9 research outputs found
On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution
Recognizer P systems with active membranes have proven to be very powerful
computing devices, being able to solve NP-complete decision problems in a polynomial
time. However such solutions usually exploit many powerful features, such as electrical
charges (polarizations) associated to membranes, evolution rules, communication rules,
and strong or weak forms of division rules. In this paper we contribute to the study
of the computational power of polarizationless recognizer P systems with active membranes.
Precisely, we show that such systems are able to solve in polynomial time the
NP-complete decision problem 3-sat by using only dissolution rules and a form of strong
division for non–elementary membranes, working in the maximal parallel way
A Computational Complexity Theory in Membrane Computing
In this paper, a computational complexity theory within the framework
of Membrane Computing is introduced. Polynomial complexity classes associated with
di erent models of cell-like and tissue-like membrane systems are de ned and the most
relevant results obtained so far are presented. Many attractive characterizations of P 6=
NP conjecture within the framework of a bio-inspired and non-conventional computing
model are deduced.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420
Complexity aspects of polarizationless membrane systems
We investigate polarizationless P systems with active membranes working in
maximally parallel manner, which do not make use of evolution or communication rules, in
order to find which features are sufficient to efficiently solve computationally hard problems.
We show that such systems are able to solve the PSPACE-complete problem
QUANTIFIED 3-SAT, provided that non-elementary membrane division is controlled by the
presence of a (possibly non-elementary) membrane.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58
Introducing a Space Complexity Measure for P Systems
We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time
complexity classes, and identifying some potentially interesting problems which require
further research
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
On Distributed Solution to SAT by Membrane Computing
Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called -distributed tissue P systems with evolutional communication and cell division (, for short) is proposed. A uniform solution to the SAT problem by under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform -P protocols are increased with respect to ; while a single communication is shown to be possible for bi-directional uniform -P protocols for any . We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then for solving the SAT problem work no much faster than TPec
Uniformity is weaker than semi-uniformity for some membrane systems
We investigate computing models that are presented as families of finite
computing devices with a uniformity condition on the entire family. Examples of
such models include Boolean circuits, membrane systems, DNA computers, chemical
reaction networks and tile assembly systems, and there are many others.
However, in such models there are actually two distinct kinds of uniformity
condition. The first is the most common and well-understood, where each input
length is mapped to a single computing device (e.g. a Boolean circuit) that
computes on the finite set of inputs of that length. The second, called
semi-uniformity, is where each input is mapped to a computing device for that
input (e.g. a circuit with the input encoded as constants). The former notion
is well-known and used in Boolean circuit complexity, while the latter notion
is frequently found in literature on nature-inspired computation from the past
20 years or so.
Are these two notions distinct? For many models it has been found that these
notions are in fact the same, in the sense that the choice of uniformity or
semi-uniformity leads to characterisations of the same complexity classes. In
other related work, we showed that these notions are actually distinct for
certain classes of Boolean circuits. Here, we give analogous results for
membrane systems by showing that certain classes of uniform membrane systems
are strictly weaker than the analogous semi-uniform classes. This solves a
known open problem in the theory of membrane systems. We then go on to present
results towards characterising the power of these semi-uniform and uniform
membrane models in terms of NL and languages reducible to the unary languages
in NL, respectively.Comment: 28 pages, 1 figur
Modelo de computación conexionista inspirado en las redes de procesadores evolutivos y su aprendizaje
La informática teórica es una disciplina básica ya que la mayoría de los
avances en informática se sustentan en un sólido resultado de esa materia.
En los últimos a~nos debido tanto al incremento de la potencia de los ordenadores,
como a la cercanía del límite físico en la miniaturización de los
componentes electrónicos, resurge el interés por modelos formales de computación alternativos a la arquitectura clásica de von Neumann. Muchos de
estos modelos se inspiran en la forma en la que la naturaleza resuelve eficientemente problemas muy complejos. La mayoría son computacionalmente
completos e intrínsecamente paralelos. Por este motivo se les está llegando
a considerar como nuevos paradigmas de computación (computación natural).
Se dispone, por tanto, de un abanico de arquitecturas abstractas tan
potentes como los computadores convencionales y, a veces, más eficientes:
alguna de ellas mejora el rendimiento, al menos temporal, de problemas NPcompletos
proporcionando costes no exponenciales. La representación formal
de las redes de procesadores evolutivos requiere de construcciones, tanto independientes,
como dependientes del contexto, dicho de otro modo, en general
una representación formal completa de un NEP implica restricciones, tanto
sintácticas, como semánticas, es decir, que muchas representaciones aparentemente
(sintácticamente) correctas de casos particulares de estos dispositivos
no tendrían sentido porque podrían no cumplir otras restricciones semánticas.
La aplicación de evolución gramatical semántica a los NEPs pasa por la
elección de un subconjunto de ellos entre los que buscar los que solucionen
un problema concreto.
En este trabajo se ha realizado un estudio sobre un modelo inspirado en
la biología celular denominado redes de procesadores evolutivos [55, 53], esto
es, redes cuyos nodos son procesadores muy simples capaces de realizar únicamente
un tipo de mutación puntual (inserción, borrado o sustitución de un
símbolo). Estos nodos están asociados con un filtro que está definido por alguna
condición de contexto aleatorio o de pertenencia. Las redes están formadas
a lo sumo de seis nodos y, teniendo los filtros definidos por una pertenencia
a lenguajes regulares, son capaces de generar todos los lenguajes enumerables
recursivos independientemente del grafo subyacente. Este resultado no
es sorprendente ya que semejantes resultados han sido documentados en la literatura. Si se consideran redes con nodos y filtros definidos por contextos
aleatorios {que parecen estar más cerca a las implementaciones biológicas{
entonces se pueden generar lenguajes más complejos como los lenguajes no
independientes del contexto. Sin embargo, estos mecanismos tan simples son
capaces de resolver problemas complejos en tiempo polinomial. Se ha presentado
una solución lineal para un problema NP-completo, el problema de los
3-colores.
Como primer aporte significativo se ha propuesto una nueva dinámica de
las redes de procesadores evolutivos con un comportamiento no determinista
y masivamente paralelo [55], y por tanto todo el trabajo de investigación en
el área de la redes de procesadores se puede trasladar a las redes masivamente
paralelas. Por ejemplo, las redes masivamente paralelas se pueden modificar
de acuerdo a determinadas reglas para mover los filtros hacia las conexiones.
Cada conexión se ve como un canal bidireccional de manera que los filtros de
entrada y salida coinciden. A pesar de esto, estas redes son computacionalmente
completas. Se pueden también implementar otro tipo de reglas para
extender este modelo computacional. Se reemplazan las mutaciones puntuales
asociadas a cada nodo por la operación de splicing. Este nuevo tipo de
procesador se denomina procesador splicing. Este modelo computacional de
Red de procesadores con splicing ANSP es semejante en cierto modo a los
sistemas distribuidos en tubos de ensayo basados en splicing.
Además, se ha definido un nuevo modelo [56] {Redes de procesadores
evolutivos con filtros en las conexiones{ , en el cual los procesadores tan solo
tienen reglas y los filtros se han trasladado a las conexiones. Dicho modelo
es equivalente, bajo determinadas circunstancias, a las redes de procesadores
evolutivos clásicas. Sin dichas restricciones el modelo propuesto es un superconjunto
de los NEPs clásicos. La principal ventaja de mover los filtros a las
conexiones radica en la simplicidad de la modelización.
Otras aportaciones de este trabajo ha sido el dise~no de un simulador en
Java [54, 52] para las redes de procesadores evolutivos propuestas en esta
Tesis.
Sobre el término "procesador evolutivo" empleado en esta Tesis, el proceso
computacional descrito aquí no es exactamente un proceso evolutivo en el sentido Darwiniano. Pero las operaciones de reescritura que se han considerado
pueden interpretarse como mutaciones y los procesos de filtrado se
podrían ver como procesos de selección. Además, este trabajo no abarca la
posible implementación biológica de estas redes, a pesar de ser de gran importancia.
A lo largo de esta tesis se ha tomado como definición de la medida de complejidad
para los ANSP, una que denotaremos como tama~no (considerando
tama~no como el número de nodos del grafo subyacente). Se ha mostrado que
cualquier lenguaje enumerable recursivo L puede ser aceptado por un ANSP
en el cual el número de procesadores está linealmente acotado por la cardinalidad
del alfabeto de la cinta de una máquina de Turing que reconoce dicho
lenguaje L. Siguiendo el concepto de ANSP universales introducido por Manea
[65], se ha demostrado que un ANSP con una estructura de grafo fija
puede aceptar cualquier lenguaje enumerable recursivo. Un ANSP se puede
considerar como un ente capaz de resolver problemas, además de tener
otra propiedad relevante desde el punto de vista práctico: Se puede definir
un ANSP universal como una subred, donde solo una cantidad limitada de
parámetros es dependiente del lenguaje. La anterior característica se puede
interpretar como un método para resolver cualquier problema NP en tiempo
polinomial empleando un ANSP de tama~no constante, concretamente treinta
y uno. Esto significa que la solución de cualquier problema NP es uniforme
en el sentido de que la red, exceptuando la subred universal, se puede ver
como un programa; adaptándolo a la instancia del problema a resolver, se
escogerín los filtros y las reglas que no pertenecen a la subred universal. Un
problema interesante desde nuestro punto de vista es el que hace referencia
a como elegir el tama~no optimo de esta red.---ABSTRACT---This thesis deals with the recent research works in the area of Natural
Computing {bio-inspired models{, more precisely Networks of Evolutionary
Processors first developed by Victor Mitrana and they are based on P Systems
whose father is Georghe Paun. In these models, they are a set of processors
connected in an underlying undirected graph, such processors have an object
multiset (strings) and a set of rules, named evolution rules, that transform
objects inside processors[55, 53],. These objects can be sent/received using
graph connections provided they accomplish constraints defined at input and
output filters processors have. This symbolic model, non deterministic one
(processors are not synchronized) and massive parallel one[55] (all rules can
be applied in one computational step) has some important properties regarding
solution of NP-problems in lineal time and of course, lineal resources.
There are a great number of variants such as hybrid networks, splicing processors,
etc. that provide the model a computational power equivalent to Turing
machines.
The origin of networks of evolutionary processors (NEP for short) is a
basic architecture for parallel and distributed symbolic processing, related to
the Connection Machine as well as the Logic Flow paradigm, which consists
of several processors, each of them being placed in a node of a virtual complete
graph, which are able to handle data associated with the respective node.
All the nodes send simultaneously their data and the receiving nodes handle
also simultaneously all the arriving messages, according to some strategies.
In a series of papers one considers that each node may be viewed as a cell
having genetic information encoded in DNA sequences which may evolve by
local evolutionary events, that is point mutations. Each node is specialized
just for one of these evolutionary operations. Furthermore, the data in each
node is organized in the form of multisets of words (each word appears in
an arbitrarily large number of copies), and all the copies are processed in
parallel such that all the possible events that can take place do actually take
place. Obviously, the computational process just described is not exactly an
evolutionary process in the Darwinian sense. But the rewriting operations we
have considered might be interpreted as mutations and the filtering process
might be viewed as a selection process. Recombination is missing but it was asserted that evolutionary and functional relationships between genes can be
captured by taking only local mutations into consideration.
It is clear that filters associated with each node allow a strong control of
the computation. Indeed, every node has an input and output filter; two nodes
can exchange data if it passes the output filter of the sender and the input
filter of the receiver. Moreover, if some data is sent out by some node and
not able to enter any node, then it is lost. In this paper we simplify the ANSP
model considered in by moving the filters from the nodes to the edges. Each
edge is viewed as a two-way channel such that the input and output filters
coincide.
Clearly, the possibility of controlling the computation in such networks
seems to be diminished. For instance, there is no possibility to loose data during
the communication steps. In spite of this and of the fact that splicing is
not a powerful operation (remember that splicing systems generates only regular
languages) we prove here that these devices are computationally complete.
As a consequence, we propose characterizations of two complexity classes, namely
NP and PSPACE, in terms of accepting networks of restricted splicing
processors with filtered connections.
We proposed a uniform linear time solution to SAT based on ANSPFCs
with linearly bounded resources. This solution should be understood correctly:
we do not solve SAT in linear time and space. Since any word and auxiliary
word appears in an arbitrarily large number of copies, one can generate
in linear time, by parallelism and communication, an exponential number of
words each of them having an exponential number of copies. However, this
does not seem to be a major drawback since by PCR (Polymerase Chain Reaction)
one can generate an exponential number of identical DNA molecules in
a linear number of reactions.
It is worth mentioning that the ANSPFC constructed above remains unchanged
for any instance with the same number of variables. Therefore, the
solution is uniform in the sense that the network, excepting the input and
output nodes, may be viewed as a program according to the number of variables,
we choose the filters, the splicing words and the rules, then we assign
all possible values to the variables, and compute the formula.We proved that ANSP are computationally complete. Do the ANSPFC
remain still computationally complete? If this is not the case, what other
problems can be eficiently solved by these ANSPFCs? Moreover, the complexity
class NP is exactly the class of all languages decided by ANSP in
polynomial time. Can NP be characterized in a similar way with ANSPFCs