Spiking Neural P Systems with Thresholds

2014 ◽  
Vol 26 (7) ◽  
pp. 1340-1361 ◽  
Author(s):  
Xiangxiang Zeng ◽  
Xingyi Zhang ◽  
Tao Song ◽  
Linqiang Pan
Keyword(s):  
Parallel Computing ◽  
Open Problem ◽  
Spiking Neurons ◽  
P Systems ◽  
Spiking Neural P Systems ◽  
New Class ◽  
Semilinear Sets ◽  
The Family ◽  
Distributed And Parallel Computing ◽  
Computing Models

Spiking neural P systems with weights are a new class of distributed and parallel computing models inspired by spiking neurons. In such models, a neuron fires when its potential equals a given value (called a threshold). In this work, spiking neural P systems with thresholds (SNPT systems) are introduced, where a neuron fires not only when its potential equals the threshold but also when its potential is higher than the threshold. Two types of SNPT systems are investigated. In the first one, we consider that the firing of a neuron consumes part of the potential (the amount of potential consumed depends on the rule to be applied). In the second one, once a neuron fires, its potential vanishes (i.e., it is reset to zero). The computation power of the two types of SNPT systems is investigated. We prove that the systems of the former type can compute all Turing computable sets of numbers and the systems of the latter type characterize the family of semilinear sets of numbers. The results show that the firing mechanism of neurons has a crucial influence on the computation power of the SNPT systems, which also answers an open problem formulated in Wang, Hoogeboom, Pan, Păun, and Pérez-Jiménez ( 2010 ).

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.

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.

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 Spiking Neural P Systems with Weights

2010 ◽  
Vol 22 (10) ◽  
pp. 2615-2646 ◽  
Author(s):  
Jun Wang ◽  
Hendrik Jan Hoogeboom ◽  
Linqiang Pan ◽  
Gheorghe Păun ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Rational Numbers ◽  
P Systems ◽  
Natural Numbers ◽  
Open Problems ◽  
Spiking Neural P Systems ◽  
Semilinear Sets ◽  
The Family ◽  
Neuron Fire ◽  
Hard Problems

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values—weights, firing thresholds, potential consumed by each rule—can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, −1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

scholarly journals A Note on the Generative Power of Axon P Systems

2009 ◽  
Vol 4 (1) ◽  
pp. 92 ◽  
Author(s):  
Xingyi Zhang ◽  
Jun Wang ◽  
Linqiang Pan
Keyword(s):  
P Systems ◽  
Number Generator ◽  
Finite Sets ◽  
Open Problems ◽  
Spiking Neural P Systems ◽  
Generative Power ◽  
Semilinear Sets ◽  
The Family ◽  
Context Free

Axon P systems are a class of spiking neural P systems. In this paper, the axon P systems are used as number generators and language generators. As a language generator, the relationships of the families of languages generated by axon P systems with finite and context-free languages are considered. As a number generator, a characterization of the family of finite sets can be obtained by axon P systems with only one node. The relationships of sets of numbers generated by axon P systems with semilinear sets of numbers are also investigated. This paper partially answers some open problems formulated by H. Chen, T.-O. Ishdorj and Gh. Păun.

Homogeneous Spiking Neural P Systems without Delays

2013 ◽  
Vol 380-384 ◽  
pp. 2880-2883 ◽  
Author(s):  
Xian Wu Peng ◽  
Jian Xun Liu
Keyword(s):  
Neural Networks ◽  
Open Problem ◽  
Spiking Neural Networks ◽  
P Systems ◽  
Spiking Neural P Systems ◽  
New Class

Spiking neural P systems are a new class of bio-inspired computing devices incorporating the ideas of spiking neural networks into P systems. Homogeneous spiking neural P systems are a variant of spiking neural P systems, where each neuron has the same set of rules. The universality of homogeneous spiking neural P systems without delays is investigated and proved. This paper provides an answer to an open problem formulated by Zeng Xiangxiang, etal.

scholarly journals Implementation of Arithmetic Operations by SN P Systems with Communication on Request

2018 ◽  
Vol 13 (3) ◽  
pp. 353-364
Author(s):  
Yun Jiang ◽  
Yuan Kong ◽  
Chaoping Zhu
Keyword(s):  
Parallel Computing ◽  
P Systems ◽  
Arithmetic Operations ◽  
Spiking Neural P Systems ◽  
Grammar Systems ◽  
Distributed And Parallel Computing ◽  
The Way

Spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing devices inspired from the way neurons communicate by means of spikes. In most of the SN P systems investigated so far, the system communicates on command, and the application of evolution rules depends on the contents of a neuron. However, inspired from the parallel-cooperating grammar systems, it is natural to consider the opposite strategy: the system communicates on request, which means spikes are requested from neighboring neurons, depending on the contents of the neuron. Therefore, SN P systems with communication on request were proposed, where the spikes should be moved from a neuron to another one when the receiving neuron requests that. In this paper, we consider implementing arithmetical operations by means of SN P systems with communication on request. Specifically, adder, subtracter and multiplier are constructed by using SN P systems with communication on request.

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 Astrocytes

2012 ◽  
Vol 24 (3) ◽  
pp. 805-825 ◽  
Author(s):  
Linqiang Pan ◽  
Jun Wang ◽  
Hendrik Jan Hoogeboom
Keyword(s):  
Nervous System ◽  
Simple Form ◽  
P Systems ◽  
Inhibitory Influence ◽  
Spiking Neural P Systems ◽  
Biological Inspiration ◽  
Semilinear Sets

In a biological nervous system, astrocytes play an important role in the functioning and interaction of neurons, and astrocytes have excitatory and inhibitory influence on synapses. In this work, with this biological inspiration, a class of computation devices that consist of neurons and astrocytes is introduced, called spiking neural P systems with astrocytes (SNPA systems). The computation power of SNPA systems is investigated. It is proved that SNPA systems with simple neurons (all neurons have the same rule, one per neuron, of a very simple form) are Turing universal in both generative and accepting modes. If a bound is given on the number of spikes present in any neuron along a computation, then the computation power of SNPA systems is diminished. In this case, a characterization of semilinear sets of numbers is obtained.

scholarly journals A Comparative Analysis of Distributed and Parallel Computing

2018 ◽  
pp. 60-67
Keyword(s):  
Parallel Computing ◽  
Comparative Analysis ◽  
Distributed Systems ◽  
Data Centers ◽  
Parallel Systems ◽  
The Other ◽  
Pros And Cons ◽  
Distributed And Parallel Computing ◽  
Better Than ◽  
Computing Models

In the age of emerging technologies, the amount of data is increasing very rapidly. Due to massive increase of data the level of computations are increasing. Computer executes instructions sequentially. But the time has now changed and innovation has been advanced. We are currently managing gigantic data centers that perform billions of executions on consistent schedule. Truth be- hold, if we dive deep into the processor engineering and mechanism, even a successive machine works parallel. Parallel computing is growing faster as a substitute of distributing computing. The performance to functionality ratio of parallel systems is high. Also, the I/O usage of parallel systems is lower because of ability to perform all operations simultaneously. On the other hand, the performance to functionality ratio of distributed systems is low. The I/O usage of distributed systems is higher because of incapability to perform all operations simultaneously. In this paper, an overview of distributed and parallel computing is described. The basic concept of these two computing is discussed. In addition to this, pros and cons of distributed and parallel computing models are described. Through many aspects, we can conclude that parallel systems are better than distributed systems.

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