Area Of Membrane Computing Research Articles

Rule synchronization for monodirectional tissue-like P systems with channel states

Monodirectional tissue-like P systems with channel states is a kind of computation model in the area of membrane computing, which evolves by the transfer of objects in one direction for two given regions. In this article, we consider monodirectional tissue-like P systems with channel states, wherein rules are used sequentially for each channel and in a maximally parallel manner for the system by incorporating rule synchronization. We prove that the designed monodirectional tissue-like P systems are universal when using two cells, three states, and rules with a maximal length of 1, or using two cells, two states, and rules with a maximal length of 2, or using any number of cells, two states, and rules with a maximal length of 1. The results show that rule synchronization is an effective strategy to enhance the computational power of monodirectional tissue-like P systems with channel states.

Numerical Spiking Neural P Systems.

Spiking neural P (SN P) systems are a class of discrete neuron-inspired computation models, where information is encoded by the numbers of spikes in neurons and the timing of spikes. However, due to the discontinuous nature of the integrate-and-fire behavior of neurons and the symbolic representation of information, SN P systems are incompatible with the gradient descent-based training algorithms, such as the backpropagation algorithm, and lack the capability of processing the numerical representation of information. In this work, motivated by the numerical nature of numerical P (NP) systems in the area of membrane computing, a novel class of SN P systems is proposed, called numerical SN P (NSN P) systems. More precisely, information is encoded by the values of variables, and the integrate-and-fire way of neurons and the distribution of produced values are described by continuous production functions. The computation power of NSN P systems is investigated. We prove that NSN P is Turing universal as number generating devices, where the production functions in each neuron are linear functions, each involving at most one variable; as number accepting devices, NSN P systems are proved to be universal as well, even if each neuron contains only one production function. These results show that even if a single neuron is simple in the sense that it contains one or two production functions and the production functions in each neuron are linear functions with one variable, a network of simple neurons are still computationally powerful. With the powerful computation power and the characteristic of continuous production functions, developing learning algorithms for NSN P systems is potentially exploitable.

A Bio-Inspired Model of Picture Array Generating P System with Restricted Insertion Rules

In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating P system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array P system.

Cell-like P systems with polarizations and minimal rules

P systems with active membranes are a class of computation models in the area of membrane computing, which are inspired from the mechanism by which chemicals interact and cross cell membranes. In this work, we consider a normal form of P systems with active membranes, called cell-like P systems with polarizations and minimal rules, where rules are minimal in the sense that an object evolves to exactly one object with the application of an evolution rule or a communication rule, or an object evolves to two objects that are assigned to the two new generated membranes by applying a division rule. The present work investigates the computational power of P systems with polarizations and minimal rules. Specifically, results about Turing universality and non-universality are obtained with the combination of the number of membranes, the number of polarizations, and the types of rules. We also show that polarizationless P systems with minimal rules are equivalent to Turing machines working in a polynomial space, that is, the class of problems that can be solved in polynomial time by polarizationless P systems with minimal rules is equal to the class PSPACE.

TRIANGULAR TILE PASTING $P$ SYSTEM AND ARRAY GENERATING PETRI NETS

In the area of membrane computing, a new computability model, called P system is a highly distributed and parallel theoretical computing model. Generating two dimensional picture languages is one of the applications of P systems. Ceterachi et al. began a study on connecting the two areas, membrane computing and array grammars. Triangular tile pasting system and the Triangular Tile pasting P system models have been introduced for pattern generation. This paper introduce the k-order TTPS and ETTPS. Also this paper has extended the theory of Triangular tile pasting P system to generate two dimensional picture languages. A comparative study between triangular tile pasting system and Triangular tile pasting P system is made. Comparison is also made with the array generating Petri nets.

Membrane Computing to Enhance Time Efficiency of Minimum Dominating Set

Graph theory is widely used in numerous fields, such as, engineering, physics, social and biological sciences; linguistics etc. The minimum dominating set (MDS) problem is one of the main problems of algorithmic graph theory and has numerous applications especially in graph mining. Since it is NP-hard to solve the MDS problem approximately, much work has been dedicated to central and distributed approximation algorithms for restricted graph classes. In recent research exponential time \(O(k^{n})\) algorithms are used for some graph classes for solving the MDS problem. In the approach of using the algorithmic tile self-assembly model, the MDS problem has been solved in \(O(n^{2})\) steps. On the other hand, in the area of membrane computing, P systems introduce two levels of parallelism: every membrane works concurrently with other membranes,and, rules are applied in parallel in each membrane. This paper introduces an algorithm based on the parallelism feature of the P systems model for solving the MDS problem in linear time O(n).

Iso-array rewriting P systems with context-free iso-array rules

A new computing model called P system is a highly distributed and parallel theoretical model, which is proposed in the area of membrane computing. Ceterchi et al. initially proposed array rewriting P systems by extending the notion of string rewriting P systems to arrays (2003). A theoretical model for picture generation using context-free iso-array grammar rules and puzzle iso-array grammar rules are introduced by Kalyani et al. (2004, 2006). Also iso-array rewriting P systems for iso-picture languages have been studied by Annadurai et al. (2008). In this paper we consider the context-free iso-array rules and context-free puzzle iso-array rules in iso-array rewriting P systems and examine the generative powers of these P systems.

A [formula omitted] system model with pure context-free rules for picture array generation

Syntactic models constitute one of the main areas of mathematical studies on picture array generation. A number of 2D grammar models have been proposed motivated by a variety of applications. A P system is a biologically motivated new computing model, proposed by Păun in the area of membrane computing. It is a rich framework for dealing with different problems, including the problem of handling picture array generation. In this paper, the generative power of the array-rewriting P system with pure 2D context-free rules is investigated by comparing it with other 2D grammar models, thus bringing out the suitability of this P system model for picture array generation.

Experiments on the reliability of stochastic spiking neural P systems

In the area of membrane computing, time-freeness has been defined as the ability for a timed membrane system to produce always the same result, independently of the execution times associated to the rules. In this paper, we use a similar idea in the framework of spiking neural P systems, a model inspired by the structure and the functioning of neural cells. In particular, we introduce stochastic spiking neural P systems where the time of firing for an enabled spiking rule is probabilistically chosen and we investigate when, and how, these probabilities can influence the ability of the systems to simulate, in a reliable way, universal machines, such as register machines.

Modelling metapopulations with stochastic membrane systems

Metapopulations, or multi-patch systems, are models describing the interactions and the behavior of populations living in fragmented habitats. Dispersal, persistence and extinction are some of the characteristics of interest in ecological studies of metapopulations. In this paper, we propose a novel method to analyze metapopulations, which is based on a discrete and stochastic modelling framework in the area of Membrane Computing. New structural features of membrane systems, necessary to appropriately describe a multi-patch system, are introduced, such as the reduction of the maximal parallel consumption of objects, the spatial arrangement of membranes and the stochastic creation of objects. The role of the additional features, their meaning for a metapopulation model and the emergence of relevant behaviors are then investigated by means of stochastic simulations. Conclusive remarks and ideas for future research are finally presented.

Spiking Neural P Systems

This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural ...

On determinism versus nondeterminism in P systems

An important open problem in the area of membrane computing is whether there is a model of P systems for which the nondeterministic version is strictly more powerful than the deterministic version. We resolve this problem in the following sense—we exhibit two classes of P system acceptors with only communicating rules and show:1.For the first class, the deterministic and nondeterministic versions are equivalent if and only if deterministic and nondeterministic linear bounded automata are equivalent. The latter problem is a long-standing open question in complexity theory.2.For the second class, the deterministic version is strictly weaker than the nondeterministic version.Both classes are nonuniversal, but can accept fairly complex languages.

P Systems with Global Rules

We contribute to the vivid area of membrane computing (P systems) by considering the case when the same evolution rules are valid in all regions of a system. Such a P system is called with global rules . We consider the case of string-objects, with the evolution rules based on splicing and by rewriting. Universality results are proved for both types of systems. For splicing we also try to minimize the diameter of the used rules, while for rewriting systems we improve a result from the literature, proving that two membranes suffice for simulating Turing machines.