Multiset Patterns and Their Application to Dynamic Causalities in Membrane Systems

  • Roberto Barbuti
  • Roberta Gori
  • Paolo MilazzoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10725)


In this paper we investigate dynamic causalities in membrane systems by proposing the concept of “predictor”, originally defined in the context of Ehrenfeucht and Rozemberg’s reaction systems. The goal is to characterize sufficient conditions for the presence of a molecule of interest in the configuration of a P system after a given number of evolution steps (independently from the non-deterministic choices taken). Such conditions can be used to study causal relationships between molecules. To achieve our goal, we introduce the new concept of “multiset pattern” representing a logical formula on multisets. A predictor can be expressed as a pattern characterizing the initial multisets that will surely lead (sufficient condition) to the presence of the molecule of interest after the given number of evolution steps. We define also an operator that computes such a predictor.


  1. 1.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Specialized predictor for reaction systems with context properties. In: Proceedings of the 24th International Workshop on Concurrency, Specification and Programming, CS&P 2015, pp. 31–43 (2015)Google Scholar
  2. 2.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Investigating dynamic causalities in reaction systems. Theor. Comput. Sci. 623, 114–145 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Specialized predictor for reaction systems with context properties. Fundamenta Informaticae 147(2–3), 173–191 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Generalized contexts for reaction systems: definition and study of dynamic causalities. Acta Informatica (2017).
  5. 5.
    Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tini, S.: Flat form preserving step-by-step behaviour. Fundamenta Informaticae 87, 1–34 (2008)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bodei, C., Gori, R., Levi, F.: An analysis for causal properties of membrane interactions. Electron. Notes Theor. Comput. Sci. 299, 15–31 (2013)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bodei, C., Gori, R., Levi, F.: Causal static analysis for brane calculi. Theor. Comput. Sci. 587, 73–103 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Brijder, R., Ehrenfeucht, A., Main, M.G., Rozenberg, G.: A tour of reaction systems. Int. J. Found. Comput. Sci. 22(7), 1499–1517 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Brijder, R., Ehrenfeucht, A., Rozenberg, G.: A Note on causalities in reaction systems. ECEASST 30 (2010)Google Scholar
  10. 10.
    Busi, N.: Causality in membrane systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 160–171. Springer, Heidelberg (2007). CrossRefGoogle Scholar
  11. 11.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta Informaticae 75(1–4), 263–280 (2007)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Gori, R., Levi, F.: Abstract interpretation based verification of temporal properties for bioambients. Inf. Comput. 208(8), 869–921 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Pǎun, G.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

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