P Systems with Boundary Rules

  • Francesco Bernardini
  • Vincenzo Manca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2597)


We propose a new variant of P Systems, based on boundary rules, shortly called PB Systems. Boundary rules means that rules are not internal to regions but theyare able to “see” even externally, that is, theyare sensible to what happens around the border of the membranes. We prove the computational universality for PB systems with three membranes which sense at most one symbol outside and one symbol inside a membrane. Finally, we investigate the relationships with the basic model of P systems by proving an equivalence between P systems without priority, thickness or dissolution operator, and PB systems that use communication rules of a restricted form.


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  1. 1.
    Alberts, B.: Essential Cell Biology. An Introduction to the Molecular Biology of the Cell. Garland Publ. Inc. London (1998)Google Scholar
  2. 2.
    Bernardini, F.: Analisi dinamica di sistemi a membrane. “Tesi di Laurea in Informatica” Pisa (2002)Google Scholar
  3. 3.
    Bernardini, F., Manca, V.: Dynamical Aspects of P Systems. BioSystems (to appear)Google Scholar
  4. 4.
    Bonanno, C., Manca, V.: Discrete Dynamics in Biological Models. Romanian Journal of Information Science and Technology 5 (1–2) (2002) 45–67Google Scholar
  5. 5.
    Dassow, J., Păun Gh.: Regulated Rewriting in Formal Languages. Springer-Verlag Berlin (1989)Google Scholar
  6. 6.
    Marcus, S., Păun, Gh.: Infinite (Almost Periodic) Words, Formal Languages and Dynamical Systems. Bulletin EATCS 54 (1994) 224–231MATHGoogle Scholar
  7. 7.
    Păun, A., Păun, Gh.: The Power of Communication: P Systems with Symport/Antiport. New Generation Computing 20 (3) (2002) 295–306MATHCrossRefGoogle Scholar
  8. 8.
    Păun, Gh.: Computing with Membranes. Journal of Computer and System Sciences 61 (1) (2000) 108–143MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Păun, Gh.: From Cells to Computers: Computing with Membranes (P Systems). BioSystems 59 (2001) 139–151CrossRefGoogle Scholar
  10. 10.
    Păun, Gh.: Membrane Computing. An Introduction. Springer-Verlag Berlin (2002)Google Scholar
  11. 11.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer-Verlag, vol. 1–3, Heidelberg (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Francesco Bernardini
    • 1
  • Vincenzo Manca
    • 2
  1. 1.Dipartimento di InformaticaUniversità degli Studi di PisaPisaItaly
  2. 2.Dipartimento di InformaticaUniversità degli Studi di VeronaVeronaItaly

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