Discrete Morse Theory Based Dynamic P Systems

2018 ◽  
Vol 22 (1) ◽  
pp. 104-112
Author(s):  
Jie Xue ◽  
◽  
Xiyu Liu ◽  
Wenxing Sun ◽  
Shuo Yan
Keyword(s):  
Air Quality ◽  
Quality Evaluation ◽  
Morse Function ◽  
Membrane Computing ◽  
Linear Time ◽  
P Systems ◽  
P System ◽  
Gradient Vector ◽  
Evaluation Problem ◽  
Gradient Vector Field

This paper proposes a class of dynamic P systems with constraint of discrete Morse function (DMDP systems). Membrane structure is extended on complex. Rules control activities of membranes. New classes of rules and mechanism to change types of rules by discrete gradient vector field are provided as well.DMDP system extends P systems both in structures and rules. Solving air quality evaluation problem in linear time verifies the effectiveness ofDMDP systems. Since air quality evaluation problem has significance in many areas. The new P systems provide an alternative for traditional membrane computing.

Membrane Computing

2017 ◽  
pp. 15-34
Keyword(s):  
Robot Control ◽  
Membrane Computing ◽  
P Systems ◽  
System Model ◽  
P System ◽  
Input Output ◽  
Control Models ◽  
P Colonies ◽  
Theoretical Computing ◽  
Computing Models

The theoretical computing models that are used throughout this book are described in this chapter. These models are based on the initial P system model and include: Numerical P systems, Enzymatic Numerical P systems, P colonies and P swarms. Detailed examples and execution diagrams help the reader allow the reader to understand the functioning principle of each model and also its potential in various applications. The similarity between P systems (and their variants) and robot control models is also addressed. This analysis is presented to the reader in a side-by-side manner using a table where each row represents an analysis topic. Among others we mention: (1) Architectural structure, (2) Modularity and hierarchy, (3) Input-output relationships, (4) Parallelism.

scholarly journals Solving Vertex Cover Problem by Means of Tissue P Systems with Cell Separation

2010 ◽  
Vol 5 (4) ◽  
pp. 540 ◽  
Author(s):  
Chun Lu ◽  
Xingyi Zhang
Keyword(s):  
Cell Separation ◽  
Membrane Computing ◽  
Linear Time ◽  
Vertex Cover ◽  
P Systems ◽  
Computing Model ◽  
Vertex Cover Problem ◽  
Complete Problems ◽  
Np Complete ◽  
Cover Problem

Tissue P systems is a computing model in the framework of membrane computing inspired from intercellular communication and cooperation between neurons. Many different variants of this model have been proposed. One of the most important models is known as tissue P systems with cell separation. This model has the ability of generating an exponential amount of workspace in linear time, thus it allows us to design cellular solutions to NP-complete problems in polynomial time. In this paper, we present a solution to the Vertex Cover problem via a family of such devices. This is the first solution to this problem in the framework of tissue P systems with cell separation.

scholarly journals Automatic Implementation of Fuzzy Reasoning Spiking Neural P Systems for Diagnosing Faults in Complex Power Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Haina Rong ◽  
Kang Yi ◽  
Gexiang Zhang ◽  
Jianping Dong ◽  
Prithwineel Paul ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Power Systems ◽  
Large Scale ◽  
Membrane Computing ◽  
Good Description ◽  
Fuzzy Reasoning ◽  
P Systems ◽  
P System ◽  
Spiking Neural P Systems ◽  
Complex Power

As an important variant of membrane computing models, fuzzy reasoning spiking neural P systems (FRSN P systems) were introduced to build a link between P systems and fault diagnosis applications. An FRSN P system offers an intuitive illustration based on a strictly mathematical expression, a good fault-tolerant capacity, a good description for the relationships between protective devices and faults, and an understandable diagnosis model-building process. However, the implementation of FRSN P systems is still at a manual process, which is a time-consuming and hard labor work, especially impossible to perform on large-scale complex power systems. This manual process seriously limits the use of FRSN P systems to diagnose faults in large-scale complex power systems and has always been a challenging and ongoing task for many years. In this work we develop an automatic implementation method for automatically fulfilling the hard task, named membrane computing fault diagnosis (MCFD) method. This is a very significant attempt in the development of FRSN P systems and even of the membrane computing applications. MCFD is realized by automating input and output, and diagnosis processes consists of network topology analysis, suspicious fault component analysis, construction of FRSN P systems for suspicious fault components, and fuzzy inference. Also, the feasibility of the FRSN P system is verified on the IEEE14, IEEE 39, and IEEE 118 node systems.

LOGIC AND ARITHMETIC OPERATIONS WITH A CONSTANT NUMBER OF STEPS IN MEMBRANE COMPUTING

2011 ◽  
Vol 22 (03) ◽  
pp. 547-564 ◽  
Author(s):  
AKIHIRO FUJIWARA ◽  
TAKESHI TATEISHI
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
P System ◽  
Binary Number ◽  
Constant Number ◽  
Arithmetic Operations ◽  
Vector Addition ◽  
Multiple Input ◽  
Logic Functions

In the present paper, we propose P systems that work in a constant number of steps. We first propose two P systems for computing multiple input logic functions. An input of the logic functions is a set of n binary numbers of m bits, and an output is a binary number defined by the logic functions. The first and second P systems compute AND and EX-OR functions for the input, and both of the P systems work in a constant number of steps by using O(mn) types of objects, a constant number of membranes, and evolution rules of size O(mn). Next, we propose a P system for the addition of two binary numbers of m bits. The P system works in a constant number of steps by using O(m) types of objects, a constant number of membranes and evolution rules of size O(m2). We also introduce a P system that computes the addition of two vectors of n binary numbers of m bits by using the above P system as a sub-system. The P system for vector addition works in a constant number of steps by using O(mn) types of objects, a constant number of membranes, and evolution rules of size O(m2n).

Semi-Uniform Solution for Common Algorithmic Problem by P System in the Minimally Parallel Mode

2014 ◽  
Vol 568-570 ◽  
pp. 802-806
Author(s):  
Yun Yun Niu ◽  
Zhi Gao Wang
Keyword(s):  
Linear Time ◽  
P Systems ◽  
P System ◽  
Algorithmic Problem ◽  
Complete Problems ◽  
Active Membranes ◽  
Uniform Solution ◽  
Parallel Mode ◽  
The Common ◽  
Np Complete

It is known that the Common Algorithmic Problem (CAP) has a nice property that several other NP-complete problems can be reduced to it in linear time. In the literature, the decision version of this problem can be efficiently solved with a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes that do not use polarizations and present a semi-uniform solution to CAP in the minimally parallel mode.

scholarly journals Generation of Two-Dimensional Grammar Based Pattern Languages using Array Rewriting P System

2019 ◽  
Vol 8 (12) ◽  
pp. 1271-1276
Keyword(s):  
Theoretical Model ◽  
Computational Model ◽  
Special Interest ◽  
Membrane Computing ◽  
Living Cells ◽  
P Systems ◽  
P System ◽  
Two Dimensional ◽  
Pattern Languages ◽  
New Class

The theory of membrane computing was formulated by Paun as an attempt to formulate a computational model inspired by the way in which the living cells function. P systems which is a highly distributed, parallel, theoretical model and is an area of special interest in recent times. P systems have various application one such area of research is the generation of array grammars using them. In this study we define a model of P system to generate a new class of languages called grammar based two-dimensional pattern languages and their picture generation.

scholarly journals ON STRONG REVERSIBILITY IN P SYSTEMS AND RELATED PROBLEMS

2011 ◽  
Vol 22 (01) ◽  
pp. 7-14 ◽  
Author(s):  
OSCAR H. IBARRA
Keyword(s):  
Early Result ◽  
Open Problem ◽  
Membrane Computing ◽  
P Systems ◽  
P System ◽  
Seminal Paper ◽  
Direct Predecessor

We consider transition P systems as originally defined in the seminal paper of Gh. Păun, where he introduced the field of membrane computing. We show that it is decidable to determine, given a P system Π, whether it is strongly reversible (i.e., every configuration has at most one direct predecessor), resolving in the affirmative a recent open problem in the field. We also show that the set of all direct predecessors of a given configuration in a P system is an effectively computable semilinear set, which can effectively be expressed as a Presburger formula, strengthening an early result in the literature. We also prove other related results.

scholarly journals An Adaptive Optimization Spiking Neural P System for Binary Problems

2020 ◽  
Vol 31 (01) ◽  
pp. 2050054 ◽  
Author(s):  
Ming Zhu ◽  
Qiang Yang ◽  
Jianping Dong ◽  
Gexiang Zhang ◽  
Xiantai Gou ◽  
...  
Keyword(s):  
Knapsack Problem ◽  
Membrane Computing ◽  
Combinatorial Problems ◽  
P Systems ◽  
P System ◽  
Adaptive Optimization ◽  
Spiking Neural P System ◽  
Multiple Faults ◽  
Computing Model ◽  
Bus System

Optimization Spiking Neural P System (OSNPS) is the first membrane computing model to directly derive an approximate solution of combinatorial problems with a specific reference to the 0/1 knapsack problem. OSNPS is composed of a family of parallel Spiking Neural P Systems (SNPS) that generate candidate solutions of the binary combinatorial problem and a Guider algorithm that adjusts the spiking probabilities of the neurons of the P systems. Although OSNPS is a pioneering structure in membrane computing optimization, its performance is competitive with that of modern and sophisticated metaheuristics for the knapsack problem only in low dimensional cases. In order to overcome the limitations of OSNPS, this paper proposes a novel Dynamic Guider algorithm which employs an adaptive learning and a diversity-based adaptation to control its moving operators. The resulting novel membrane computing model for optimization is here named Adaptive Optimization Spiking Neural P System (AOSNPS). Numerical result shows that the proposed approach is effective to solve the 0/1 knapsack problems and outperforms multiple various algorithms proposed in the literature to solve the same class of problems even for a large number of items (high dimensionality). Furthermore, case studies show that a AOSNPS is effective in fault sections estimation of power systems in different types of fault cases: including a single fault, multiple faults and multiple faults with incomplete and uncertain information in the IEEE 39 bus system and IEEE 118 bus system.

scholarly journals Delayed Spiking Neural P Systems with Scheduled Rules

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Qianqian Ren ◽  
Xiyu Liu
Keyword(s):  
Time Delay ◽  
Membrane Computing ◽  
P Systems ◽  
Time Range ◽  
P System ◽  
System Delay ◽  
Spiking Neural P Systems ◽  
Time Control ◽  
New Variant ◽  
Delay Phenomenon

Due to the inevitable delay phenomenon in the process of signal conversion and transmission, time delay is bound to occur between neurons. Therefore, it is necessary to introduce the concept of time delay into the membrane computing models. Spiking neural P systems (SN P systems), as an attractive type of neural-like P systems in membrane computing, are widely followed. Inspired by the phenomenon of time delay, in our work, a new variant of spiking neural P systems called delayed spiking neural P systems (DSN P systems) is proposed. Compared with normal spiking neural P systems, the proposed systems achieve time control by setting the schedule on spiking rules and forgetting rules, and the schedule is also used to realize the system delay. A schedule indicates the time difference between receiving and outputting spikes, and it also makes the system work in a certain time, which means that a rule can only be used within a specified time range. We specify that each rule is performed only in the continuous schedule, during which the neuron is locked and cannot send or receive spikes. If the neuron is not available at a given time, it will not receive or send spikes due to the lack of a schedule for this period of time. Moreover, the universality of DSN P systems in both generating and accepting modes is proved. And a universal DSN P system having 81 neurons for computing functions is also proved.

scholarly journals A Survey of Nature-Inspired Computing

2021 ◽  
Vol 54 (1) ◽  
pp. 1-31
Author(s):  
Bosheng Song ◽  
Kenli Li ◽  
David Orellana-Martín ◽  
Mario J. Pérez-Jiménez ◽  
Ignacio PéRez-Hurtado
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Natural Computing ◽  
P System ◽  
Open Problems ◽  
Membrane Function ◽  
Natural Systems ◽  
Computing Paradigm ◽  
Complete Problems ◽  
Nature Inspired Computing

Nature-inspired computing is a type of human-designed computing motivated by nature, which is based on the employ of paradigms, mechanisms, and principles underlying natural systems. In this article, a versatile and vigorous bio-inspired branch of natural computing, named membrane computing is discussed. This computing paradigm is aroused by the internal membrane function and the structure of biological cells. We first introduce some basic concepts and formalisms of membrane computing, and then some basic types or variants of P systems (also named membrane systems ) are presented. The state-of-the-art computability theory and a pioneering computational complexity theory are presented with P system frameworks and numerous solutions to hard computational problems (especially NP -complete problems) via P systems with membrane division are reported. Finally, a number of applications and open problems of P systems are briefly described.

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