Spiking Neural P Systems - Advancing Artificial Intelligence Through Biological Process Applications - page 62

se computational devices. Membrane systems,
currently called P systems , were introduced in
this context, taking as basic architecture the
structure of a cell, with chemical objects evolving
in compartments delimited by membranes. In a
cell, the membranes are hierarchically arranged
(hence placed in the nodes of a tree), but also P
systems with membranes placed in the nodes of
a general graph were considered.
The (mathematical) theory of membrane
computing is well developed, and a lot of classes
of P systems were introduced and investigated
- details can be found at the web site from
http://psystems.disco.unimib.it, as well in the
monograph (Păun, 2002). The main directions
of research concern the computing power of
P systems and their usefulness for solving
computationally hard problems in a feasible time,
by making use of the parallelism intrinsic to the
model. Thus, most classes of P systems were
proved to be Turing complete, and, in the cases
where an exponential workspace can be produced
in a linear time (e.g., by dividing membranes
- mitosis ), polynomial solutions to NP -complete
problems were devised.
Recently, a series of applications of P systems
were reported, expecially using membrane
computing as a framework for building models
of biological phenomena (approached at a micro
level, thus contrasting with the models based on
differential equations, which approach the reality
at a macro level). The above mentioned web page
contains information in this respect; details can
be also found in the volume (Ciobanu et al., eds.,
2006),
Also the neural cell was considered as an
inspiration source for membrane computing.
The present chapter is a quick introduction to so-
called spiking neural P systems (in short, SN P
systems ), a class of P systems defined in (Ionescu
et al., 2006), starting from the way the neurons
cooperate in large neural nets communicating by
electrical impulses ( spikes ). Neurons are sending
to each others electrical impulses of identical shape

(duration, voltage, etc.), with the information “en-
coded” in the frequency of these impulses, hence
in the time passed between consecutive spikes. For
neurologists, this is nothing new, related draw-
ings already appear in papers by Ramon y Cajal,
a pioneer of neuroscience at the beginning of the
last century, but in the recent years “computing
by spiking” became a vivid research area, with
the hope to lead to a neural computing “of the
third generation” - see, e.g., (Gerstner and Kistler,
2002), (Maass and Bishop, eds., 1999).
For membrane computing it is natural to incor-
porate the idea of spiking neurons (already neural-
like P systems exist, based on different ingredients,
efforts to compute with a small number of objects
were recently made in several papers, using the
time as a support of information, for instance,
taking the time between two events as the result
of a computation, was also considered), but still
important differences exist between the general
way of working with multisets of objects in the
compartments of a cell-like membrane structure
- as in usual P systems - and the way the neurons
communicate by spikes. A way to answer this
challenge was proposed in (Ionescu et al., 2006):
neurons taken as single membranes, placed in the
nodes of a graph corresponding to synapses, only
one type of objects present in neurons, the spikes,
with specific rules for handling them, and with
the distance in time between consecutive spikes
playing an important role (e.g., the result of a
computation being defined either as the whole
spike train of a distinguished output neuron, or as
the distance between consecutive spikes). Details
will be given immediately.
What is obtained is a computing device whose
behaviour resembles the process from the neuron
nets, meant to generate strings or infinite sequenc-
es (like in formal language theory), to recognize
or translate strings or infinite sequences (like in
automata theory), to generate or accept natural
numbers, or to compute number functions (like
in membrane computing). Results of all these
types will be mentioned below. Nothing is said