(Tissue) P Systems with Anti-Membranes

Abstract

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for membranes as objects and anti-membranes as the corresponding annihilation counterpart in P systems. Natural numbers can be represented by the corresponding number of membranes with a speci c label. Computational completeness in this setting then can be obtained with using only elementary membrane division rules, without using objects. A similar result can be obtained for tissue P systems with cell division rules and cell / anti-cell annihilation rules. In both cases, as derivation modes we may take the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects).