OPTIMAL RESULTS FOR THE COMPUTATIONAL COMPLETENESS OF GEMMATING (TISSUE) P SYSTEMS

Abstract

Gemmating P systems were introduced as a theoretical model based on the biological idea of the gemmation of mobile membranes. In the general model of extended gemmating P systems, strings are modified either by evolution rules in the membranes or while sending them to another membrane. We here consider the restricted variant of extended gemmating P systems with pre-dynamic rules where strings are only modified at the ends while sending them from one membrane to another one. In a series of papers the number of membranes being sufficient for obtaining computational completeness has steadily been decreased. In this paper we now prove the optimal result, i.e., gemmating P systems only using pre-dynamic rules are already computationally complete with three membranes, even in the non-extended case and with the minimal weight of rules possible. Moreover, we also show that for gemmating tissue P systems two cells suffice, and if we allow the environment to be fully involved in the communication of strings, even one cell together with the environment can manage the task to generate any recursively enumerable language.