scholarly journals Novel Numerical Spiking Neural P Systems with a Variable Consumption Strategy

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 549
Author(s):  
Xiu Yin ◽  
Xiyu Liu ◽  
Minghe Sun ◽  
Qianqian Ren
Keyword(s):  
Production Functions ◽  
P Systems ◽  
P System ◽  
Computing Device ◽  
Spiking Neural P Systems ◽  
Distributed Parallel Computing ◽  
Production Values ◽  
Novel Variant ◽  
Turing Universality ◽  
Variable Consumption

A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by modifying the form of the production functions used in NSN P systems. Similar to the delay feature of the spiking rules, NSNVC P systems introduce a postponement feature into the production functions. The execution of the production functions in NSNVC P systems is controlled by two, i.e., polarization and threshold, conditions. Multiple synaptic channels are used to transmit the charges and the production values in NSNVC P systems. The proposed NSNVC P systems are a type of distributed parallel computing models with a directed graphical structure. The Turing universality of the proposed NSNVC P systems is proved as number generating/accepting devices. Detailed descriptions are provided for NSNVC P systems as number generating/accepting devices. In addition, a universal NSNVC P system with 66 neurons is constructed as a function computing device.

scholarly journals Turing Universality of Weighted Spiking Neural P Systems with Anti-spikes

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qianqian Ren ◽  
Xiyu Liu ◽  
Minghe Sun
Keyword(s):  
P Systems ◽  
P System ◽  
Number Generator ◽  
Working Process ◽  
Computing Device ◽  
Spiking Neural P Systems ◽  
Turing Universality

Weighted spiking neural P systems with anti-spikes (AWSN P systems) are proposed by adding anti-spikes to spiking neural P systems with weighted synapses. Anti-spikes behave like spikes of inhibition of communication between neurons. Both spikes and anti-spikes are used in the rule expressions. An illustrative example is given to show the working process of the proposed AWSN P systems. The Turing universality of the proposed P systems as number generating and accepting devices is proved. Finally, a universal AWSN P system having 34 neurons is proved to work as a function computing device by using standard rules, and one having 30 neurons is proved to work as a number generator.

Spiking Neural P Systems with Extended Channel Rules

2020 ◽  
Vol 31 (01) ◽  
pp. 2050049 ◽  
Author(s):  
Zeqiong Lv ◽  
Tingting Bao ◽  
Nan Zhou ◽  
Hong Peng ◽  
Xiangnian Huang ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Control Mechanism ◽  
P Systems ◽  
Multiple Channels ◽  
Spiking Neural P Systems ◽  
Distributed Parallel Computing ◽  
New Variant ◽  
New Type ◽  
Turing Universality ◽  
Computing Models

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices.

scholarly journals Universal Nonlinear Spiking Neural P Systems with Delays and Weights on Synapses

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Liping Wang ◽  
Xiyu Liu ◽  
Yuzhen Zhao
Keyword(s):  
Parallel Computing ◽  
P Systems ◽  
Real Numbers ◽  
Spiking Neural P Systems ◽  
Subset Sum Problem ◽  
Computing Model ◽  
Distributed Parallel Computing ◽  
Subset Sum ◽  
Computing Performance ◽  
Turing Universality

The nonlinear spiking neural P systems (NSNP systems) are new types of computation models, in which the state of neurons is represented by real numbers, and nonlinear spiking rules handle the neuron’s firing. In this work, in order to improve computing performance, the weights and delays are introduced to the NSNP system, and universal nonlinear spiking neural P systems with delays and weights on synapses (NSNP-DW) are proposed. Weights are treated as multiplicative constants by which the number of spikes is increased when transiting across synapses, and delays take into account the speed at which the synapses between neurons transmit information. As a distributed parallel computing model, the Turing universality of the NSNP-DW system as number generating and accepting devices is proven. 47 and 43 neurons are sufficient for constructing two small universal NSNP-DW systems. The NSNP-DW system solving the Subset Sum problem is also presented in this work.

scholarly journals Simplified and Yet Turing Universal Spiking Neural P Systems with Communication on Request

2018 ◽  
Vol 28 (08) ◽  
pp. 1850013 ◽  
Author(s):  
Tingfang Wu ◽  
Florin-Daniel Bîlbîe ◽  
Andrei Păun ◽  
Linqiang Pan ◽  
Ferrante Neri
Keyword(s):  
Neural Networks ◽  
Membrane Computing ◽  
P Systems ◽  
P System ◽  
Third Generation ◽  
Turing Machines ◽  
Spiking Neural P System ◽  
Spiking Neural P Systems ◽  
Turing Universality ◽  
Theoretical Results

Spiking neural P systems are a class of third generation neural networks belonging to the framework of membrane computing. Spiking neural P systems with communication on request (SNQ P systems) are a type of spiking neural P system where the spikes are requested from neighboring neurons. SNQ P systems have previously been proved to be universal (computationally equivalent to Turing machines) when two types of spikes are considered. This paper studies a simplified version of SNQ P systems, i.e. SNQ P systems with one type of spike. It is proved that one type of spike is enough to guarantee the Turing universality of SNQ P systems. Theoretical results are shown in the cases of the SNQ P system used in both generating and accepting modes. Furthermore, the influence of the number of unbounded neurons (the number of spikes in a neuron is not bounded) on the computation power of SNQ P systems with one type of spike is investigated. It is found that SNQ P systems functioning as number generating devices with one type of spike and four unbounded neurons are Turing universal.

scholarly journals A Grid-Density Based Algorithm by Weighted Spiking Neural P Systems with Anti-Spikes and Astrocytes in Spatial Cluster Analysis

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1132
Author(s):  
Deting Kong ◽  
Yuan Wang ◽  
Xinyan Wu ◽  
Xiyu Liu ◽  
Jianhua Qu ◽  
...  
Keyword(s):  
Dimensional Space ◽  
P Systems ◽  
High Dimensional ◽  
P System ◽  
Inhibitory Influence ◽  
Spiking Neural P Systems ◽  
Clustering Approach ◽  
Spatial Cluster Analysis ◽  
Effectiveness And Efficiency ◽  
Real World Datasets

In this paper, we propose a novel clustering approach based on P systems and grid- density strategy. We present grid-density based approach for clustering high dimensional data, which first projects the data patterns on a two-dimensional space to overcome the curse of dimensionality problem. Then, through meshing the plane with grid lines and deleting sparse grids, clusters are found out. In particular, we present weighted spiking neural P systems with anti-spikes and astrocyte (WSNPA2 in short) to implement grid-density based approach in parallel. Each neuron in weighted SN P system contains a spike, which can be expressed by a computable real number. Spikes and anti-spikes are inspired by neurons communicating through excitatory and inhibitory impulses. Astrocytes have excitatory and inhibitory influence on synapses. Experimental results on multiple real-world datasets demonstrate the effectiveness and efficiency of our approach.

Performing Balanced Ternary Logic and Arithmetic Operations with Spiking Neural P Systems with Anti-Spikes

2012 ◽  
Vol 505 ◽  
pp. 378-385 ◽  
Author(s):  
Xian Wu Peng ◽  
Xiao Ping Fan ◽  
Jian Xun Liu
Keyword(s):  
Logic Gates ◽  
P Systems ◽  
P System ◽  
Ternary Logic ◽  
Arithmetic Operations ◽  
Spiking Neural P Systems ◽  
Addition And Subtraction ◽  
Distributed And Parallel Computing ◽  
Computing Models ◽  
Natural Way

Spiking neural P systems are a class of distributed and parallel computing models inspired by P systems and spiking neural networks.Spiking neural P system with anti-spikes can encode the balanced ternary three digits in a natural way using three states called anti-spikes, no-input and spikes. In this paper we use this variant of SN P system to simulate universal balanced ternary logic gates including AND,OR and NOT gate and to perform some basic balanced ternary arithmetic operations like addition and subtraction on balanced ternary integers. This paper provides an applicational answer to an open problem formulated by L.Pan and Gh. Păun.

Evolution-Communication Spiking Neural P Systems

2020 ◽  
pp. 2050064
Author(s):  
Tingfang Wu ◽  
Qiang Lyu ◽  
Linqiang Pan
Keyword(s):  
Parallel Computation ◽  
Fire Behavior ◽  
Information Storage ◽  
P Systems ◽  
Computational Power ◽  
Spiking Neural P Systems ◽  
Integrate And Fire ◽  
Restricted Form ◽  
The Family ◽  
Novel Variant

Spiking neural P systems (SNP systems) are a class of distributed and parallel computation models, which are inspired by the way in which neurons process information through spikes, where the integrate-and-fire behavior of neurons and the distribution of produced spikes are achieved by spiking rules. In this work, a novel mechanism for separately describing the integrate-and-fire behavior of neurons and the distribution of produced spikes, and a novel variant of the SNP systems, named evolution-communication SNP (ECSNP) systems, is proposed. More precisely, the integrate-and-fire behavior of neurons is achieved by spike-evolution rules, and the distribution of produced spikes is achieved by spike-communication rules. Then, the computational power of ECSNP systems is examined. It is demonstrated that ECSNP systems are Turing universal as number-generating devices. Furthermore, the computational power of ECSNP systems with a restricted form, i.e. the quantity of spikes in each neuron throughout a computation does not exceed some constant, is also investigated, and it is shown that such restricted ECSNP systems can only characterize the family of semilinear number sets. These results manifest that the capacity of neurons for information storage (i.e. the quantity of spikes) has a critical impact on the ECSNP systems to achieve a desired computational power.

Spiking Neural P Systems with a Generalized Use of Rules

2014 ◽  
Vol 26 (12) ◽  
pp. 2925-2943 ◽  
Author(s):  
Xingyi Zhang ◽  
Bangju Wang ◽  
Linqiang Pan
Keyword(s):  
Parallel Computing ◽  
Spiking Neurons ◽  
P Systems ◽  
Computational Power ◽  
Finite Sets ◽  
Spiking Neural P Systems ◽  
Semilinear Sets ◽  
Distributed Parallel Computing

Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired by spiking neurons, where the spiking rules are usually used in a sequential way (an applicable rule is applied one time at a step) or an exhaustive way (an applicable rule is applied as many times as possible at a step). In this letter, we consider a generalized way of using spiking rules by “combining” the sequential way and the exhaustive way: if a rule is used at some step, then at that step, it can be applied any possible number of times, nondeterministically chosen. The computational power of SN P systems with a generalized use of rules is investigated. Specifically, we prove that SN P systems with a generalized use of rules consisting of one neuron can characterize finite sets of numbers. If the systems consist of two neurons, then the computational power of such systems can be greatly improved, but not beyond generating semilinear sets of numbers. SN P systems with a generalized use of rules consisting of three neurons are proved to generate at least a non-semilinear set of numbers. In the case of allowing enough neurons, SN P systems with a generalized use of rules are computationally complete. These results show that the number of neurons is crucial for SN P systems with a generalized use of rules to achieve a desired computational power.

scholarly journals SPIKE TRAINS IN SPIKING NEURAL P SYSTEMS

2006 ◽  
Vol 17 (04) ◽  
pp. 975-1002 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
GRZEGORZ ROZENBERG
Keyword(s):  
Spike Train ◽  
Spike Trains ◽  
P Systems ◽  
P System ◽  
Spiking Neural P System ◽  
Spiking Neural P Systems ◽  
Semilinear Sets ◽  
Research Problems ◽  
Electrical Impulses

We continue here the study of the recently introduced spiking neural P systems, which mimic the way that neurons communicate with each other by means of short electrical impulses, identical in shape (voltage), but emitted at precise moments of time. The sequence of moments when a neuron emits a spike is called the spike train (of this neuron); by designating one neuron as the output neuron of a spiking neural P system II, one obtains a spike train of II. Given a specific way of assigning sets of numbers to spike trains of II, we obtain sets of numbers computed by II. In this way, spiking neural P systems become number computing devices. We consider a number of ways to assign (code) sets of numbers to (by) spike trains, and prove then computational completeness: the computed sets of numbers are exactly Turing computable sets. When the number of spikes present in the system is bounded, a characterization of semilinear sets of numbers is obtained. A number of research problems is also formulated.

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.

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