Energy-Controlled P Systems

As already considered in [13], we investigate P systems where each evolution rule "produces" or "consumes" some quantity of energy, in amounts which are expressed as integer numbers. Yet in contrast to P systems with energy accounting as considered in [13], for energy-controlled P systems we demand that in each evolution step and in each membrane the total energy consumed by the application of a multiset of evolution rules has to be the maximum possible within a specific non-negative range. Only equipped with this control feature, energy-controlled P systems are very powerful. In the case of multisets of symbol objects we find that energy-controlled P systems with even only one membrane and an energy range of {0, 1} for the total energy involved in an evolution step characterize the recursively enumerable sets of vectors of natural numbers (without using catalysts or priorities or membrane dissolving features). In the case of string objects similar results can be obtained. Energy-controlled P systems with even only one membrane and the minimal energy range of {0} for the total energy involved in an evolution step at least generate any set of vectors of natural numbers that can be generated by matrix grammars without appearance checking.