Generalized Communicating P Systems Working in Fair Sequential Model

In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition. We show that PP can be seen as a particular variant of GCPS. We also consider a particular stochastic evolution satisfying the fairness condition and obtain that it corresponds to the run of a Gillespie's SSA. This permits to further describe the dynamics of GCPS by a system of ODEs when the population size goes to the infinity.Comment: Presented at MeCBIC 201

Minimization Strategies for Maximally Parallel Multiset Rewriting Systems

Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and many variants of P systems). In particular, this means that MPMRS are computationally complete; however, a direct translation leads to quite a big number of rules. Like for other classes of computationally complete devices, there is a challenge to find a universal system having the smallest number of rules. In this article we present different rule minimization strategies for MPMRS based on encodings and structural transformations. We apply these strategies to the translation of a small universal register machine (Korec, 1996) and we show that there exists a universal MPMRS with 23 rules. Since MPMRS are identical to a restricted variant of P systems with antiport rules, the results we obtained improve previously known results on the number of rules for those systems.Comment: This article is an improved version of [1

A Note on the Probabilistic Evolution for P Systems

In this note we propose a method that permits to describe in a uniform man- ner variants of probabilistic/stochastic P systems. We give examples of such a description for existing models of P systems using probabilities

(Tissue) P Systems with Vesicles of Multisets

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.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Input-Driven Tissue P Automata

We introduce several variants of input-driven tissue P automata where the rules to be applied only depend on the input symbol. Both strings and multisets are considered as input objects; the strings are either read from an input tape or defined by the sequence of symbols taken in, and the multisets are given in an input cell at the beginning of a computation, enclosed in a vesicle. Additional symbols generated during a computation are stored in this vesicle, too. An input is accepted when the vesicle reaches a final cell and it is empty. The computational power of some variants of input-driven tissue P automata is illustrated by examples and compared with the power of the input-driven variants of other automata as register machines and counter automata

Computational Completeness of P Systems Using Maximal Variants of the Set Derivation Mode

We consider P systems only allowing rules to be used in at most one copy in each derivation step, especially the variant of the maximally parallel derivation mode where each rule may only be used at most once. Moreover, we also consider the derivation mode where from those sets of rules only those are taken which have the maximal number of rules. We check the computational completeness proofs of several variants of P systems and show that some of them even literally still hold true for the for these two new set derivation modes. Moreover, we establish two new results for P systems using target selection for the rules to be chosen together with these two new set derivation modes

P Systems with Minimal Left and Right Insertion and Deletion

Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.

P Systems with Minimal Insertion and Deletion

In this paper we consider insertion-deletion P systems with priority of deletion over the insertion.We show that such systems with one symbol context-free insertion and deletion rules are able to generate PsRE. If one-symbol one-sided context is added to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important and in its absence the corresponding class of P systems is strictly included in MAT