Size and Power of Extended Gemmating P Pystems

Abstract

In P systems with gemmation of mobile membranes were ex- amined. It was shown that (extended) systems with eight membranes are as powerful as the Turing machines. Moreover, it was also proved that extended gemmating P systems with only pre-dynamical rules are still computationally complete: in this case nine membranes are needed to obtain this computational power. In this paper we improve the above results concerning the size bound of extended gemmating P systems, namely we prove that these systems with at most ¯ve membranes (with meta-priority relations and without (in=out) communication rules) form a class of universal computing devices, while in the case of extended systems with only pre-dynamical rules six membranes are enough to determine any recursively enumerable language.