Asynchronous Spiking Neural P Systems with Structural Plasticity

Spiking neural P (in short, SNP) systems are computing devices inspired by biological spiking neurons. In this work we consider SNP systems with structural plasticity (in short, SNPSP systems) working in the asynchronous (in short, asyn mode). SNPSP systems represent a class of SNP systems that have dynamic synapses, i.e. neurons can use plasticity rules to create or remove synapses. We prove that for asyn mode, bounded SNPSP systems (where any neuron produces at most one spike each step) are not universal, while unbounded SNPSP systems with weighted synapses (a weight associated with each synapse allows a neuron to produce more than one spike each step) are universal. The latter systems are similar to SNP systems with extended rules in asyn mode (known to be universal) while the former are similar to SNP systems with standard rules only in asyn mode (conjectured not to be universal). Our results thus provide support to the conjecture of the still open problem.Ministerio de Economía y Competitividad TIN2012-3743

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

Matrix representation and simulation algorithm of spiking neural P systems with structural plasticity

Abstract(#br)In this paper, we create a matrix representation for spiking neural P systems with structural plasticity (SNPSP, for short), taking inspiration from existing algorithms and representations for related variants. Using our matrix representation, we provide a simulation algorithm for SNPSP systems. We prove that the algorithm correctly simulates an SNPSP system: our representation and algorithm are able to capture the syntax and semantics of SNPSP systems, e.g. plasticity rules, dynamism in the synapse set. Analyses of the time and space complexity of our algorithm show that its implementation can benefit using parallel computers. Our representation and simulation algorithm can be useful when implementing SNPSP systems and related variants with a dynamic topology, in software or..

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

Matrix representations of spiking neural P systems: Revisited

In the 2010, matrix representation of SN P system without delay was presented while in the case of SN P systems with delay, matrix representation was suggested in the 2017. These representations brought about series of simulation of SN P systems using computer software and hardware technology. In this work, we revisit these representation and provide some observations on the behavior of the computations of SN P systems. The concept of reachability of configuration is considered in both SN P systems with and without delays. A better computation of next configuration is proposed in the case of SN P system with delay.Comment: In: Gheorghe Paun (Ed) Proceedings of the 20th International Conference on Membrane Computing (CMC20), Editura Bibliostar, Ramnicu Valcea (2019) pp 227-24

Spiking neural P systems: matrix representation and formal verification

YesStructural and behavioural properties of models are very important in development of complex systems and applications. In this paper, we investigate such properties for some classes of SN P systems. First, a class of SN P systems associated to a set of routing problems are investigated through their matrix representation. This allows to make certain connections amongst some of these problems. Secondly, the behavioural properties of these SN P systems are formally verified through a natural and direct mapping of these models into kP systems which are equipped with adequate formal verification methods and tools. Some examples are used to prove the effectiveness of the verification approach.EPSRC research grant EP/R043787/1; DOST-ERDT research grants; Semirara Mining Corp; UPD-OVCRD

Asynchronous Spiking neural P systems with structural plasticity

Spiking neural P (in short, SNP) systems are computing devices inspired by biological spiking neurons. In this work we consider SNP systems with structural plasticity (in short, SNPSP systems) working in the asynchronous (in short, asyn mode). SNPSP systems represent a class of SNP systems that have dynamic synapses, i.e. neurons can use plasticity rules to create or remove synapses. We prove that for asyn mode, bounded SNPSP systems (where any neuron produces at most one spike each step) are not universal, while unbounded SNPSP systems with weighted synapses (a weight associated with each synapse allows a neuron to produce more than one spike each step) are universal. The latter systems are similar to SNP systems with extended rules in asyn mode (known to be universal) while the former are similar to SNP systems with standard rules only in asyn mode (conjectured not to be universal). Our results thus provide support to the conjecture of the still open problem.Ministerio de Economía y Competitividad TIN2012-3743

Spiking Neural P Systems with Structural Plasticity

Spiking neural P (SNP) systems are a class of parallel, distributed, and nondeterministic computing models inspired by the spiking of biological neurons. In this work, the biological feature known as structural plasticity is introduced in the framework of SNP systems. Structural plasticity refers to synapse creation and deletion, thus changing the synapse graph. The \programming" therefore of a brain-like model, the SNP system with structural plasticity (SNPSP system), is based on how neurons connect to each other. SNPSP systems are also a partial answer to an open question on SNP systems with dynamism only for synapses. For both the accepting and generative modes, we prove that SNPSP systems are universal. Modifying SNPSP systems semantics, we introduce the spike saving mode and prove that universality is maintained. In saving mode however, a deadlock state can arise, and we prove that reaching such a state is undecidable. Lastly, we provide one technique in order to use structural plasticity to solve a hard problem: a constant time, nondeterministic, and semi-uniform solution to the NP-complete problem Subset Sum.Ministerio de Economía y Competitividad TIN2012-3743