On the Computability Power of Membrane Systems with Controlled Mobility

  • Shankara Narayanan Krishna
  • Bogdan Aman
  • Gabriel Ciobanu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


In a previous paper we have shown that membrane systems with controlled mobility are able to solve a \(\Pi_2^\mathrm{P}\) complete problem. Then, an enriched model with forced endocytosis and forced exocytosis enables us to move to the fourth level in the polynomial hierarchy, the model having \(\Sigma_4^\mathrm{P} \cup \Pi_4^\mathrm{P}\) as lower bound. In this paper we study the computability power of this model (using forced endocytosis and forced exocytosis), and determine the border condition for achieving computational completeness: 4 membranes provide Turing completeness, while 3 membranes do not. Moreover, we show that the restricted division operation (which is crucial in achieving the \(\Sigma_4^\mathrm{P} \cup \Pi_4^\mathrm{P}\) lower bound) does not provide computational completeness. However, Turing completeness can be achieved with pairs of operations (exocytosis, inhibitive endocytosis) and (inhibitive exocytosis, endocytosis) by using 4 membranes. Finally, we present some computability results expressing that membrane systems which use the operations of restricted division, restricted exocytosis and inhibitive endocytosis cannot yield computational completeness.


Turing Machine Membrane System Complete Problem Control Mobility Membrane Computing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shankara Narayanan Krishna
    • 1
  • Bogdan Aman
    • 2
    • 3
  • Gabriel Ciobanu
    • 2
    • 3
  1. 1.Department of Computer Science and EngineeringIIT BombayMumbaiIndia
  2. 2.Institute of Computer ScienceRomanian AcademyIasiRomania
  3. 3.“A. I.Cuza” University of IaşiIasiRomania

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