629 research outputs found
A Framework for Complexity Classes in Membrane Computing
The purpose of the present work is to give a general idea about the existing results and open problems
concerning the study of complexity classes within the membrane computing framework. To this aim,
membrane systems (seen as computing devices) are briefly introduced, providing the basic definition and
summarizing the key ideas, trying to cover the various approaches that are under investigation in this area
– of course, special attention is paid to the study of complexity classes. The paper concludes with some
final remarks that hint the reasons why this field (as well as other unconventional models of computation)
is attracting the attention of a growing community.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58
Simulating counting oracles with cooperation
We prove that monodirectional shallow chargeless P systems with active
membranes and minimal cooperation working in polynomial time precisely characterise
P#P
k , the complexity class of problems solved in polynomial time by deterministic
Turing machines with a polynomial number of parallel queries to an oracle for a counting
problem
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Membrane dissolution and division in P
Membrane systems with dividing and dissolving membranes
are known to solve PSPACE problems in polynomial time. However,
we give a P upperbound on an important restriction of such systems. In
particular we examine systems with dissolution, elementary division and
where each membrane initially has at most one child membrane. Even
though such systems may create exponentially many membranes, each
with di erent contents, we show that their power is upperbounded by PJunta de Andalucía TIC-581Ministerio de Educación y Ciencia TIN2006-1342
Monodirectional P Systems
We investigate the in
uence that the
ow of information in membrane systems
has on their computational complexity. In particular, we analyse the behaviour of P systems
with active membranes where communication only happens from a membrane towards
its parent, and never in the opposite direction. We prove that these \monodirectional
P systems" are, when working in polynomial time and under standard complexity-theoretic
assumptions, much less powerful than unrestricted ones: indeed, they characterise classes
of problems de ned by polynomial-time Turing machines with NP oracles, rather than
the whole class PSPACE of problems solvable in polynomial space
A Toolbox for Simpler Active Membrane Algorithms
We show that recogniser P systems with active membranes can be
augmented with a priority over their set of rules and any number of membrane
charges without loss of generality, as they can be simulated by standard P systems
with active membranes, in particular using only two charges. Furthermore, we
show that more general accepting conditions, such as sending out several, possibly
contradictory results and keeping only the first one, or rejecting by halting without
output, are also equivalent to the standard accepting conditions. The simulations
we propose are always without significant loss of efficiency, and thus the results of
this paper can hopefully simplify the design of algorithms for P systems with active
membranes
Frontiers of Membrane Computing: Open Problems and Research Topics
This is a list of open problems and research topics collected after the Twelfth
Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August
2011), meant initially to be a working material for Tenth Brainstorming Week on
Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was
circulated in several versions before the brainstorming and then modified according to
the discussions held in Sevilla and according to the progresses made during the meeting.
In the present form, the list gives an image about key research directions currently active
in membrane computing
Subroutines in P Systems and Closure Properties of Their Complexity Classes
The literature on membrane computing describes several variants of P systems
whose complexity classes C are "closed under exponentiation", that is, they satisfy
the inclusion PC C, where PC is the class of problems solved by polynomial-time
Turing machines with oracles for problems in C. This closure automatically implies closure
under many other operations, such as regular operations (union, concatenation,
Kleene star), intersection, complement, and polynomial-time mappings, which are inherited
from P. Such results are typically proved by showing how elements of a family of
P systems can be embedded into P systems simulating Turing machines, which exploit
the elements of as subroutines. Here we focus on the latter construction, abstracting
from the technical details which depend on the speci c variant of P system, in order to
describe a general strategy for proving closure under exponentiation
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