FTCS finite difference scheme GPGPU parallel computing for the heat conduction equation = Programación en paralelo GPGPU del método en diferencias finitas FTCS para la ecuación del calor

En el presente artículo se muestran las ventajas de la programación en paralelo resolviendo numéricamente la ecuación del calor en dos dimensiones a través del método de diferencias finitas explícito centrado en el espacio FTCS. De las conclusiones de este trabajo se pone de manifiesto la importancia de la programación en paralelo para tratar problemas grandes, en los que se requiere un elevado número de cálculos, para los cuales la programación secuencial resulta impracticable por el elevado tiempo de ejecución. En la primera sección se describe brevemente los conceptos básicos de programación en paralelo. Seguidamente se resume el método de diferencias finitas explícito centrado en el espacio FTCS aplicado a la ecuación parabólica del calor. Seguidamente se describe el problema de condiciones de contorno y valores iniciales específico al que se va a aplicar el método de diferencias finitas FTCS, proporcionando pseudocódigos de una implementación secuencial y dos implementaciones en paralelo. Finalmente tras la discusión de los resultados se presentan algunas conclusiones. In this paper the advantages of parallel computing are shown by solving the heat conduction equation in two dimensions with the forward in time central in space (FTCS) finite difference method. Two different levels of parallelization are consider and compared with traditional serial procedures. We show in this work the importance of parallel computing when dealing with large problems that are impractical or impossible to solve them with a serial computing procedure. In the first section a summary of parallel computing approach is presented. Subsequently, the forward in time central in space (FTCS) finite difference method for the heat conduction equation is outline, describing how the heat flow equation is derived in two dimensions and the particularities of the finite difference numerical technique considered. Then, a specific initial boundary value problem is solved by the FTCS finite difference method and serial and parallel pseudo codes are provided. Finally after results are discussed some conclusions are presented.

Using Virtual Reality in the teaching of manufacturing processes with material removal in CNC Machine-Tools

This paper presents a methodology for the incorporation of a Virtual Reality development applied to the teaching of manufacturing processes, namely the group of machining processes in numerical control of machine tools. The paper shows how it is possible to supplement the teaching practice through virtual machine-tools whose operation is similar to the 'real' machines while eliminating the risks of use for both users and the machines.

A Semantic-Based Approach to Attain Reproducibility of Computational Environments in Scientic Work ows: A Case Study

Reproducible research in scientic work ows is often addressed by tracking the provenance of the produced results. While this approach allows inspecting intermediate and nal results, improves understanding, and permits replaying a work ow execution, it does not ensure that the computational environment is available for subsequent executions to reproduce the experiment. In this work, we propose describing the resources involved in the execution of an experiment using a set of semantic vocabularies, so as to conserve the computational environment. We dene a process for documenting the work ow application, management system, and their dependencies based on 4 domain ontologies. We then conduct an experimental evaluation sing a real work ow application on an academic and a public Cloud platform. Results show that our approach can reproduce an equivalent execution environment of a predened virtual machine image on both computing platforms.

A semantic-based approach to attain reproducibility of computational environments in scientific workflows: a case study

Reproducible research in scientific workflows is often addressed by tracking the provenance of the produced results. While this approach allows inspecting intermediate and final results, improves understanding, and permits replaying a workflow execution, it does not ensure that the computational environment is available for subsequent executions to reproduce the experiment. In this work, we propose describing the resources involved in the execution of an experiment using a set of semantic vocabularies, so as to conserve the computational environment. We define a process for documenting the workflow application, management system, and their dependencies based on 4 domain ontologies. We then conduct an experimental evaluation using a real workflow application on an academic and a public Cloud platform. Results show that our approach can reproduce an equivalent execution environment of a predefined virtual machine image on both computing platforms.

Independent AND-parallel implementation of narrowing

We present a parallel graph narrowing machine, which is used to implement a functional logic language on a shared memory multiprocessor. It is an extensión of an abstract machine for a purely functional language. The result is a programmed graph reduction machine which integrates the mechanisms of unification, backtracking, and independent and-parallelism. In the machine, the subexpressions of an expression can run in parallel. In the case of backtracking, the structure of an expression is used to avoid the reevaluation of subexpressions as far as possible. Deterministic computations are detected. Their results are maintained and need not be reevaluated after backtracking.

Tecnología cloud para el hogar digital

El mundo tecnológico está cambiando hacia la optimización en la gestión de recursos gracias a la poderosa influencia de tecnologías como la virtualización y la computación en la nube (Cloud Computing). En esta memoria se realiza un acercamiento a las mismas, desde las causas que las motivaron hasta sus últimas tendencias, pasando por la identificación de sus principales características, ventajas e inconvenientes. Por otro lado, el Hogar Digital es ya una realidad para la mayoría de los seres humanos. En él se dispone de acceso a múltiples tipos de redes de telecomunicaciones (3G, 4G, WI-FI, ADSL…) con más o menos capacidad pero que permiten conexiones a internet desde cualquier parte, en todo momento, y con prácticamente cualquier dispositivo (ordenadores personales, smartphones, tabletas, televisores…). Esto es aprovechado por las empresas para ofrecer todo tipo de servicios. Algunos de estos servicios están basados en el cloud computing sobre todo ofreciendo almacenamiento en la nube a aquellos dispositivos con capacidad reducida, como son los smarthphones y las tabletas. Ese espacio de almacenamiento normalmente está en los servidores bajo el control de grandes compañías. Guardar documentos, videos, fotos privadas sin tener la certeza de que estos no son consultados por alguien sin consentimiento, puede despertar en el usuario cierto recelo. Para estos usuarios que desean control sobre su intimidad, se ofrece la posibilidad de que sea el propio usuario el que monte sus propios servidores y su propio servicio cloud para compartir su información privada sólo con sus familiares y amigos o con cualquiera al que le dé permiso. Durante el proyecto se han comparado diversas soluciones, la mayoría de código abierto y de libre distribución, que permiten desplegar como mínimo un servicio de almacenamiento accesible a través de Internet. Algunas de ellas lo complementan con servicios de streaming tanto de música como de videos, compartición y sincronización de documentos entre múltiples dispositivos, calendarios, copias de respaldo (backups), virtualización de escritorios, versionado de ficheros, chats, etc. El proyecto finaliza con una demostración de cómo utilizar dispositivos de un hogar digital interactuando con un servidor Cloud, en el que previamente se ha instalado y configurado una de las soluciones comparadas. Este servidor quedará empaquetado en una máquina virtual para que sea fácilmente transportable e utilizable. ABSTRACT. The technological world is changing towards optimizing resource management thanks to the powerful influence of technologies such as Virtualization and Cloud Computing. This document presents a closer approach to them, from the causes that have motivated to their last trends, as well as showing their main features, advantages and disadvantages. In addition, the Digital Home is a reality for most humans. It provides access to multiple types of telecommunication networks (3G, 4G, WI-FI, ADSL...) with more or less capacity, allowing Internet connections from anywhere, at any time, and with virtually any device (computer personal smartphones, tablets, televisions...).This is used by companies to provide all kinds of services. Some of these services offer storage on the cloud to devices with limited capacity, such as smartphones and tablets. That is normally storage space on servers under the control of important companies. Saving private documents, videos, photos, without being sure that they are not viewed by anyone without consent, can wake up suspicions in some users. For those users who want control over their privacy, it offers the possibility that it is the user himself to mount his own server and its own cloud service to share private information only with family and friends or with anyone with consent. During the project I have compared different solutions, most open source and with GNU licenses, for deploying one storage facility accessible via the Internet. Some supplement include streaming services of music , videos or photos, sharing and syncing documents across multiple devices, calendars, backups, desktop virtualization, file versioning, chats... The project ends with a demonstration of how to use our digital home devices interacting with a cloud server where one of the solutions compared is installed and configured. This server will be packaged in a virtual machine to be easily transportable and usable.

Optimizing the reliability and resource efficiency of MapReduce-based systems

Debido al gran incremento de datos digitales que ha tenido lugar en los últimos años, ha surgido un nuevo paradigma de computación paralela para el procesamiento eficiente de grandes volúmenes de datos. Muchos de los sistemas basados en este paradigma, también llamados sistemas de computación intensiva de datos, siguen el modelo de programación de Google MapReduce. La principal ventaja de los sistemas MapReduce es que se basan en la idea de enviar la computación donde residen los datos, tratando de proporcionar escalabilidad y eficiencia. En escenarios libres de fallo, estos sistemas generalmente logran buenos resultados. Sin embargo, la mayoría de escenarios donde se utilizan, se caracterizan por la existencia de fallos. Por tanto, estas plataformas suelen incorporar características de tolerancia a fallos y fiabilidad. Por otro lado, es reconocido que las mejoras en confiabilidad vienen asociadas a costes adicionales en recursos. Esto es razonable y los proveedores que ofrecen este tipo de infraestructuras son conscientes de ello. No obstante, no todos los enfoques proporcionan la misma solución de compromiso entre las capacidades de tolerancia a fallo (o de manera general, las capacidades de fiabilidad) y su coste. Esta tesis ha tratado la problemática de la coexistencia entre fiabilidad y eficiencia de los recursos en los sistemas basados en el paradigma MapReduce, a través de metodologías que introducen el mínimo coste, garantizando un nivel adecuado de fiabilidad. Para lograr esto, se ha propuesto: (i) la formalización de una abstracción de detección de fallos; (ii) una solución alternativa a los puntos únicos de fallo de estas plataformas, y, finalmente, (iii) un nuevo sistema de asignación de recursos basado en retroalimentación a nivel de contenedores. Estas contribuciones genéricas han sido evaluadas tomando como referencia la arquitectura Hadoop YARN, que, hoy en día, es la plataforma de referencia en la comunidad de los sistemas de computación intensiva de datos. En la tesis se demuestra cómo todas las contribuciones de la misma superan a Hadoop YARN tanto en fiabilidad como en eficiencia de los recursos utilizados. ABSTRACT Due to the increase of huge data volumes, a new parallel computing paradigm to process big data in an efficient way has arisen. Many of these systems, called dataintensive computing systems, follow the Google MapReduce programming model. The main advantage of these systems is based on the idea of sending the computation where the data resides, trying to provide scalability and efficiency. In failure-free scenarios, these frameworks usually achieve good results. However, these ones are not realistic scenarios. Consequently, these frameworks exhibit some fault tolerance and dependability techniques as built-in features. On the other hand, dependability improvements are known to imply additional resource costs. This is reasonable and providers offering these infrastructures are aware of this. Nevertheless, not all the approaches provide the same tradeoff between fault tolerant capabilities (or more generally, reliability capabilities) and cost. In this thesis, we have addressed the coexistence between reliability and resource efficiency in MapReduce-based systems, looking for methodologies that introduce the minimal cost and guarantee an appropriate level of reliability. In order to achieve this, we have proposed: (i) a formalization of a failure detector abstraction; (ii) an alternative solution to single points of failure of these frameworks, and finally (iii) a novel feedback-based resource allocation system at the container level. Finally, our generic contributions have been instantiated for the Hadoop YARN architecture, which is the state-of-the-art framework in the data-intensive computing systems community nowadays. The thesis demonstrates how all our approaches outperform Hadoop YARN in terms of reliability and resource efficiency.

Computación celular con membranas: un estudio de modelos de cómputo bioinspirados

Los resultados presentados en la memoria de esta tesis doctoral se enmarcan en la denominada computación celular con membranas una nueva rama de investigación dentro de la computación natural creada por Gh. Paun en 1998, de ahí que habitualmente reciba el nombre de sistemas P. Este nuevo modelo de cómputo distribuido está inspirado en la estructura y funcionamiento de la célula. El objetivo de esta tesis ha sido analizar el poder y la eficiencia computacional de estos sistemas de computación celular. En concreto, se han analizado dos tipos de sistemas P: por un lado los sistemas P de neuronas de impulsos, y por otro los sistemas P con proteínas en las membranas. Para el primer tipo, los resultados obtenidos demuestran que es posible que estos sistemas mantengan su universalidad aunque muchas de sus características se limiten o incluso se eliminen. Para el segundo tipo, se analiza la eficiencia computacional y se demuestra que son capaces de resolver problemas de la clase de complejidad ESPACIO-P (PSPACE) en tiempo polinómico. Análisis del poder computacional: Los sistemas P de neuronas de impulsos (en adelante SN P, acrónimo procedente del inglés «Spiking Neural P Systems») son sistemas inspirados en el funcionamiento neuronal y en la forma en la que los impulsos se propagan por las redes sinápticas. Los SN P bio-inpirados poseen un numeroso abanico de características que ha cen que dichos sistemas sean universales y por tanto equivalentes, en poder computacional, a una máquina de Turing. Estos sistemas son potentes a nivel computacional, pero tal y como se definen incorporan numerosas características, quizás demasiadas. En (Ibarra et al. 2007) se demostró que en estos sistemas sus funcionalidades podrían ser limitadas sin comprometer su universalidad. Los resultados presentados en esta memoria son continuistas con la línea de trabajo de (Ibarra et al. 2007) y aportan nuevas formas normales. Esto es, nuevas variantes simplificadas de los sistemas SN P con un conjunto mínimo de funcionalidades pero que mantienen su poder computacional universal. Análisis de la eficiencia computacional: En esta tesis se ha estudiado la eficiencia computacional de los denominados sistemas P con proteínas en las membranas. Se muestra que este modelo de cómputo es equivalente a las máquinas de acceso aleatorio paralelas (PRAM) o a las máquinas de Turing alterantes ya que se demuestra que un sistema P con proteínas, es capaz de resolver un problema ESPACIOP-Completo como el QSAT(problema de satisfacibilidad de fórmulas lógicas cuantificado) en tiempo polinómico. Esta variante de sistemas P con proteínas es muy eficiente gracias al poder de las proteínas a la hora de catalizar los procesos de comunicación intercelulares. ABSTRACT The results presented at this thesis belong to membrane computing a new research branch inside of Natural computing. This new branch was created by Gh. Paun on 1998, hence usually receives the name of P Systems. This new distributed computing model is inspired on structure and functioning of cell. The aim of this thesis is to analyze the efficiency and computational power of these computational cellular systems. Specifically there have been analyzed two different classes of P systems. On the one hand it has been analyzed the Neural Spiking P Systems, and on the other hand it has been analyzed the P systems with proteins on membranes. For the first class it is shown that it is possible to reduce or restrict the characteristics of these kind of systems without loss of computational power. For the second class it is analyzed the computational efficiency solving on polynomial time PSACE problems. Computational Power Analysis: The spiking neural P systems (SN P in short) are systems inspired by the way of neural cells operate sending spikes through the synaptic networks. The bio-inspired SN Ps possess a large range of features that make these systems to be universal and therefore equivalent in computational power to a Turing machine. Such systems are computationally powerful, but by definition they incorporate a lot of features, perhaps too much. In (Ibarra et al. in 2007) it was shown that their functionality may be limited without compromising its universality. The results presented herein continue the (Ibarra et al. 2007) line of work providing new formal forms. That is, new SN P simplified variants with a minimum set of functionalities but keeping the universal computational power. Computational Efficiency Analisys: In this thesis we study the computational efficiency of P systems with proteins on membranes. We show that this computational model is equivalent to parallel random access machine (PRAM) or alternating Turing machine because, we show P Systems with proteins can solve a PSPACE-Complete problem as QSAT (Quantified Propositional Satisfiability Problem) on polynomial time. This variant of P Systems with proteins is very efficient thanks to computational power of proteins to catalyze inter-cellular communication processes.

Virtualización de laboratorios

Para empezar, se ha hecho un análisis de las diferentes posibilidades que se podían implementar para poder conseguir el objetivo del trabajo. El resultado final debe ser, disponer de máquinas para que el sistema operativo fuese independiente del hardware que se tiene instalado en él . Para ello, se decide montar un sistema operativo de base en todos los equipos del laboratorio, que tenga las necesidades mínimas que se necesitan, las cuales son una interfaz gráfica y conexión de red. Hay que intentar reducir el consumo de recursos al máximo con este sistema operativo mínimo para que el rendimiento de las máquinas sea lo más fluido posible para los usuarios. El sistema elegido fue Linux con su distribución Ubuntu [ubu, http] con los módulos mínimos que permita funcionar el software necesario. Una vez se instala el sistema operativo anfitrión, se instala el escritorio Xfce [ubu2, http], que es el más ligero de Ubuntu, pero que proporciona buen rendimiento. Después, se procedió a instalar un software de virtualización en cada equipo. En este caso se decidió, por las buenas prestaciones que ofrecía, que fuera VirtualBox [vir2,http] de Oracle. Sobre éste software se crean tantas máquinas virtuales (con sistema operativo Windows) como asignaturas diferentes se cursan en el laboratorio donde se trabaje. Con esto, se consigue que al arrancar el programa los alumnos pudieran escoger qué máquina arrancar y lo que es más importante, se permite realizar cualquier cambio en el hardware (exceptuando el disco duro porque borraría todo lo que se tuviera guardado). Además de no tener que volver a reinstalar el sistema operativo nuevamente, se consigue la abstracción del software y hardware. También se decide que, para tener un respaldo de las máquinas virtuales que se tengan creadas en VirtualBox, se utiliza un servidor NAS. Uno de los motivos de utilizar dicho servidor fue por aprovechar una infraestructura ya creada. Un servidor NAS da la posibilidad de recuperar cualquier archivo (máquina virtual) cuando haga falta porque haya alguna máquina virtual corrupta en algún equipo, o en varios. Este tipo de servidor tiene la gran ventaja de ser multicast, es decir, permite solicitudes simultáneas. ABSTRACT For starters, there has been an analysis of the different possibilities that could be implemented to achieve the objective of the work. This objective was to have machines for the operating system to be independent of the hardware we have installed on it. Therefore, we decided to create an operating system based on all computers in the laboratory, taking the minimum needs we need. This is a graphical interface and network connection. We must try to reduce the consumption of resources to the maximum for the performance of the machines is as fluid as possible for users. The system was chosen with its Ubuntu Linux distribution with minimum modules that allow us to run software that is necessary for us. Once the base is installed, we install the Xfce desktop, which is the lightest of Ubuntu, but which provided good performance. Then we proceeded to install a virtualization software on each computer. In this case we decided, for good performance that gave us, it was Oracle VirtualBox. About this software create many virtual machines (Windows operating system) as different subjects are studied in the laboratory where we are. With that, we got it at program startup students could choose which machine start and what is more important, allowed us to make any changes to the hardware (except the hard drive because it would erase all we have). Besides not having to reinstall the operating system again, we get the software and hardware abstraction. We also decided that in order to have a backup of our virtual machines that we created in VirtualBox, we use a NAS server. One reason to use that server was to leverage their existing network infrastructure. A NAS server gives us the ability to retrieve any file (image) when we do need because there is some corrupt virtual machine in a team, or several. This is possible because this type of server allows multicast connection.

Parallelizing irregular and pointer-based computations automatically: perspectives from logic and constraint programming

Irregular computations pose sorne of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures, which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. Starting in the mid 80s there has been significant progress in the development of parallelizing compilers for logic pro­gramming (and more recently, constraint programming) resulting in quite capable paralle­lizers. The typical applications of these paradigms frequently involve irregular computations, and make heavy use of dynamic data structures with pointers, since logical variables represent in practice a well-behaved form of pointers. This arguably makes the techniques used in these compilers potentially interesting. In this paper, we introduce in a tutoríal way, sorne of the problems faced by parallelizing compilers for logic and constraint programs and provide pointers to sorne of the significant progress made in the area. In particular, this work has resulted in a series of achievements in the areas of inter-procedural pointer aliasing analysis for independence detection, cost models and cost analysis, cactus-stack memory management, techniques for managing speculative and irregular computations through task granularity control and dynamic task allocation such as work-stealing schedulers), etc.

Towards description and optimization of abstract machines in an extension of prolog

Competitive abstract machines for Prolog are usually large, intricate, and incorpórate sophisticated optimizations. This makes them difñcult to code, optimize, and, especially, maintain and extend. This is partly due to the fact that efñciency considerations make it necessary to use low-level languages in their implementation. Writing the abstract machine (and ancillary code) in a higher-level language can help harness this inherent complexity. In this paper we show how the semantics of basic components of an efficient virtual machine for Prolog can be described using (a variant of) Prolog which retains much of its semantics. These descriptions are then compiled to C and assembled to build a complete bytecode emulator. Thanks to the high level of the language used and its closeness to Prolog the abstract machine descriptions can be manipulated using standard Prolog compilation and optimization techniques with relative ease. We also show how, by applying program transformations selectively, we obtain abstract machine implementations whose performance can match and even exceed that of highly-tuned, hand-crafted emulators.

A static heap analysis for shape and connectivity: Unified memory analysis: The base framework

Modeling the evolution of the state of program memory during program execution is critical to many parallehzation techniques. Current memory analysis techniques either provide very accurate information but run prohibitively slowly or produce very conservative results. An approach based on abstract interpretation is presented for analyzing programs at compile time, which can accurately determine many important program properties such as aliasing, logical data structures and shape. These properties are known to be critical for transforming a single threaded program into a versión that can be run on múltiple execution units in parallel. The analysis is shown to be of polynomial complexity in the size of the memory heap. Experimental results for benchmarks in the Jolden suite are given. These results show that in practice the analysis method is efflcient and is capable of accurately determining shape information in programs that créate and manipúlate complex data structures.

Adaptación de un reproductor de contenidos multimedia para la recepción de vídeo escalable sobre un protocolo de tiempo real

En los últimos años, debido al notable desarrollo de los terminales portátiles, que han pasado de ser “simples” teléfonos o reproductores a puros ordenadores, ha crecido el número de servicios que ofrecen cada vez mayor cantidad de contenido multimedia a través de internet. Además, la distinta evolución de estos terminales hace que nos encontremos en el mercado con una amplísima gama de productos de diferentes tamaños y capacidades de procesamiento, lo que hace necesario encontrar una fórmula que permita satisfacer la demanda de dichos servicios sea cual sea la naturaleza de nuestro dispositivo. Para poder ofrecer una solución adecuada se ha optado por la integración de un protocolo como RTP y un estándar de video como SVC. RTP (Real-time Transport Protocol), en contraposición a los protocolos de propósito general fue diseñado para aplicaciones de tiempo real por lo que es ideal para el streaming de contenido multimedia. Por su parte, SVC es un estándar de video escalable que permite transmitir en un mismo stream una capa base y múltiples capas de mejora, por lo que podremos adaptar la calidad y tamaño del contenido a la capacidad y tamaño de nuestro dispositivo. El objetivo de este proyecto consiste en integrar y modificar tanto el reproductor MPlayer como la librería RTP live555 de tal forma que sean capaces de soportar el formato SVC sobre el protocolo RTP y montar un sistema servidorcliente para comprobar su funcionamiento. Aunque este proceso esté orientado a llevarse a cabo en un dispositivo móvil, para este proyecto se ha optado por realizarlo en el escenario más sencillo posible, para lo cual, se emitirán secuencias a una máquina virtual alojada en el mismo ordenador que el servidor. ABSTRACT In recent years, due to the remarkable development of mobile devices, which have evolved from "simple" phones or players to computers, the amount of services that offer multimedia content over the internet have shot up. Furthermore, the different evolution of these terminals causes that we can find in the market a wide range of different sizes and processing capabilities, making necessary to find a formula that will satisfy the demand for such services regardless of the nature of our device. In order to provide a suitable solution we have chosen to integrate a protocol as RTP and a video standard as SVC. RTP (Real-time Transport Protocol), in opposition to general purpose protocols was designed for real-time applications making it ideal for media streaming. Meanwhile, SVC is a scalable video standard which can transmit a single stream in a base layer and multiple enhancement layers, so that we can adapt the quality and size of the content to the capacity and size of our device. The objective of this project is to integrate and modify both MPlayer and RTP library live555 so that they support the SVC format over RTP protocol and set up a client-server system to check its behavior. Although this process has been designed to be done on a mobile device, for this project we have chosen to do it in the simplest possible scenario so we will stream to a virtual machine hosted on the same computer where we have the server.

Ada real-time services and virtualization

Virtualization techniques have received increased attention in the field of embedded real-time systems. Such techniques provide a set of virtual machines that run on a single hardware platform, thus allowing several application programs to be executed as though they were running on separate machines, with isolated memory spaces and a fraction of the real processor time available to each of them.This papers deals with some problems that arise when implementing real-time systems written in Ada on a virtual machine. The effects of virtualization on the performance of the Ada real-time services are analysed, and requirements for the virtualization layer are derived. Virtual-machine time services are also defined in order to properly support Ada real-time applications. The implementation of the ORK+ kernel on the XtratuM supervisor is used as an example.

Limits of the power of Tissue P systems with cell division

Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic opera- tions in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was shown to range between P and NP ? co-NP , thus characterizing some interesting borderlines between tractability and intractability. In this paper we show that com- putational power of these uniform families in polynomial time is limited by the class PSPACE . This class characterizes the power of many clas- sical parallel computing models