Arithmetic Operations with Spiking Neural P Systems with Rules and Weights on Synapses

The application of spiking neural P systems with rules and weights on synapses to arithmetic operations is discussed in this paper. We design specific spiking neural P systems with rules and weights on synapses for successfully performing addition, multiplication and the greatest common divisor. This is the first attempt to discuss the application of the new variant of spiking neural P systems, spiking neural P systems with rules and weights on synapses, and especially the use of spiking neural P systems to perform the greatest common divisor. Comparing with the results reported in the literature, smaller number of neurons are required to fulfill the arithmetic operations

Spiking Neural P Systems with Communication on Request

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Spiking Neural P Systems are Neural System models characterised by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural P systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these P systems, a speci ed number of spikes are consumed and a speci ed number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron. In the present work, a novel communication strategy among neurons of Spiking Neural P Systems is proposed. In the resulting models, called Spiking Neural P Systems with Communication on Request, the spikes are requested from neighbouring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural P systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron). The Spiking Neural P Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems

Spiking Neural P systems with weights

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.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC-0420

Spiking Neural P Systems with Addition/Subtraction Computing on Synapses

Spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing models inspired from biological spiking neurons. In this paper, we introduce a variant called SN P systems with addition/subtraction computing on synapses (CSSN P systems). CSSN P systems are inspired and motivated by the shunting inhibition of biological synapses, while incorporating ideas from dynamic graphs and networks. We consider addition and subtraction operations on synapses, and prove that CSSN P systems are computationally universal as number generators, under a normal form (i.e. a simplifying set of restrictions)

Spiking Neural P Systems with Structural Plasticity: Attacking the Subset Sum Problem

Spiking neural P systems with structural plasticity (in short, SNPSP systems) are models of computations inspired by the function and structure of biological neurons. In SNPSP systems, neurons can create or delete synapses using plasticity rules. We report two families of solutions: a non-uniform and a uniform one, to the NP-complete problem Subset Sum using SNPSP systems. Instead of the usual rule-level nondeterminism (choosing which rule to apply) we use synapse-level nondeterminism (choosing which synapses to create or delete). The nondeterminism due to plasticity rules have the following improvements from a previous solution: in our non-uniform solution, plasticity rules allowed for a normal form to be used (i.e. without forgetting rules or rules with delays, system is simple, only synapse-level nondeterminism); in our uniform solution the number of neurons and the computation steps are reduced.Ministerio de Economía y Competitividad TIN2012-3743

Logic Negation with Spiking Neural P Systems

Nowadays, the success of neural networks as reasoning systems is doubtless. Nonetheless, one of the drawbacks of such reasoning systems is that they work as black-boxes and the acquired knowledge is not human readable. In this paper, we present a new step in order to close the gap between connectionist and logic based reasoning systems. We show that two of the most used inference rules for obtaining negative information in rule based reasoning systems, the so-called Closed World Assumption and Negation as Finite Failure can be characterized by means of spiking neural P systems, a formal model of the third generation of neural networks born in the framework of membrane computing.Comment: 25 pages, 1 figur

A CMOS Spiking Neuron for Brain-Inspired Neural Networks with Resistive Synapses and In-Situ Learning

Nanoscale resistive memories are expected to fuel dense integration of electronic synapses for large-scale neuromorphic system. To realize such a brain-inspired computing chip, a compact CMOS spiking neuron that performs in-situ learning and computing while driving a large number of resistive synapses is desired. This work presents a novel leaky integrate-and-fire neuron design which implements the dual-mode operation of current integration and synaptic drive, with a single opamp and enables in-situ learning with crossbar resistive synapses. The proposed design was implemented in a 0.18 $\mu$m CMOS technology. Measurements show neuron's ability to drive a thousand resistive synapses, and demonstrate an in-situ associative learning. The neuron circuit occupies a small area of 0.01 mm$^2$ and has an energy-efficiency of 9.3 pJ$/$spike$/$synapse

Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective

On metrics of density and power efficiency, neuromorphic technologies have the potential to surpass mainstream computing technologies in tasks where real-time functionality, adaptability, and autonomy are essential. While algorithmic advances in neuromorphic computing are proceeding successfully, the potential of memristors to improve neuromorphic computing have not yet born fruit, primarily because they are often used as a drop-in replacement to conventional memory. However, interdisciplinary approaches anchored in machine learning theory suggest that multifactor plasticity rules matching neural and synaptic dynamics to the device capabilities can take better advantage of memristor dynamics and its stochasticity. Furthermore, such plasticity rules generally show much higher performance than that of classical Spike Time Dependent Plasticity (STDP) rules. This chapter reviews the recent development in learning with spiking neural network models and their possible implementation with memristor-based hardware