P Systems with Communication Based on Concentration

 Jürgen Dassow  1 - Gheorghe Paun  2

Abstract:

 We consider a variant of P systems where the communication of objects is controlled by the ``concentration" of these objects: after each evolution step, the objects are redistributed among the regions of the system in such a way that each region contains the same number of copies of each object (plus/minus one, when the number of objects is not divisible by the number of regions). We show that P systems of this form, with only one flip-flop catalyst but without using other control ingredients, can generate the Parikh images of all matrix languages. When an unbounded number of catalysts is available, a characterization of recursively enumerable sets of vectors of natural numbers is obtained (by systems with only one membrane).  

Footnotes

  1 Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, D-39016 Magdeburg, Germany, E-mail: dassow@iws.cs.uni-magdeburg.de 2 Corresponding author. Research supported by Alexander von Humboldt Foundation. Institute of Mathematics of the Romanian Academy, PO Box 1 - 764, 70700 Bucuresti, Romania, E-mail: gpaun@imar.ro