1. ways to control operations, computing models, etc.)

1.    Introduction Thearea of Membrane computing5 introduced by Gh. Paun in 1 isone of the recent branches of natural computing, and is considered one of thefast emerging research area in computer science1. The goal is toabstract computing ideas (data structures, operations with data, ways tocontrol operations, computing models, etc.) from the structure and thefunctioning of a single cell and from complexes of cells, such as tissues andorgans, including the brain.

The obtained models are distributed and parallelcomputing devices, usually called P systems. There are three mainclasses of P systems investigated: cell-like P systems, tissue-like P systems,and neural-like P systems. Many variants of all these systems have beenconsidered. The present work deals with a class of neural like P systems,called spiking neural P systems (SN P systems, for short), introduced in2. SN P systems are a class of distributed and parallel computingmodels inspired by spiking neurons. As we know, neurons are one of the mostinteresting cell-types in the human body.

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A large number of neurons working ina cooperative manner are able to perform tasks (such as learning, thought,self-awareness, intuition) that are not yet matched by the tools we can buildwith our current technology. Briefly, an SN P systemconsists of a set of neurons placed in the nodes of a directed graph,where neurons send signals (called spikes and denoted by the symbol a inwhat follows) along synapses (arcs of the graph). Spikes evolve by meansof standard spiking rules, which are of the form E/ac ? a; d, where E is a regularexpression over {a} andc, d are natural numbers, c ? 1,       d ? 0. The meaning is that if a neuroncontains k spikes such that ak ? L(E) and k ? c, then it can consume c spikes andproduce one spike after a delay of d steps. This spike is sent to all neuronsconnected by an outgoing synapse starting in the neuron where the rule wasapplied. There are also standard forgetting rules, of the form as? ?, with the meaning that s ? 1spikes are forgotten if the neuron contains exactly s spikes. In the standardSN P Systems neurons work in parallel way however several authors have recentlynoticed that the maximal parallelism way of rule application(which is widelyused in membrane systems) is rather non-realistic in some cases .

This factmotivated the consideration of various”strategies” and changes in the ruleapplication in membrane systems(or neuron firing in SN P systems). Thesequentiality induced by the spike number:at each step,the neuron with themaximum(or minimum) number of spikes among the neurons that are active(canspike) will fire. This strategy corresponds to a global view of the wholenetwork that makes the system sequential cite{2}. Another variation in SN PSystems is introduced by cite{3} with rules allowed to introduce zero, one ormore spikes at the same time called SN P Systems with extended rules.

Theconstruction with extended rules are always simple and useful as compared tostandard rules, the number of neurons is much smaller in each construction.Moreover standard rules can not generate all finite languages, but extendedrules help in this respect. Another variation with synapse-centric evolution incite{4} is inspired and motivated by the structural dynamism of biologicalsynapses, while incorporating ideas from non-static (i.e.

dynamic) graphs andnetworks called-SN P systems with scheduled synapses (in short, SSN P systems).SSN P systems are computationally universal with both local and globalschedules, even with a normal form.But let’s touch a more modern approach, that of considering sequentialSN P system, SN P system with scheduled synapses and SN P system with extendedrules altogether. The hybrid of all these three variants.

The maximalsequentiality on the basis of maximum number of spikes in neurons, thescheduling of synapses with respect to the reference neuron and applying extendedrules along with standard rules. How this can be incorporated in SN P systems?It is the objective of our research. 

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