13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 143 - 159.
On Structures and Behaviors of Spiking Neural
P Systems and Petri Nets
Francis George C. Cabarle, Henry N. Adorna
Algorithms & Complexity Lab
Department of Computer Science
University of the Philippines Diliman
Diliman 1101 Quezon City, Philippines
E-mail: fccabarle@up.edu.ph, hnadorna@dcs.upd.edu.ph
Abstract. We investigate the relationship between Petri nets and Spiking
Neural P (SNP) systems. In particular, we consider a special kind
of Petri nets such that (1) all places and transitions shall be connected
on path from the input place to the output place, (2) every place and
transition should contribute in the processing of tokens, (3) for any case,
the procedure will halt, and when it halts token is only in output place
and all the other places are empty, and (4) there should be no dead
place/transition. Using the building blocks of this special type of Petri
nets we construct an SNP system that simulates this special net. We
observed that the structural and behavioral properties of these nets are
carried over to the SNP that simulates it. Certain routing types such as
AND-split and OR-join are natural in SNP systems, but AND-joins ans
especially OR-splits turn out to be more complex. Finally our results
suggested the possibility of analysing workflow.
Key words: Spiking Neural P systems, routing, joins, splits, Petri nets, simulations
1 Introduction
SNP systems, first introduced in 2006 in [9], are inspired by the way biological
spiking neurons compute: neurons are abstracted by treating them as monomembranar
cells placed on nodes of a directed graph, where synapses or connections
between neurons are the directed arcs. Indistinct signals in the neurons,
called action potential or simply spike in biology, are modeled using only the
symbol a. Information is encoded not in the symbol or spike itself but in the
time interval when spikes are produced or in the spike multiplicity. Time is not
just a resource in SNP systems but a way to represent information. Since the
introduction of SNP systems they have been used mostly as computing devices
with universality results in [9,3], as well as solving NP-complete problems as in
[16]. Petri nets however, since their introduction in 1962, have enjoyed an extensive
theory on Petri net behavior and structure. Petri nets are bipartite directed
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