Abstract.
We propose here a variant of P systems with polarized membranes of variable thickness, in which the charge of a membrane is equal to the net charge of the string-objects it contains. As the charge of the membrane changes, applicable rules of that membrane will also change, i.e., the set of rules of a membrane with the positive charge is different from the set of rules of the same membrane with the negative charge or with the neutral charge. With this new variant of P systems, with degree 3 we achieve computational completeness. With a fixed membrane structure with each membrane having thickness one computational completeness is achieved with four membranes. A generalization of this system is also considered where computational completeness is achieved with two membranes.

Keywords: P systems, Membrane computing, Dynamic membrane polarization, Matrix grammar, Strong binary normal form, Recursively enumerable languages.