58 research outputs found
On Complexity Classes of Spiking Neural P Systems
A sequence of papers have been recently published, pointing out various
intractable problems which may be solved in certain fashions within the framework of
spiking neural (SN) P systems. On the other hand, there are also results demonstrating
limitations of SN P systems. In this paper we define recognizer SN P systems providing a
general platform for this type of results. We intend to give a more systematic characterization
of computational power of variants of SN P systems, and establish their relation
to standard complexity classes
On The Semantics of Annihilation Rules in Membrane Computing
It is well known that polarizationless recognizer P systems with active membranes,
without dissolution, with division of elementary and non-elementary membranes,
with antimatter and matter/antimatter annihilation rules can solve all problems in NP
when the annihilation rules have (weak) priority over all the other rules. Until now, it was
an open problem whether these systems can still solve all NP problems if the priority of
the matter/antimatter annihilation rules is removed.
In this paper we provide a negative answer to this question: we prove that the class of
problems solvable by this model of P systems without priority of the matter/antimatter
annihilation rules is exactly P. To the best of our knowledge, this is the rst paper in the
literature of P systems where the semantics of applying the rules constitutes a frontier
of tractability.Ministerio de Economía y Competitividad TIN2012-3743
Limits on P Systems with Proteins and Without Division
In the field of Membrane Computing, computational complexity theory has
been widely studied trying to nd frontiers of efficiency by means of syntactic or semantical ingredients. The objective of this is to nd two kinds of systems, one non-efficient
and another one, at least, presumably efficient, that is, that can solve NP-complete prob-
lems in polynomial time, and adapt a solution of such a problem in the former. If it is
possible, then P = NP. Several borderlines have been defi ned, and new characterizations
of different types of membrane systems have been published.
In this work, a certain type of P system, where proteins act as a supporting element
for a rule to be red, is studied. In particular, while division rules, the abstraction of
cellular mitosis is forbidden, only problems from class P can be solved, in contrast to the
result obtained allowing them.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600
A new perspective on computational complexity theory in Membrane Computing
A single Turing machine can solve decision problems with an in nite number
of instances. On the other hand, in the framework of membrane computing, a \solution"
to an abstract decision problem consists of a family of membrane systems (where each
system of the family is associated with a nite set of instances of the problem to be
solved). An interesting question is to analyze the possibility to nd a single membrane
system able to deal with the in nitely many instances of a decision problem.
In this context, it is fundamental to de ne precisely how the instances of the problem
are introduced into the system. In this paper, two different methods are considered:
pre-computed (in polynomial time) resources and non-treated resources.
An extended version of this work will be presented in the 20th International Conference
on Membrane Computing.Ministerio de Economía, Industria y Competitividad TIN2017-89842-
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
The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules
Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical
systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when
moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in
the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems
is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with
evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper
bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary
between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new
simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution
to the SAT problem
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
Counting Membrane Systems
A decision problem is one that has a yes/no answer, while
a counting problem asks how many possible solutions exist associated
with each instance. Every decision problem X has associated a counting
problem, denoted by #X, in a natural way by replacing the question
“is there a solution?” with “how many solutions are there?”. Counting
problems are very attractive from a computational complexity point of
view: if X is an NP-complete problem then the counting version #X is
NP-hard, but the counting version of some problems in class P can also
be NP-hard.
In this paper, a new class of membrane systems is presented in order
to provide a natural framework to solve counting problems. The class is
inspired by a special kind of non-deterministic Turing machines, called
counting Turing machines, introduced by L. Valiant. A polynomial-time
and uniform solution to the counting version of the SAT problem (a
well-known #P-complete problem) is also provided, by using a family
of counting polarizationless P systems with active membranes, without
dissolution rules and division rules for non-elementary membranes but
where only very restrictive cooperation (minimal cooperation and minimal
production) in object evolution rules is allowed
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
P systems with evolutional symport and membrane creation rules solving QSAT
P systems are computing devices based on sets of rules that dictate how they work.
While some of these rules can change the objects within the system, other rules can even
change the own structure, like creation rules. They have been used in cell-like membrane
systems with active membranes to efficiently solve NP-complete problems. In this work,
we improve a previous result where a uniform family of P systems with evolutional
communication rules whose left-hand side (respectively, right-hand side) have most 2
objects (resp., 2 objects) and membrane creation solved SAT efficiently, and we obtain
an efficient solution to solve QBF-SAT or QSAT (a PSPACE-complete problem) having at
most 1 object (respectively, 1 object) in their left-hand side (resp., right-hand side) and not
making use of the environmentMinisterio de Ciencia e Innovación TIN2017-89842-
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