930 research outputs found
One and Two Polarizations, Membrane Creation and Objects Complexity in P Systems
We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind. We here show that they generate all recursively enumerable languages, and two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case. Then we prove that 10 + m symbols are enough to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative integers, only using rules of rewriting and sending objects out. We show that accepting can be done by deterministic systems. Finally, remarks and open questions are presented.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
Membrane division, restricted membrane creation and object complexity in P systems
We improve, by using register machines, some existing universality results for specific models of
P systems. P systems with membrane creation are known to generate all recursively enumerable sets
of vectors of non-negative integers, even when no region (except the environment) contains more than
one object of the same kind.We showhere that they generate all recursively enumerable languages, and
that two membrane labels are sufficient (the same result holds for accepting all recursively enumerable
vectors of non-negative integers). Moreover, at most two objects are present inside the system at any
time in the generative case.We then prove that 10 + msymbols are sufficient to generate any recursively
enumerable language over m symbols. P systems with active membranes without polarizations are
known to generate all recursively enumerable sets of vectors of non-negative integers. We show that
they generate all recursively enumerable languages; four starting membranes with three labels or
seven starting membranes with two labels are sufficient. P systems with active membranes and two
polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative
integers, using only rules of rewriting and sending objects out.We show that accepting can be done by
deterministic systems. Finally, we show that P systems with restricted membrane creation (the newly
created membrane can only be of the same kind as the parent one) generate at least matrix languages,
even when having at most one object in the configuration (except the environment). We conclude by
presenting a summary of the main results obtained in this paper and a list of open questions.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
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
Solving SAT with Antimatter in Membrane Computing
The set of NP-complete problems is split into weakly and strongly NP-
complete ones. The di erence consists in the in
uence of the encoding scheme of the
input. In the case of weakly NP-complete problems, the intractability depends on the
encoding scheme, whereas in the case of strongly NP-complete problems the problem
is intractable even if all data are encoded in a unary way. The reference for strongly
NP-complete problems is the Satis ability Problem (the SAT problem). In this paper,
we provide a uniform family of P systems with active membranes which solves SAT {
without polarizations, without dissolution, with division for elementary membranes and
with matter/antimatter annihilation. To the best of our knowledge, it is the rst solution
to a strongly NP-complete problem in this P system model.Ministerio de Economía y Competitividad TIN2012-3743
Recognizer P Systems with Antimatter
In this paper, we consider recognizer P systems with antimatter
and the in
uence of the matter/antimatter annihilation rules having weak
priority over all the other rules or not. We rst provide a uniform family of P
systems with active membranes which solves the strongly NP-complete problem
SAT, the Satis ability Problem, without polarizations and without dissolution,
yet with division for elementary membranes and with matter/antimatter annihilation
rules having weak priority over all the other rules. Then we show that
without this weak priority of the matter/antimatter annihilation rules over all
the other rules we only obtain the complexity class PMinisterio de Economía y Competitividad TIN2012-3743
Further Open Problems in Membrane Computing
A series of open problems and research topics in membrane com-
puting are pointed out, most of them suggested by recent developments in this
area. Many of these problems have several facets and branchings, and further
facets and branchings can surely be found after addressing them in a more
careful manner
P Systems with Active Membranes, Without Polarizations and Without Dissolution: A Characterization of P
We study the computational efficiency of recognizer P systems
with active membranes without polarizations and without dissolution.
The main result of the paper is the following: the polynomial
computational complexity class associated with the class of recognizer P
systems is equal to the standard complexity class P.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
A Characterization of PSPACE with Antimatter and Membrane Creation
The use of negative information provides a new tool for exploring the limits
of P systems as computational devices. In this paper we prove that the combination of
antimatter and annihilation rules (based on the annihilation of physical particles and
antiparticles) and membrane creation (based on autopoiesis) provides a P system model
able to solve PSPACE-complete problems. Namely, we provide a uniform family of
P system in such P system model which solves the satis ability problem for quanti ed
Boolean formulas (QSAT). In the second part of the paper, we prove that all the decision
problems which can be solved with this P system model belong to the complexity class
PSPACE, so this P system model characterises PSPACE.Ministerio de Economía y Competitividad TIN2012-3743
Design Patterns for Efficient Solutions to NP-Complete Problems in Membrane Computing
Many variants of P systems have the ability to generate an
exponential number of membranes in linear time. This feature has been
exploited to elaborate (theoretical) efficient solutions to NP-complete, or
even harder, problems. A thorough review of the existent solutions shows
the utilization of common techniques and procedures. The abstraction
of the latter into design patterns can serve to ease and accelerate the
construction of efficient solutions to new hard problems.Ministerio de Economía y Competitividad TIN2017-89842-
Polarizationless P Systems with One Active Membrane
The aim of this paper is to study the computational power of P systems with
one active membrane without polarizations. For P systems with active membranes, it is
known that computational completeness can be obtained with either of the following combinations
of features: 1)two polarizations, 2)membrane creation and dissolution, 3)four
membranes with three labels, membrane division and dissolution, 4)seven membranes
with two labels, membrane division and dissolution.
Clearly, with one membrane only object evolution rules and send-out rules are permitted.
Two variants are considered: external output and internal output
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