Skip to main content

Memory associated with membranes systems


We study the notion of memory associated with membranes systems. Such a memory can be used in various ways; in this paper, we focus on two of them. One way is to consider the memory as a device for tracking how objects evolve. In this perspective, the memory is coded into objects which are enriched with suitable information to keep track on how they have been produced. This kind of memory allows to study the reversibility of membrane evolution. Another way is to consider the memory as a storing device for the objects consumed previously in the same evolution step. This kind of memory allows to describe a dynamic allocation of objects; two semantics are presented (a dynamic one and a static one), and it is proved their equivalence.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    Agrigoroaiei, O., & Ciobanu, G. (2009). Rewriting logic specification of membrane systems with promoters and inhibitors. Electronic Notes of Theoretical Computer Science, 238, 5–22.

    Article  Google Scholar 

  2. 2.

    Agrigoroaiei, O., & Ciobanu, G. (2010). Reversing computation in membrane systems. Journal of Logic and Algebraic Programming, 79, 278–288.

    MathSciNet  Article  Google Scholar 

  3. 3.

    Aman, B., & Ciobanu, G. (2009). Turing completeness using three mobile membranes. Lecture Notes in Computer Science, 5715, 42–55.

    MathSciNet  Article  Google Scholar 

  4. 4.

    Aman, B., & Ciobanu, G. (2011). Mobility in Process Calculi and Natural Computing. New York: Springer.

    Book  Google Scholar 

  5. 5.

    Aman, B., & Ciobanu, G. (2017). Reversibility in parallel rewriting systems. Journal of Universal Computer Science, 23, 692–703.

    MathSciNet  Google Scholar 

  6. 6.

    Aman, B., & Ciobanu, G. (2019). Adaptive P systems. Lecture Notes in Computer Science, 11399, 57–72.

    Article  Google Scholar 

  7. 7.

    Aman, B., & Ciobanu, G. (2019). Synchronization of rules in membrane computing. Journal of Membrane Computing, 1, 233–240.

    MathSciNet  Article  Google Scholar 

  8. 8.

    Aman, B., Ciobanu, G., Pinna, G. M., et al. (2020). Foundations of reversible computation. Lecture Notes in Computer Science, 12070, 1–40.

    Article  Google Scholar 

  9. 9.

    Ciobanu, G. (2010). Semantics of P systems. In The Oxford Handbook of Membrane Computing (pp. 413-436). Oxford University Press.

  10. 10.

    Ciobanu, G., Marcus, S., & Păun, G. (2009). New strategies of using the rules of a P system in a maximal way. Romanian Journal of Information Science and Technology, 12, 21–37.

    Google Scholar 

  11. 11.

    Ciobanu, G., & Pinna, G. M. (2012). Catalytic Petri nets are Turing complete. Lecture Notes in Computer Science, 7183, 192–203.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Ciobanu, G., & Pinna, G. M. (2014). Catalytic and communicating Petri nets are Turing complete. Information and Computation, 239, 55–70.

    MathSciNet  Article  Google Scholar 

  13. 13.

    Ciobanu, G., & Todoran, E. N. (2017). Denotational semantics of membrane systems by using complete metric spaces. Theoretical Computer Science, 701, 85–108.

    MathSciNet  Article  Google Scholar 

  14. 14.

    van Glabbeek, R. J. (2005). The individual and collective token interpretation of Petri nets. Lecture Notes in Computer Science, 3653, 323–337.

    MathSciNet  Article  Google Scholar 

  15. 15.

    Giachino, E., Lanese, I., Mezzina, C.A., Tiezzi, F. (2015). Causal-consistent reversibility in a tuple-based language. In M. Daneshtalab, M. Aldinucci, V. Leppänen, J. Lilius, M. Brorsson (Eds.) PDP 2015 (pp. 467–475). IEEE Computer Society

  16. 16.

    Kleijn, J., & Koutny, M. (2009). A Petri net model for membrane systems with dynamic structure. Natural Computing, 8, 781–796.

    MathSciNet  Article  Google Scholar 

  17. 17.

    Kleijn, J., Koutny, M., & Rozenberg, G. (2005). Towards a Petri net semantics for membrane systems. Lecture Notes in Computer Science, 3850, 292–309.

    Article  Google Scholar 

  18. 18.

    Lanese, I., Mezzina, C. A., & Tiezzi, F. (2014). Causal-consistent reversibility. Bulletin of the EATCS vol. 114

  19. 19.

    Păun, G. (2002). Membrane Computing. An Introduction. New York: Springer.

    Book  Google Scholar 

  20. 20.

    Păun, G., Rozenberg, G., & Salomaa, A. (2010). The Oxford Handbook of Membrane Computing. Oxford: Oxford University Press.

    Book  Google Scholar 

  21. 21.

    Pinna, G. M. (2017). Reversing steps in membrane systems computations. Lecture Notes in Computer Science, 10725, 245–261.

    MathSciNet  Article  Google Scholar 

  22. 22.

    Pinna, G. M., & Saba, A. (2012). Modeling dependencies and simultaneity in membrane system computations. Theoretical Computer Science, 431, 13–39.

    MathSciNet  Article  Google Scholar 

  23. 23.

    Zhang, G., Pérez-Jiménez, M. J., & Gheorghe, M. (2017). Real-Life Applications with Membrane Computing. New York: Springer.

    Book  Google Scholar 

Download references


The authors would like to thank the reviewers for their useful criticisms and suggestions.

Author information



Corresponding author

Correspondence to Gabriel Ciobanu.

Ethics declarations

Conflicts of interest

The authors declare they have no financial interests, and have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The initial work was presented at the 20th Conference on Membrane Computing (CMC20)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ciobanu, G., Pinna, G.M. Memory associated with membranes systems. J Membr Comput 3, 116–132 (2021).

Download citation


  • Membrane systems with memory
  • Reversibility
  • Backward computation