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A Calculus of Chemical Systems

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In Search of Elegance in the Theory and Practice of Computation

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8000))

Abstract

We present the Calculus of Chemical Systems for the modular presentation of systems of chemical equations; it is intended to be a core calculus for rule-based modelling in systems biology. The calculus is loosely modelled after Milner’s Calculus of Communicating Systems, but with communication replaced by chemical reactions. We give a variety of compositional semantics for qualitative and quantitative versions of our calculus, employing a commutative monoid semantical framework. These semantics include (qualitative and quantitative) Petri nets, transition relations, ordinary differential equations (ODEs), and stochastic matrices. Standard semantics of Petri nets, whether of transition relations, ODEs, or stochastic matrices, fit within the framework as commutative monoid homomorphisms. We give complete equational axiomatisations and normal forms for all the semantics, and full abstraction results for the ODE and stochastic semantics. Definability can be characterised in some cases, as was already known for ODEs; other cases, including the stochastic one, remain open.

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Author information

Authors and Affiliations

  1. LFCS, School of Informatics, University of Edinburgh, UK

    Gordon D. Plotkin

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  1. Gordon D. Plotkin
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Editors and Affiliations

  1. Department of Computer and Information Science, University of Pennsylvania, 3330 Walnut St., 19104, Philadelphia, PA, USA

    Val Tannen

  2. School of Computing, National University of Singapore, 13 Computing Drive, 117417, Singapore, Singapore

    Limsoon Wong

  3. School of Informatics, The University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK

    Leonid Libkin , Wenfei Fan  & Michael Fourman ,  & 

  4. Department of Computer Science, University of California, 1156 High Street, 95064, Santa Cruz, CA, USA

    Wang-Chiew Tan

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Plotkin, G.D. (2013). A Calculus of Chemical Systems. In: Tannen, V., Wong, L., Libkin, L., Fan, W., Tan, WC., Fourman, M. (eds) In Search of Elegance in the Theory and Practice of Computation. Lecture Notes in Computer Science, vol 8000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41660-6_24

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  • DOI: https://doi.org/10.1007/978-3-642-41660-6_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41659-0

  • Online ISBN: 978-3-642-41660-6

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