Polymorphic P Systems with Non-cooperative Rules and No Ingredients

Abstract

Polymorphic P systems represent a variant of the bio-inspired computational model of P systems, in which the rules are not explicitly given in the description of the system, but are implicitly defined by the contents of certain membranes. In this paper we give a characterisation of the most basic class of such systems, in which only non-cooperative rules are allowed and no ingredients are included. We start by formulating two different formal definitions of non-cooperativity and then show that they have the same generative power. We also show that the generative power of polymorphic P systems is less than $NRE$ and, finally, that the languages produced by such systems form a hierarchy related to the maximal allowed depth of the membrane structure.