Abstract
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.
Highlights
Membrane computing (MC) is a representative of a new type of computing, abstracted from the phenomenon of signal transmission between cells in animals
Different from NSNP systems, the main novelties of this work are as follows: (i) We propose a novel P system called universal nonlinear spiking neural P systems with delays and weights on synapses closer to biological neurons
In the proposed NSNP-DW system, we find more applicable nonlinear functions that are common in neural networks and machine learning, so as to abstract the complex responses generated by spikes
Summary
Membrane computing (MC) is a representative of a new type of computing, abstracted from the phenomenon of signal transmission between cells in animals. Considering the difference in the number of synapses connected between neurons, Pan et al [26] previously proposed spiking neural P systems with weighted synapses. Song et al [31] proposed spiking neural P systems with delay on synapses (SNP-DS) in 2020. For SNP systems and variants mentioned above, the number of spikes in neurons is in integer form. NSNP systems need 117 and 164 neurons to construct Turing universal systems as functional computing device and number generator, respectively. (i) We propose a novel P system called universal nonlinear spiking neural P systems with delays and weights on synapses closer to biological neurons. In the proposed NSNP-DW system, we find more applicable nonlinear functions that are common in neural networks and machine learning, so as to abstract the complex responses generated by spikes. When the number of neurons is uncertain, m is often replaced by ∗
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