Distributed models in P-Systems architectures to reduce computation time

Membrane systems are computational equivalent to Turing machines. However, their distributed and massively parallel nature obtains polynomial solutions opposite to traditional non-polynomial ones. At this point, it is very important to develop dedicated hardware and software implementations exploiting those two membrane systems features. Dealing with distributed implementations of P systems, the bottleneck communication problem has arisen. When the number of membranes grows up, the network gets congested. The purpose of distributed architectures is to reach a compromise between the massively parallel character of the system and the needed evolution step time to transit from one configuration of the system to the next one, solving the bottleneck communication problem. The goal of this paper is twofold. Firstly, to survey in a systematic and uniform way the main results regarding the way membranes can be placed on processors in order to get a software/hardware simulation of P-Systems in a distributed environment. Secondly, we improve some results about the membrane dissolution problem, prove that it is connected, and discuss the possibility of simulating this property in the distributed model. All this yields an improvement in the system parallelism implementation since it gets an increment of the parallelism of the external communication among processors. Proposed ideas improve previous architectures to tackle the communication bottleneck problem, such as reduction of the total time of an evolution step, increase of the number of membranes that could run on a processor and reduction of the number of processors.

Análisis estático de sistemas de membranas para la determinación de reglas activas

Esta tesis doctoral se enmarca dentro de la computación con membranas. Se trata de un tipo de computación bio-inspirado, concretamente basado en las células de los organismos vivos, en las que se producen múltiples reacciones de forma simultánea. A partir de la estructura y funcionamiento de las células se han definido diferentes modelos formales, denominados P sistemas. Estos modelos no tratan de modelar el comportamiento biológico de una célula, sino que abstraen sus principios básicos con objeto de encontrar nuevos paradigmas computacionales. Los P sistemas son modelos de computación no deterministas y masivamente paralelos. De ahí el interés que en los últimos años estos modelos han suscitado para la resolución de problemas complejos. En muchos casos, consiguen resolver de forma teórica problemas NP-completos en tiempo polinómico o lineal. Por otra parte, cabe destacar también la aplicación que la computación con membranas ha tenido en la investigación de otros muchos campos, sobre todo relacionados con la biología. Actualmente, una gran cantidad de estos modelos de computación han sido estudiados desde el punto de vista teórico. Sin embargo, el modo en que pueden ser implementados es un reto de investigación todavía abierto. Existen varias líneas en este sentido, basadas en arquitecturas distribuidas o en hardware dedicado, que pretenden acercarse en lo posible a su carácter no determinista y masivamente paralelo, dentro de un contexto de viabilidad y eficiencia. En esta tesis doctoral se propone la realización de un análisis estático del P sistema, como vía para optimizar la ejecución del mismo en estas plataformas. Se pretende que la información recogida en tiempo de análisis sirva para configurar adecuadamente la plataforma donde se vaya a ejecutar posteriormente el P sistema, obteniendo como consecuencia una mejora en el rendimiento. Concretamente, en esta tesis se han tomado como referencia los P sistemas de transiciones para llevar a cabo el estudio de dicho análisis estático. De manera un poco más específica, el análisis estático propuesto en esta tesis persigue que cada membrana sea capaz de determinar sus reglas activas de forma eficiente en cada paso de evolución, es decir, aquellas reglas que reúnen las condiciones adecuadas para poder ser aplicadas. En esta línea, se afronta el problema de los estados de utilidad de una membrana dada, que en tiempo de ejecución permitirán a la misma conocer en todo momento las membranas con las que puede comunicarse, cuestión que determina las reglas que pueden aplicarse en cada momento. Además, el análisis estático propuesto en esta tesis se basa en otra serie de características del P sistema como la estructura de membranas, antecedentes de las reglas, consecuentes de las reglas o prioridades. Una vez obtenida toda esta información en tiempo de análisis, se estructura en forma de árbol de decisión, con objeto de que en tiempo de ejecución la membrana obtenga las reglas activas de la forma más eficiente posible. Por otra parte, en esta tesis se lleva a cabo un recorrido por un número importante de arquitecturas hardware y software que diferentes autores han propuesto para implementar P sistemas. Fundamentalmente, arquitecturas distribuidas, hardware dedicado basado en tarjetas FPGA y plataformas basadas en microcontroladores PIC. El objetivo es proponer soluciones que permitan implantar en dichas arquitecturas los resultados obtenidos del análisis estático (estados de utilidad y árboles de decisión para reglas activas). En líneas generales, se obtienen conclusiones positivas, en el sentido de que dichas optimizaciones se integran adecuadamente en las arquitecturas sin penalizaciones significativas. Summary Membrane computing is the focus of this doctoral thesis. It can be considered a bio-inspired computing type. Specifically, it is based on living cells, in which many reactions take place simultaneously. From cell structure and operation, many different formal models have been defined, named P systems. These models do not try to model the biological behavior of the cell, but they abstract the basic principles of the cell in order to find out new computational paradigms. P systems are non-deterministic and massively parallel computational models. This is why, they have aroused interest when dealing with complex problems nowadays. In many cases, they manage to solve in theory NP problems in polynomial or lineal time. On the other hand, it is important to note that membrane computing has been successfully applied in many researching areas, specially related to biology. Nowadays, lots of these computing models have been sufficiently characterized from a theoretical point of view. However, the way in which they can be implemented is a research challenge, that it is still open nowadays. There are some lines in this way, based on distributed architectures or dedicated hardware. All of them are trying to approach to its non-deterministic and parallel character as much as possible, taking into account viability and efficiency. In this doctoral thesis it is proposed carrying out a static analysis of the P system in order to optimize its performance in a computing platform. The general idea is that after data are collected in analysis time, they are used for getting a suitable configuration of the computing platform in which P system is going to be performed. As a consequence, the system throughput will improve. Specifically, this thesis has made use of Transition P systems for carrying out the study in static analysis. In particular, the static analysis proposed in this doctoral thesis tries to achieve that every membrane can efficiently determine its active rules in every evolution step. These rules are the ones that can be applied depending on the system configuration at each computational step. In this line, we are going to tackle the problem of the usefulness states for a membrane. This state will allow this membrane to know the set of membranes with which communication is possible at any time. This is a very important issue in determining the set of rules that can be applied. Moreover, static analysis in this thesis is carried out taking into account other properties such as membrane structure, rule antecedents, rule consequents and priorities among rules. After collecting all data in analysis time, they are arranged in a decision tree structure, enabling membranes to obtain the set of active rules as efficiently as possible in run-time system. On the other hand, in this doctoral thesis is going to carry out an overview of hardware and software architectures, proposed by different authors in order to implement P systems, such as distributed architectures, dedicated hardware based on PFGA, and computing platforms based on PIC microcontrollers. The aim of this overview is to propose solutions for implementing the results of the static analysis, that is, usefulness states and decision trees for active rules. In general, conclusions are satisfactory, because these optimizations can be properly integrated in most of the architectures without significant penalties.

Métodos acotados de aplicación de reglas de evolución para la implementación de Sistemas P de Transición

La característica fundamental de la Computación Natural se basa en el empleo de conceptos, principios y mecanismos del funcionamiento de la Naturaleza. La Computación Natural -y dentro de ésta, la Computación de Membranas- surge como una posible alternativa a la computación clásica y como resultado de la búsqueda de nuevos modelos de computación que puedan superar las limitaciones presentes en los modelos convencionales. En concreto, la Computación de Membranas se originó como un intento de formular un nuevo modelo computacional inspirado en la estructura y el funcionamiento de las células biológicas: los sistemas basados en este modelo constan de una estructura de membranas que actúan a la vez como separadores y como canales de comunicación, y dentro de esa estructura se alojan multiconjuntos de objetos que evolucionan de acuerdo a unas determinadas reglas de evolución. Al conjunto de dispositivos contemplados por la Computación de Membranas se les denomina genéricamente como Sistemas P. Hasta el momento los Sistemas P sólo han sido estudiados a nivel teórico y no han sido plenamente implementados ni en medios electrónicos, ni en medios bioquímicos, sólo han sido simulados o parcialmente implementados. Por tanto, la implantación de estos sistemas es un reto de investigación abierto. Esta tesis aborda uno de los problemas que debe ser resuelto para conseguir la implantación de los Sistemas P sobre plataformas hardware. El problema concreto se centra en el modelo de los Sistemas P de Transición y surge de la necesidad de disponer de algoritmos de aplicación de reglas que, independientemente de la plataforma hardware sobre la que se implementen, cumplan los requisitos de ser no deterministas, masivamente paralelos y además su tiempo de ejecución esté estáticamente acotado. Como resultado se ha obtenido un conjunto de algoritmos (tanto para plataformas secuenciales, como para plataformas paralelas) que se adecúan a las diferentes configuraciones de los Sistemas P. ABSTRACT The main feature of Natural Computing is the use of concepts, principles and mechanisms inspired by Nature. Natural Computing and within it, Membrane Computing emerges as an potential alternative to conventional computing and as from the search for new models of computation that may overcome the existing limitations in conventional models. Specifically, Membrane Computing was created to formulate a new computational paradigm inspired by the structure and functioning of biological cells: it consists of a membrane structure, which acts as separators as well as communication channels, and within this structure are stored multisets of objects that evolve according to certain evolution rules. The set of computing devices addressed by Membrane Computing are generically known P systems. Up to now, no P systems have been fully implemented yet in electronic or biochemical means. They only have been studied in theory, simulated or partially implemented. Therefore, the implementation of these systems is an open research challenge. This thesis addresses one of the problems to be solved in order to deploy P systems on hardware platforms. This specific problem is focused on the Transition P System model and emerges from the need of providing application rules algorithms that independently on the hardware platform on which they are implemented, meets the requirements of being nondeterministic, massively parallel and runtime-bounded. As a result, this thesis has developed a set of algorithms for both platforms, sequential and parallel, adapted to all possible configurations of P systems.

An Architecture forRepresenting Biological Processes based on Networks of Bio-inspired Processors

n this paper we propose the use of Networks of Bio-inspired Processors (NBP) to model some biological phenomena within a computational framework. In particular, we propose the use of an extension of NBP named Network Evolutionary Processors Transducers to simulate chemical transformations of substances. Within a biological process, chemical transformations of substances are basic operations in the change of the state of the cell. Previously, it has been proved that NBP are computationally complete, that is, they are able to solve NP complete problems in linear time, using massively parallel computations. In addition, we propose a multilayer architecture that will allow us to design models of biological processes related to cellular communication as well as their implications in the metabolic pathways. Subsequently, these models can be applied not only to biological-cellular instances but, possibly, also to configure instances of interactive processes in many other fields like population interactions, ecological trophic networks, in dustrial ecosystems, etc.