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

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.

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On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

Herald of Omsk University ◽

10.24147/1812-3996.2020.25(4).10-15 ◽

2020 ◽

Vol 25 (4) ◽

pp. 10-15

Author(s):

Alexander Nikolaevich Rybalov

Keyword(s):

Linear Group ◽

Modular Group ◽

Special Linear Group ◽

Second Order ◽

Integer Matrix ◽

Subset Sum ◽

Algorithmic Problems ◽

Almost All ◽

Subset Sum Problems ◽

Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

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On Structures and Behaviors of Spiking Neural P Systems and Petri Nets

Membrane Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-36751-9_11 ◽

2013 ◽

pp. 145-160 ◽

Cited By ~ 6

Author(s):

Francis George C. Cabarle ◽

Henry N. Adorna

Keyword(s):

Petri Nets ◽

P Systems ◽

Spiking Neural P Systems ◽

And Behaviors

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Small universal spiking neural P systems with dendritic/axonal delays and dendritic trunk/feedback

Neural Networks ◽

10.1016/j.neunet.2021.02.010 ◽

2021 ◽

Vol 138 ◽

pp. 126-139

Author(s):

Luis Garcia ◽

Giovanny Sanchez ◽

Eduardo Vazquez ◽

Gerardo Avalos ◽

Esteban Anides ◽

...

Keyword(s):

P Systems ◽

Spiking Neural P Systems

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Novel Numerical Spiking Neural P Systems with a Variable Consumption Strategy

Processes ◽

10.3390/pr9030549 ◽

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.

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