33,555 research outputs found
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
Computational efficiency of dissolution rules in membrane systems
Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to
efficiently solve computationally hard problems. On the one hand, an exponential number of objects
generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time.
On the other hand, when an exponential number of membranes is created and used as workspace, the
situation is very different. Two operations in P systems (membrane division and membrane creation)
capable of constructing an exponential number of membranes in linear time are studied in this paper.
NP-complete problems can be solved in polynomial time using P systems with active membranes
and with polarizations, but when electrical charges are not used, then dissolution rules turn out to
be very important. We show that in the framework of P systems with active membranes but without
polarizations and in the framework of P systems with membrane creation, dissolution rules play a
crucial role from the computational efficiency point of view.Ministerio de Educación y Ciencia TIN2005-09345-C04-0
Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes
In this paper we consider three restricted variants of P systems with active
membranes: (1) P systems using out communication rules only, (2) P systems using elementary
membrane division and dissolution rules only, and (3) polarizationless P systems
using dissolution and restricted evolution rules only. We show that every problem in P
can be solved with uniform families of any of these variants. This, using known results on
the upper bound of the computational power of variants (1) and (3) yields new characterizations
of the class P. In the case of variant (2) we provide a further characterization
of P by giving a semantic restriction on the computations of P systems of this varian
Minimal cooperation in polarizationless P systems with active membranes
P systems with active membranes is a well developed framework in the eld
of Membrane Computing. Using evolution, communication, dissolution and division rules,
we know that some kinds of problems can be solved by those systems, but taking into
account which ingredients are used. All these rules are inspired by the behavior of living
cells, who \compute" with their proteins in order to obtain energy, create components,
send information to other cells, kill themselves (in a process called apoptosis), and so on.
But there are other behaviors not captured in this framework. As mitosis is simulated
by division rules (for elementary and non-elementary membranes), meiosis, that is,
membrane ssion inspiration is captured in separation rules. It di ers from the rst in the
sense of duplication of the objects (that is, in division rules, we duplicate the objects not
involved in the rule, meanwhile in separation rules we divide the content of the original
membrane into the new membranes created).
Evolution rules simulate the transformation of components in membranes, but it is
well known that elements interact with another ones in order to obtain new components.
Cooperation in evolution rules is considered. More speci cally, minimal cooperation (in
the sense that only two objects can interact in order to create one or two objects
P Systems with Active Cells
P systems with active membranes is a widely studied framework within the
field of Membrane Computing since the creation of the discipline. The abstraction of the
structure and behavior of living cells is reflected in the tree-like hierarchy and the kinds
of rules that can be used in these kinds of systems.
Resembling the organization and communication between cells within tissues
that form organs, tissue-like P systems were defined as their abstractions, using
symport/antiport rules, that is, moving and exchanging elements from one cell to another
one. All the cells are located in an environment where there exist an arbitrary
number of some elements.
Lately, symport/antiport rules have been used in the framework of cell-like membrane
systems in order to study their computational power. Interesting results have been
reached, since they act similarly to their counterparts in the framework of tissue P systems.
Here, the use of the former defined rules (that is, evolution, communication, dissolution
and division/separation rules) is considered, but not working with a tree-like
structure. Some remarks about choosing good semantics are given
On acceptance conditions for membrane systems: characterisations of L and NL
In this paper we investigate the affect of various acceptance conditions on
recogniser membrane systems without dissolution. We demonstrate that two
particular acceptance conditions (one easier to program, the other easier to
prove correctness) both characterise the same complexity class, NL. We also
find that by restricting the acceptance conditions we obtain a characterisation
of L. We obtain these results by investigating the connectivity properties of
dependency graphs that model membrane system computations
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
Restricted Polarizationless P Systems with Active Membranes: Minimal Cooperation Only Outwards
Membrane computing is a computing paradigm providing a class of distributed
parallel computing devices of a biochemical type whose process units represent
biological membranes. In the cell-like basic model, a hierarchical membrane structure
formally described by a rooted tree is considered. It is well known that families of such
systems where the number of membranes can only decrease during a computation (for
instance by dissolving membranes), can only solve in polynomial time problems in class
P. P systems with active membranes is a variant where membranes play a central role in
their dynamics. In the seminal version, membranes have an electrical polarization (positive,
negative, or neutral) associated in any instant, and besides being dissolved, they can
also replicate by using division rules. These systems are computationally universal, that
is, equivalent in power to deterministic Turing machines, and computationally e fficient,
that is, able to solve computationally hard problems in polynomial time. If polarizations
in membranes are removed and dissolution rules are forbidden, then only problems in
class P can be solved in polynomial time by these systems (even in the case when division
rules for non-elementary membranes are permitted). In that framework it has been
shown that by considering minimal cooperation (left-hand side of such rules consists of
at most two symbols) and minimal production (only one object is produced by the application
of such rules) in object evolution rules, such systems provide e cient solutions to
NP{complete problems. In this paper, minimal cooperation and minimal production in
communication rules instead of object evolution rules is studied, and the computational
e fficiency of these systems is obtained in the case where division rules for non-elementary
membranes are permitted
Restricted Polarizationless P Systems with Active Membranes: Minimal Cooperation Only Inwards
Membrane computing is a computing paradigm providing a class of distributed
parallel computing devices of a biochemical type whose process units represent
biological membranes. In the cell-like basic model, a hierarchical membrane structure
formally described by a rooted tree is considered. It is well known that families of such
systems where the number of membranes can only decrease during a computation (for
instance by dissolving membranes), can only solve in polynomial time problems in class
P. P systems with active membranes is a variant where membranes play a central role in
their dynamics. In the seminal version, membranes have an electrical polarization (positive,
negative, or neutral) associated in any instant, and besides being dissolved, they can
also replicate by using division rules. These systems are computationally universal, that
is, equivalent in power to deterministic Turing machines, and computationally effi cient,
that is, able to solve computationally hard problems in polynomial time. If polarizations
in membranes are removed and dissolution rules are forbidden, then only problems in
class P can be solved in polynomial time by these systems (even in the case when division
rules for non-elementary membranes are permitted). In that framework it has been
shown that by considering minimal cooperation (left-hand side of such rules consists of
at most two symbols) and minimal production (only one object is produced by the application
of such rules) in object evolution rules, such systems provide effi cient solutions to
NP{complete problems. In this paper, minimal cooperation and minimal production in
communication rules instead of object evolution rules is studied, and the computational
e fficiency of these systems is obtained in the case where division rules for non-elementary
membranes are permitted
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