On the computability power of membrane systems with controlled mobility

  • Authors:

  • Shankara Narayanan Krishna;Bogdan Aman;Gabriel Ciobanu

  • Affiliations:

  • Department of Computer Science and Engineering, IIT Bombay, Mumbai, India;Institute of Computer Science, Romanian Academy, Iasi, Romania,"A. I.Cuza" University of Iaşi, Iasi, Romania;Institute of Computer Science, Romanian Academy, Iasi, Romania,"A. I.Cuza" University of Iaşi, Iasi, Romania

  • Venue:
  • CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
  • Year:
  • 2012

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Abstract

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.