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A Global Occurrence Counting Analysis for Brane Calculi

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Book cover Logic-Based Program Synthesis and Transformation (LOPSTR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9527))

Abstract

We propose a polynomial static analysis for Brane Calculi [6], based on Abstract Interpretation [8] techniques. The analysis provides a description of the possible hierarchical structure of membranes and of the processes possibly associated to each membrane, together with global occurrence counting information. Our analysis can be applied in the biological setting to investigate systems in which the information on the number of membranes occurring in the system plays a crucial role.

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Notes

  1. 1.

    For brevity, from now on, we will usually write membrane \(\varGamma \), instead of membrane labelled by \(\varGamma \).

  2. 2.

    Here, \(X \subseteq {\mathtt{Sys}}\) stands for the set of systems that are reachable from system P.

  3. 3.

    We also assume the system S to be well labelled.

  4. 4.

    For simplicity, we omit the explicit indication of the parameter d (assume fixed once for all).

  5. 5.

    For simplicity, we use \({t^{\circ }} \) for both abstract systems and processes.

  6. 6.

    For simplicity, we omit the explicit indication of the parameter d when is clear from the context.

  7. 7.

    where \( lfp \) is the least fixed point.

  8. 8.

    Note that giving the two membrane sources the same label does not influence the result.

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Authors and Affiliations

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

    Chiara Bodei, Roberta Gori & Francesca Levi

  2. Dipartimento di Scienze Politiche, Scienze della Comunicazione e Ingegneria dell’Informazione, Università di Sassari, Sassari, Italy

    Linda Brodo

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

    Diana Hermith

Authors
  1. Chiara Bodei
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  2. Linda Brodo
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  3. Roberta Gori
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  4. Diana Hermith
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  5. Francesca Levi
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Corresponding author

Correspondence to Chiara Bodei .

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Editors and Affiliations

  1. Università di Siena, Siena, Italy

    Moreno Falaschi

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Bodei, C., Brodo, L., Gori, R., Hermith, D., Levi, F. (2015). A Global Occurrence Counting Analysis for Brane Calculi. In: Falaschi, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2015. Lecture Notes in Computer Science(), vol 9527. Springer, Cham. https://doi.org/10.1007/978-3-319-27436-2_11

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  • DOI: https://doi.org/10.1007/978-3-319-27436-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27435-5

  • Online ISBN: 978-3-319-27436-2

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