Spiking Neural P System

SSPPIIKKIINNGG NNEEUURRAALL PP
SSYYSSTTEEMM
PROJECT PREPARED BY:
Atit Gaonkar
XII A
SESSION: 2013-2014
KENDRIYA VIDYALAYA
NAVAL BASE
ARGA, KARWAR

OBJECTIVE
A comparison between Internet based
computing and SN P system and use Internet
computing Pebble game for SN P system.

ACKNOWLEDGEMENT
I wish to express my deep gratitude and
sincere thanks to Principal Mrs.
BHANUMATHY H.D for her
encouragement and facilities that she
provided for this project. I shall remain
indebted to her.
It would be my utmost pleasure to express
my sincere thanks to my computer science
teacher for providing a helping hand in
this project.
I can’t forget to offer my sincere thanks to
my classmates who helped me to carry out
this project.
My thanking will be incomplete without
thanking my parents who where always
with me and supported me in doing this

project. It is their help which made the
project to attain its present form.
CONTENTS
(i) INTRODUCTION.
(ii) COMPUTATION DAGS
(iii) SPIKING NEURON P SYSTEM
(iv) IC PEBBLE GAME.
(v) THEOREM.
(vi) REFERENCE

INTRODUCTION
 A number of basic life processes can be considered as
computation. Natural computing studies these
computations. Mainly there are three types of Computing.
DNA, Membrane, & Quantum Computations.
 Membrane Computing inspired by computational
processes in living cells, was introduced by Gheorghe Paun
in 1998 and they are calledP systems. P systems are a
class of distributed parallelcomputing devices of a
biochemicaltype which can be seen as general computing
architecture where various types of objects can be
processed by various operations.
 Now SN P Systems are proved to be number computing
devices. A neuron (node) sends signals (spike) along its
outgoing synapses (edges).
 We use a reserved symbol or letter ‘a’ to represent a spike.
Each neuron has its own rule for either sending Spike
(firing rules) or for internally consuming spike (forgetting

rules). The spiking can take place at the moment of time or
a later moment. In this paper a comparison betweenthis
graphical model of SN P system and Internet based
computing is done. Then we use Internet Computing
pebble game to make SN P system a computational device.
COMPUTATIONAL
DAGS
 A directed graph given by a set of nodes NG and a set of
arcs or directed edges AG each having the form ( u → v),
where u, v  NG. A path in G is a sequence of arcs that
share adjacent end points, as in the path from node u1 to
node un: ( u1 → u2 ), ( u2 → u3 ), …, ( un-1 → un ).
 A dag or a directed acyclicgraph is a digraph that has no
cycles; that is G cannot contain a path from ( u1 → u2 ), (
u2 → u3 ), …, ( un-1 → un ) wherein u1 = un. When a dag is
used to model a computation it is called a computation
dag.
 Each node v  NG represents a tasks of the computation
 An arc (u → v)  AG represents the dependence of task v on
task u; v cannot be executed until u is.

 For each arc (u → v)  AG . ‘u’ & ‘v’ are related as parent &
child respectively in G. Every dag has at least one
parentless node (which is called the source). Every finite
dag has at least one childless node calledsink. Here we use
this model of dags to represent the SN P system.
SPIKING NEURON P
SYSTEM
 The brain is a vastly complicated signal system with
neuron forming the basis of the system. Electrochemical
signals flow in one directionin neurons. The majority of
neurons receives input on the cell body and dendrite tree,
and transmits output via the axon. The connection
between the ends of axons and dendrites or cell body of
the neurons is the specialized structures calledsynapses
 In SN P system electricimpulses are passes through the
synapses .Such a pulse or impulse is calledspike or action
potential .Sequences of such impulses which occur at
regular or irregular intervals are called spike trains .Since
all spikes of a given neuron look alike the form of action

potential does not carry any information .Rather it is the
number and timing of spike what matter.
 Definition2.1 Mathematicallywe represent a Spiking
Neural P system (in short, an SN P system), of degree m 
1.
 It is expressed in the form
=( O,1,…,m,syn,i0 )
Where:
1. O= {a} is the singleton alphabet (a is called Spike)
2. 1,…,m, are neurons, of the form
i = (ni, Ri), 1 i  m
Where:
a) ni  0 is the initial number of spikes contained by
the cell ;
b)Ri is a finite set of rules of the followingtwo forms :
(1) E/ar a; t, where E is a regular expression over O, r 
1, and t  0;
(2) asλ for some s  1, with the restriction that asL(E)
for any rule. E/ ar a; t, of type (1) from Ri.
(3) Syn  {1, 2, …, m} X {1, 2, …., m} with (i,i) syn for 1 i
 m (synapses among cells);

(4) i0 {1,2,..,m} indicates the output neurons.
The rules of type (1) are firing (we also
say spiking) rules, and they are applied as follows. If the
neurons i contains k spikes, and ak  L (E), k  r, then the
rule E/ ar a; d can be applied. The applicationof this rule
means consuming or removing r spikes and thus only k-r
remain in i the neuron is fired, and it produces a spike
after d time units. If d=0, then the spike is emitted
immediately, if d=1 then the spike is emitted in the next
step etc. If the rule is used in step t and d  1, then in steps
t, t + 1, t + 2 ,…,t+d-1 the neuron is closed, so that it cannot
receive new spikes .
In step t + d, the neuron spikes and becomes again open,
so that it can receive spike which can be used in step
t+d+1.
 The rule of type (2) is forgetting rules, and they are applied
as follows: if the neurons i contains exactlys spikes, then
the rule asλ from Ri can be used, meaning that all s
spikes are removed from i .
(i) If a neuron spike with times t1, t2,…then either the
set of numbers t1,t2,…can be considered as computed by  ,
that is ST ( ) or Spike train of  where ST ( ) = < t1,
t2….>.

(ii) The set of intervals between spikes ts –t s-1 , s  2
can be the set computed by Nk( ), where Nk( ) ={ n / n =
ti –t i-1 , 2  i  k }.
IC PEBBLE GAME
 As soon as a spike enters in a neuron as input in the initial
configuration or from another neuron through synapses, it
makes it active altogether with the synapses that it
establishes with other neurons. That is if a neuron uses the
rule of the form ar a; 0 one spike is sent out at the time of
spike and the neuron is active. If a neuron uses the
forgetting rule as λ the neuron willbe inactive. In a self
activating SN P system we have an arbitrary large number
of neurons which differ by the number of spikes and the
rules they contain. Some of these willbe active and others
inactive.
 If there is a spike from (u → v) that means u is the parent
node and v is the child of u. In SN P system there can be
more than one parent node, all neuron which contain
spike in the first step are parent nodes. One output neuron
that sends a spike to the environment is known as the sink
node.

 In this section we explainthe IC Pebble game and what are
the similarities of this game with the working of SN P
system. The basic idea underlying pebble game is to use
tokens called pebbles to model the progress of a
computation on a dag. The placement or removal of
pebbles of various types- which is constrained by the
dependencies modeled by the dag’s arcs – represents the
changing status of the task represented by the dag’s node.
 The IC Pebble game on a computation dag G involves one
player S, the server, who has access to unlimited supplies
of two types of pebbles:
 ELIGIBLE pebbles: whose presence indicates a task’s
eligibilityfor execution.
 EXICUTED pebbles: whose presence indicates a task’s
having been executed.
The rules of IC Pebble games are
1. S begins by placing an ELIGIBLE pebble on each unpebbled
source of G.
2. At each step, S
 Select a node that contain an ELIGIBLE pebble
 Replace that pebble by an EXICUTED pebble

 Places an ELIGIBLE pebble on each unpebbled
node of G all of whose parents contain EXICUTED
pebbles.
3. S’s goal is to allocatein such a way that every node v of G
eventually contains an executable pebble.
For each step t of the play IC pebble game on the
a dag G, let X(t) denote the number of EXICUTED pebbles
on G’s nodes at step t and let E(t) denotes the number of
ELIGIBLE pebbles. X(t) = t is the idealized version of the
game this is not true in the original version. The aim of the
game is to maximize E(t) as possible.
A Pebble game for SN P System
Consider SN P system in the form of a directed
acyclicgraph.
1. The players of IC pebble game in SN P system are
Neurons that is all the neurons which contains spikes
initially willstart the game or all the neurons of such
type are known as the sources.
2. A finite or infinite set of clients, more than one neuron
is connected to the source neuron
 Can be ELIGIBLE neuron ( EL neurons) whose
presence indicates a spike eligiblefor execution.

 EXICUTED neuron (EX neurons)whose presence
indicates a neuron already executes the task or
already a spike is send out from the neuron.
 Places an ELIGIBLE neuron on each unpebbled
node of G at least one of whose parents contain
EXICUTED pebble
THEOREM
The Theorems Are :
a) For any schedule that allocatesnodes sequentially along
successive diagonal levels of the mesh E(t) = n whenever
nC2  t < (n + 1)C2 .
b) For any schedule for the mesh, if t lies in the preceding
range, then E(t) can be as large as possible as n.
Conclusion
In this paper we introduced IC Pebble game,
which incorporated the features of SN P system. Also
present methodologies to derive a mesh structure for SN P
system using different rules inside the neurons. This
shows the computational completeness of SN P system.

REFERENCES
1) G. Malewicz, A.L.Rosenberg, On batch
scheduling dags for Internet based Computing.
Euro- Par 2005, In Lecture notes in Computer
Science 3648, Springer – Verlag, Berlin, PP 262-
271.
2) G. Malewicz, A.L.Rosenberg, A Pebble
game for Internet – Based Computing, CIRM,
Marseille, France, 29 May – 2 June 2006.
3) Gh.Paun: Membrane computing-An
introduction. Springer – Verlag, Berlin 2002.

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