9,942 research outputs found
Non-confluence in divisionless P systems with active membranes
AbstractWe describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules. Furthermore, we provide an algorithm for simulating such devices on a nondeterministic Turing machine with a polynomial slowdown. Together, these results prove that the complexity class of problems solvable non-confluently and in polynomial time by this kind of P system is exactly the class NP
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
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
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
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
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
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
New applications for an old tool
First, the dependency graph technique, not so far from its current application,
was developed trying to nd the shortest computations for membrane systems
solving instances of SAT. Certain families of membrane systems have been demonstrated
to be non-effcient by means of the reduction of nding an accepting computation (respectively,
rejecting computation) to the problem of reaching from a node of the dependency
graph to another one.
In this paper, a novel application to this technique is explained. Supposing that a
problem can be solved by means of a kind of membrane systems leads to a contradiction
by means of using the dependency graph as a reasoning method. In this case, it is demonstrated
that a single system without dissolution, polarizations and cooperation cannot
distinguish a single object from more than one object.
An extended version of this work will be presented in the 20th International Conference
on Membrane Computing.Ministerio de Industria, Economía y Competitividad TIN2017-89842-
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
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