(Tissue) P Systems with Vesicles of Multisets

TL;DR

This paper explores tissue P systems with vesicles of multisets, demonstrating how simple operations and polarization can achieve computational completeness under various modes and structures.

Contribution

It introduces the use of polarization in tissue P systems with vesicles, enabling computational completeness even in sequential mode.

Findings

Set maximal mode achieves computational completeness with tree structures.

Sequential mode with arbitrary structures is not complete without polarization.

Polarization enables completeness in sequential mode.

Abstract

We consider tissue P systems working on vesicles of multisets with the very simple operations of insertion, deletion, and substitution of single objects. With the whole multiset being enclosed in a vesicle, sending it to a target cell can be indicated in those simple rules working on the multiset. As derivation modes we consider the sequential mode, where exactly one rule is applied in a derivation step, and the set maximal mode, where in each derivation step a non-extendable set of rules is applied. With the set maximal mode, computational completeness can already be obtained with tissue P systems having a tree structure, whereas tissue P systems even with an arbitrary communication structure are not computationally complete when working in the sequential mode. Adding polarizations (-1, 0, 1 are sufficient) allows for obtaining computational completeness even for tissue P systems working in the sequential mode.