replacing R with \(R\cup J\) and I with \(I\cup Q\), because the distinction is never exploited in the SOS rules.

  2. 2.

    https://www3.diism.unisi.it/~falaschi/AssertionsForReactionSystems.

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Acknowledgments

We thank the anonymous reviewers for their detailed and very useful criticisms and recommendations that helped us to improve our paper.

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Authors and Affiliations

  1. Dipartimento di Scienze Economiche e Aziendali, Università di Sassari, Sassari, Italy

    Linda Brodo

  2. Dipartimento di Informatica, Università di Pisa, Pisa, Italy

    Roberto Bruni

  3. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Siena, Italy

    Moreno Falaschi

Authors
  1. Linda Brodo
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  2. Roberto Bruni
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  3. Moreno Falaschi
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Correspondence to Moreno Falaschi .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Michael Hanus

  2. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Brodo, L., Bruni, R., Falaschi, M. (2021). SOS Rules for Equivalences of Reaction Systems. In: Hanus, M., Sacerdoti Coen, C. (eds) Functional and Constraint Logic Programming. WFLP 2020. Lecture Notes in Computer Science(), vol 12560. Springer, Cham. https://doi.org/10.1007/978-3-030-75333-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-75333-7_1

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