LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Eilenberg P Systems with Symbol-Objects
Francesco Bernardini, Marian Gheorghe, and Mike Holcombe
Department of Computer Science
The University of Sheffield
Regent Court, Portobello Street, Sheffield, S1 4DP, UK
{F.Bernardini, M.Gheorghe, M.Holcombe}@dcs.shef.ac.uk
Abstract. A class of P systems, called EOP systems, with symbol objects
processed by evolution rules distributed alongside the transitions
of an Eilenberg machine, is introduced. A parallel variant of EOP systems,
called EOPP systems, is also defined and the power of both EOP
and EOPP systems is investigated in relationship with three parameters:
number of membranes, states and set of distributed rules. It is proven
that the family of Parikh sets of vectors of numbers generated by EOP
systems with one membrane, one state and one single set of rules coincides
with the family of Parikh sets of context-free languages. The hierarchy
collapses when at least one membrane, two states and four sets of
rules are used and in this case a characterization of the family of Parikh
sets of vectors associated with ET0L languages is obtained. It is also
shown that every EOP system may be simulated by an EOPP system
and EOPP systems may be used for solving NP-complete problems. In
particular linear time solutions are provided for the SAT problem.
1 Introduction
P systems were introduced by Gh. Păun [12] as a computational model inspired
by the structure and functioning of the cell. A central role in this context
is played by membranes delimiting regions and allowing or preventing the
transport of different molecules and chemicals among them. Different classes
of P systems dealing with string objects or symbol objects, considering sets
or multisets of elements leading to various families of languages were investigated
[13] (an up-to-date bibliography of the whole area may be found at
http://psystems.disco.unimib.it/). Because rewriting alone even in the context
of a highly parallel environment of a membrane structure is not enough to lead
to characterizations of recursively enumerable languages, various other features
have been considered, such as a priority relationship over the set of rules, permitting
or forbidding conditions associated with rules, restrictions on the derivation
mode, the possibility to control the membrane permeability [7] etc (for more details
see [13]). In general the most used priority relationship on the set of rewriting
rules is a partial order relationship, well studied in the context of generative
mechanisms with restrictions in derivation [5].
In [1] the priority relationship were replaced by a transition diagram associated
with an Eilenberg machine giving birth to two classes of Eilenberg systems,
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 49–60, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004