Time-Free Spiking Neural P Systems

2011 ◽  
Vol 23 (5) ◽  
pp. 1320-1342 ◽  
Author(s):  
Linqiang Pan ◽  
Xiangxiang Zeng ◽  
Xingyi Zhang
Keyword(s):  
Environmental Factors ◽  
P Systems ◽  
P System ◽  
Spiking Neural P Systems ◽  
Computation Result ◽  
Semilinear Sets ◽  
Execution Times ◽  
Definition Of ◽  
Robust Systems

Different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, a realistic definition of nonsynchronized spiking neural P systems (SN P systems, for short) is considered: during the work of an SN P system, the execution times of spiking rules cannot be known exactly (i.e., they are arbitrary). In order to establish robust systems against the environmental factors, a special class of SN P systems, called time-free SN P systems, is introduced, which always produce the same computation result independent of the execution times of the rules. The universality of time-free SN P systems is investigated. It is proved that these P systems with extended rules (several spikes can be produced by a rule) are equivalent to register machines. However, if the number of spikes present in the system is bounded, then the power of time-free SN P systems falls, and in this case, a characterization of semilinear sets of natural numbers is obtained.

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.

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.

ON ONE-MEMBRANE P SYSTEMS OPERATING IN SEQUENTIAL MODE

2005 ◽  
Vol 16 (05) ◽  
pp. 867-881 ◽  
Author(s):  
ZHE DANG ◽  
OSCAR H. IBARRA
Keyword(s):  
Natural Generalization ◽  
P Systems ◽  
P System ◽  
Catalytic Systems ◽  
Semilinear Sets ◽  
System A ◽  
Vector Addition ◽  
Parallel Version ◽  
Proper Subclass ◽  
Definition Of

In the standard definition of a P system, a computation step consists of a parallel application of a "maximal" set of nondeterministically chosen rules. Referring to this system as a parallel P system, we consider in this paper a sequential P system, in which each step consists of an application of a single nondeterministically chosen rule. We show the following:1. For 1-membrane purely catalytic systems (pure CS's), the sequential version is strictly weaker than the parallel version in that the former defines (i.e., generates) exactly the semilinear sets, whereas the latter is known to define nonrecursive sets.2. For 1-membrane communicating P systems (CPS's), the sequential version can only define a proper subclass of the semilinear sets, whereas the parallel version is known to define nonrecursive sets.3. Adding a new type of rule of the form: ab → axbyccomedcometo the CPS (a natural generalization of the rule ab → axbyccomein the original model), where x, y ∈ {here, out}, to the sequential 1-membrane CPS makes it equivalent to a vector addition system.4. Sequential 1-membrane symport/antiport systems (SA's) are equivalent to vector addition systems, contrasting the known result that the parallel versions can define nonrecursive sets.5. Sequential 1-membrane SA's whose rules have radius 1, (1,1), (1,2) (i.e., of the form (a, out), (a, in), (a, out; b, in), (a, out; bc, in)) generate exactly the semilinear sets. However, if the rules have radius 1, (1,1), (2,1) (i.e., of the form (ab, out; c, in)), the SA's can only generate a proper subclass of the semilinear sets.

scholarly journals Solving Multidimensional 0-1 Knapsack Problem with Time-Free Tissue P Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xiangrong Liu ◽  
Ziming Li ◽  
Juan Suo ◽  
Ying Ju ◽  
Juan Liu ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Knapsack Problem ◽  
Execution Time ◽  
Efficient Solution ◽  
P Systems ◽  
Distributed Model ◽  
P System ◽  
Biological Processes ◽  
Execution Times ◽  
Tissue P System

Tissue P system is a class of parallel and distributed model; a feature of traditional tissue P system is that the execution time of certain biological processes is very sensitive to environmental factors that might be hard to control. In this work, we construct a family of tissue P systems that works independently from the values associated with the execution times of the rules. Furthermore, we present a time-free efficient solution to multidimensional 0-1 knapsack problem by timed recognizer tissue P systems.

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.

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 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.

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.

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