Universal Nonlinear Spiking Neural P Systems with Delays and Weights on Synapses

Area of Science:

• Theoretical Computer Science
• Computational Neuroscience
• Biologically Inspired Computing

Background:

• Nonlinear spiking neural P systems (NSNP systems) are computational models using real numbers for neuron states and nonlinear rules for firing.
• Existing NSNP systems lack mechanisms for enhancing computational efficiency.

Purpose of the Study:

• To introduce weights and delays to NSNP systems to improve their computing performance.
• To propose and analyze universal nonlinear spiking neural P systems with delays and weights on synapses (NSNP-DW).

Main Methods:

• Introducing weights as multiplicative constants to modulate spike transmission across synapses.
• Incorporating delays to model the speed of information transmission between neurons.
• Proving the Turing universality of the NSNP-DW system as number generating and accepting devices.

Main Results:

• The proposed NSNP-DW systems achieve enhanced computational performance.
• Turing universality is proven for NSNP-DW systems, demonstrating their capability for universal computation.
• Small universal NSNP-DW systems were constructed using 47 and 43 neurons.
• An NSNP-DW system was presented for solving the Subset Sum problem.

Conclusions:

• NSNP-DW systems represent a significant advancement in neural P systems, offering improved computational power.
• The introduction of weights and delays enhances the efficiency and universality of these computational models.
• NSNP-DW systems hold potential for solving complex computational problems and advancing the field of theoretical computer science.