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.

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 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.

Spiking Neural P Systems with Structural Plasticity: Attacking the Subset Sum Problem

2015 ◽  
pp. 106-116 ◽  
Author(s):  
Francis George C. Cabarle ◽  
Nestine Hope S. Hernandez ◽  
Miguel Ángel Martínez-del-Amor
Keyword(s):  
Structural Plasticity ◽  
P Systems ◽  
Spiking Neural P Systems ◽  
Subset Sum Problem ◽  
Subset Sum

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 Dynamic Threshold Neural P Systems with Multiple Channels and Inhibitory Rules

Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1281
Author(s):  
Xiu Yin ◽  
Xiyu Liu
Keyword(s):  
Neural Networks ◽  
Parallel Computing ◽  
Ion Channels ◽  
Inhibitory Synapses ◽  
Dynamic Threshold ◽  
P System ◽  
Excitatory Synapses ◽  
Multiple Channels ◽  
Computing Model ◽  
Distributed Parallel Computing

In biological neural networks, neurons transmit chemical signals through synapses, and there are multiple ion channels during transmission. Moreover, synapses are divided into inhibitory synapses and excitatory synapses. The firing mechanism of previous spiking neural P (SNP) systems and their variants is basically the same as excitatory synapses, but the function of inhibitory synapses is rarely reflected in these systems. In order to more fully simulate the characteristics of neurons communicating through synapses, this paper proposes a dynamic threshold neural P system with inhibitory rules and multiple channels (DTNP-MCIR systems). DTNP-MCIR systems represent a distributed parallel computing model. We prove that DTNP-MCIR systems are Turing universal as number generating/accepting devices. In addition, we design a small universal DTNP-MCIR system with 73 neurons as function computing devices.

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.

scholarly journals Uniform solutions to SAT and Subset Sum by spiking neural P systems

2008 ◽  
Vol 8 (4) ◽  
pp. 681-702 ◽  
Author(s):  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Claudio Zandron ◽  
Gheorghe Păun ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
P Systems ◽  
Spiking Neural P Systems ◽  
Subset Sum

A time-free uniform solution to subset sum problem by tissue P systems with cell division

2015 ◽  
Vol 27 (1) ◽  
pp. 17-32 ◽  
Author(s):  
BOSHENG SONG ◽  
TAO SONG ◽  
LINQIANG PAN
Keyword(s):  
Cell Division ◽  
Execution Time ◽  
P Systems ◽  
Subset Sum Problem ◽  
Biological Inspiration ◽  
Global Clock ◽  
Subset Sum ◽  
Uniform Solution ◽  
Hard Problems ◽  
Computing Models

Tissue P systems are a class of bio-inspired computing models motivated by biochemical interactions between cells in a tissue-like arrangement. Tissue P systems with cell division offer a theoretical device to generate an exponentially growing structure in order to solve computationally hard problems efficiently with the assumption that there exists a global clock to mark the time for the system, the execution of each rule is completed in exactly one time unit. Actually, the execution time of different biochemical reactions in cells depends on many uncertain factors. In this work, with this biological inspiration, we remove the restriction on the execution time of each rule, and the computational efficiency of tissue P systems with cell division is investigated. Specifically, we solve subset sum problem by tissue P systems with cell division in a time-free manner in the sense that the correctness of the solution to the problem does not depend on the execution time of the involved rules.

scholarly journals Solving Subset Sum Problems by Time-free Spiking Neural P Systems

2014 ◽  
Vol 8 (1) ◽  
pp. 327-332 ◽  
Author(s):  
Tao Song ◽  
Liang Luo ◽  
Juanjuan He ◽  
Zhihua Chen ◽  
Kai Zhang
Keyword(s):  
P Systems ◽  
Spiking Neural P Systems ◽  
Subset Sum ◽  
Subset Sum Problems

Spiking Neural P Systems with Delay on Synapses

2020 ◽  
Vol 31 (01) ◽  
pp. 2050042
Author(s):  
Xiaoxiao Song ◽  
Luis Valencia-Cabrera ◽  
Hong Peng ◽  
Jun Wang ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Information Transmission ◽  
Delay Time ◽  
Experimental Validation ◽  
P Systems ◽  
Neural Systems ◽  
Presynaptic Neuron ◽  
Spiking Neural P Systems ◽  
Computing Model ◽  
Transmission Speed

Based on the feature and communication of neurons in animal neural systems, spiking neural P systems (SN P systems) were proposed as a kind of powerful computing model. Considering the length of axons and the information transmission speed on synapses, SN P systems with delay on synapses (SNP-DS systems) are proposed in this work. Unlike the traditional SN P systems, where all the postsynaptic neurons receive spikes at the same instant from their presynaptic neuron, the postsynaptic neurons in SNP-DS systems would receive spikes at different instants, depending on the delay time on the synapses connecting them. It is proved that the SNP-DS systems are universal as number generators. Two small universal SNP-DS systems, with standard or extended rules, are constructed to compute functions, using 56 and 36 neurons, respectively. Moreover, a simulator has been provided, in order to check the correctness of these two SNP-DS systems, thus providing an experimental validation of the universality of the systems designed.

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