Tree-size bounded alternation

AbstractThe size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure. We present a number of applications of tree-size to the study of more traditional complexity classes. Tree-size on ATMs is shown to closely correspond to time on nondeterministic TMs and on nondeterministic auxiliary pushdown automata. One application of the later is a useful new characterization of the class of languages log-space-reducible to context-free languages. Surprising relationships with parallel-time complexity are also demonstrated. ATM computations using at most space S(n) and tree-size Z(n) (simultaneously) can be simulated in alternating space S(n) and time S(n) · log Z(n) (simultaneously). Several well-known simulations, e.g., Savitch's theorem, are special cases of this result. It also leads to improved parallel complexity bounds for many problems in terms of both time and number of “processors.” As one example we show that context-free language recognition in time O(log2 n) is possible on several parallel models. Further, this bound is achievable with only a polynomial number of processors, in contrast to all previously known sub-linear time CFL recognizers

Solidification and Gravity VII

International audienc

A Multigrid Method for the Efficient Numerical Solution of Optimization Problems Constrained by Partial Differential Equations

We study the minimization of a quadratic functional subject to constraints given by a linear or semilinear elliptic partial differential equation with distributed control. Further, pointwise inequality constraints on the control are accounted for. In the linear-quadratic case, the discretized optimality conditions yield a large, sparse, and indefinite system with saddle point structure. One main contribution of this thesis consists in devising a coupled multigrid solver which avoids full constraint elimination. To this end, we define a smoothing iteration incorporating elements from constraint preconditioning. A local mode analysis shows that for discrete optimality systems, we can expect smoothing rates close to those obtained with respect to the underlying constraint PDE. Our numerical experiments include problems with constraints where standard pointwise smoothing is known to fail for the underlying PDE. In particular, we consider anisotropic diffusion and convection-diffusion problems. The framework of our method allows to include line smoothers or ILU-factorizations, which are suitable for such problems. In all cases, numerical experiments show that convergence rates do not depend on the mesh size of the finest level and discrete optimality systems can be solved with a small multiple of the computational cost which is required to solve the underlying constraint PDE. Employing the full multigrid approach, the computational cost is proportional to the number of unknowns on the finest grid level. We discuss the role of the regularization parameter in the cost functional and show that the convergence rates are robust with respect to both the fine grid mesh size and the regularization parameter under a mild restriction on the next to coarsest mesh size. Incorporating spectral filtering for the reduced Hessian in the control smoothing step allows us to weaken the mesh size restriction. As a result, problems with near-vanishing regularization parameter can be treated efficiently with a negligible amount of additional computational work. For fine discretizations, robust convergence is obtained with rates which are independent of the regularization parameter, the coarsest mesh size, and the number of levels. In order to treat linear-quadratic problems with pointwise inequality constraints on the control, the multigrid approach is modified to solve subproblems generated by a primal-dual active set strategy (PDAS). Numerical experiments demonstrate the high efficiency of this approach due to mesh-independent convergence of both the outer PDAS method and the inner multigrid solver. The PDAS-multigrid method is incorporated in the sequential quadratic programming (SQP) framework. Inexact Newton techniques further enhance the computational efficiency. Globalization is implemented with a line search based on the augmented Lagrangian merit function. Numerical experiments highlight the efficiency of the resulting SQP-multigrid approach. In all cases, locally superlinear convergence of the SQP method is observed. In combination with the mesh-independent convergence rate of the inner solver, a solution method with optimal efficiency is obtained

Verification of Automata with Storage Mechanisms

An important question in computer science is to ask, whether a given system conforms to a specification. Often this question is equivalent to ask whether a finite automaton with certain memory like a stack or queue can reach some given state. In this thesis we focus this reachability problem of automata having one or more lossy or reliable stacks or queues as their memory. Unfortunately, the reachability problem is undecidable or of high complexity in most of these cases. We circumvent this by several approximation methods. So we extend the exploration algorithm by Boigelot and Godefroid under-approximating the reachability problem of queue automata. We also study some automata having multiple stacks with a restricted behavior. These “asynchronous pushdown systems” have an efficiently decidable reachability problem. To show our results we first have to gain knowledge of several algebraic properties of the so-called transformation monoid of the studied storage mechanisms.An important research topic in computer science is the verification, i.e., the analysis of systems towards their correctness. This analysis consists of two parts: first we have to formalize the system and the desired properties. Afterwards we have to find algorithms to check whether the properties hold in the system. In many cases we can model the system as a finite automaton with a suitable storage mechanism, e.g., functional programs with recursive calls can be modeled as automata with a stack (or pushdown). Here, we consider automata with two variations of stacks and queues: 1. Partially lossy queues and stacks, which are allowed to forget some specified parts of their contents at any time. We are able to model unreliable systems with such memories. 2. Distributed queues and stacks, i.e., multiple such memories with a special synchronization in between. Often we can check the properties of our models by solving the reachability and recurrent reachability problems in our automata models. It is well-known that the decidability of these problems highly depends on the concrete data type of our automata’s memory. Both problems can be solved in polynomial time for automata with one stack. In contrast, these problems are undecidable if we attach a queue or at least two stacks to our automata. In some special cases we are still able to verify such systems. So, we will consider only special automata with multiple stacks - so-called asynchronous pushdown automata. These are multiple (local) automata each having one stack. Whenever these automata try to write something into at least one stack, we require a read action on these stacks right before these actions. We will see that the (recurrent) reachability problem is decidable for such asynchronous pushdown automata in polynomial time. We can also semi-decide the reachability problem of our queue automata by exploration of the configration space. To this end, we can join multiple consecutive transitions to so-called meta-transformations and simulate them at once. Here, we study meta-transformations alternating between writing words from a given regular language into the queues and reading words from another regular language from the queues. We will see that such metatransformations can be applied in polynomial time. To show this result we first study some algebraic properties of our stacks and queues.Ein wichtiges Forschungsthema in der Informatik ist die Verifikation, d.h., die Analyse von Systemen bezüglich ihrer Korrektheit. Diese Analyse erfolgt in zwei Schritten: Zuerst müssen wir das System und die gewünschten Eigenschaften formalisieren. Anschließend benötigen wir Algorithmen zum Testen, ob das System die Eigenschaften erfüllt. Oftmals können wir das Systemals endlichen Automaten mit geeignetem Speichermechanismus modellieren, z.B. rekursive Programme sind im Wesentlichen Automaten mit einem Stack. Hier betrachten wir Automaten mit zwei Varianten von Stacks und Queues: 1. Partiell vergessliche Stacks und Queues, welche bestimmte Teile ihrer Inhalte jederzeit vergessen können. Diese können für unzuverlässige Systeme verwendet werden. 2. Verteilte Stacks und Queues, d.h., mehrere Stacks und Queues mit vordefinierter Synchronisierung. Häufig lassen sich die Eigenschaften unserer Modelle mithilfe des (wiederholten) Erreichbarkeitsproblems in unseren Automaten lösen. Dabei ist bekannt, dass die Entscheidbarkeit dieser Probleme oftmals stark vom konkreten Datentyp des Speichers abhängt. Beide Probleme können für Automaten mit einem Stack in Polynomialzeit gelöst werden. Sie sind jedoch unentscheidbar, wenn wir Automaten mit einer Queue oder zwei Stacks betrachten. In bestimmten Spezialfällen sind aber dennoch in der Lage diese Systeme zu verifizieren. So können wir beispielsweise bestimmte Automaten mit mehreren Stacks betrachten - so genannte Asynchrone Kellerautomaten. Diese bestehen aus mehreren (lokalen) Automaten mit jeweils einem Stack. Wann immer diese Automaten etwas in mind. einen Stack schreiben, müssen sie unmittelbar zuvor von diesen Stacks etwas lesen. Das (wiederholte) Erreichbarkeitsproblem ist in asynchronen Kellerautomaten in Polynomialzeit entscheidbar. Wir können zudem das Erreichbarkeitsproblem von Queueautomaten durch Exploration des Konfigurationsraums semi-entscheiden. Hierzu können wir mehrere aufeinanderfolgende Transitionen zu so genannten Meta-Transformationen zusammenfassen und diese in einem Schritt simulieren. Hier betrachten wir Meta-Transformationen, die zwischen dem Lesen und Schreiben von Wörtern aus zwei gegebenen regulären Sprachen alternieren. Diese Meta-Transformationen können in Polynomialzeit ausgeführt werden. Für dieses Ergebnis müssen wir jedoch zunächst verschiedene algebraische Eigenschaften der Queues betrachten

Design, modelization and realization of integrated inductive components for low power supplies and microsystems

Full integration of energy conversion devices for compact power supply circuits is still encountering strong technological locks, especially to integrate passive inductive and capacitive components. The increasing working frequency of those devices, which already reaches 1 Megahertz, would enable the size reduction of passive components and then their integration. Nevertheless, losses, which highly depend on frequency and technology, may complicate or even stop this increase.\ud The objective of this thesis is the systematic study of integrated inductors structures through the developing of precise modeling and simulating methods on the frequency range from 0Hz to 1GHz. First, an analytic model based on PEEC (Partial Element Equivalent Circuit) method has been developed. This modeling approach has been adapted to the studied components: rotational symmetry, not negligible section conductors, inhomogeneous media, etc… The final model splits the physical study of the component into two steps: electromagnetic computations on subparts of the set (partial elements) and global frequency response calculus with the equivalent electrical models of the subparts. A full process for the technological realization of inductive components has also been achieved in order to experimentally verify the modeling. The improvement of design resolution and increase of copper electroplating thickness, as planarization of conductor levels with SU8 resin have been specifically studied. Those overhangs have permitted the realization of multilevel and multiconductor inductors which present good features at high frequency. Finally, the characterization of prototypes at low frequency has been enabled by the realization of an impedance measurement bench we developed for the range from 40Hz to 110MHz and high frequency characterizations have been performed with a network analyzer. This work has been completed by the development of a very fast computing analytical model for the calculus of the magnetic field in integrated inductors. This method has been used to find the repartition of the magnetic field generated by integrated planar magnetic actuators excited by a DC current for a microsystems and microfluidics application.---------------------------------------------------------------L’intégration complète des dispositifs de conversion d’énergie destinés à créer des circuits d’alimentation compacts se heurte encore aujourd’hui à des contraintes technologiques fortes sur l’intégration des composants passifs inductifs et capacitifs. La fréquence de fonctionnement de ces dispositifs, d’ores et déjà de l’ordre du MHz, en augmentant pourrait réduire la taille de ces composants passifs et donc permettre leur intégration. Cependant, les pertes fortement liées à la fréquence et à la technologie, freinent encore cette augmentation.\ud Cette thèse a pour objectif l’étude systématique de structures d’inductances intégrées à travers le développement d’une modélisation accompagnée de simulations précises pour le développement d’une méthodologie de simulation valable sur la plage de fréquence de 0Hz à 1GHz. Pour cela, un modèle analytique basé sur la méthode PEEC (Partial Element Equivalent Circuit) a d’abord été développé. Ce type de modèle a du être adapté aux topologies des composants étudiés : symétrie cylindrique, conducteurs de section non négligeable, milieux non homogènes… Ce modèle décompose l’étude du composant en deux étapes : calculs électromagnétiques menés sur des sous-parties du composant (éléments partiels) et calcul de la réponse fréquentielle globale à partir de modèles électriques des éléments partiels. Un procédé complet de réalisation technologique des composants inductifs a également été mis au point en parallèle afin de valider expérimentalement la modélisation. L’amélioration de la résolution des motifs et l’augmentation de l’épaisseur des dépôts lors des étapes de croissance électrolytique du cuivre, ainsi que la planarisation des niveaux de conducteurs avec de la résine SU8 ont fait l’objet d’études spécifiques. Ces avancées ont permis la réalisation de selfs multibrin et multiniveau qui présentent des caractéristiques électriques intéressantes en haute fréquence. Enfin, la caractérisation des prototypes en basse fréquence a été rendue possible par la mise en oeuvre d’un banc de mesure d’impédance pour la gamme de fréquence de 40 Hz à 110MHz et des caractérisations en haute fréquence effectuées à l’aide d’un analyseur de réseau. Ces travaux ont été complétés par la mise au point d’une méthode analytique de calcul du champ magnétique. Les calculs permettent de prédire la répartition du champ magnétique généré par des actionneurs magnétiques planaires intégrés excités en courant continu

Resource-efficient strategies for mobile ad-hoc networking

The ubiquity and widespread availability of wireless mobile devices with ever increasing inter-connectivity (e. g. by means of Bluetooth, WiFi or UWB) have led to new and emerging next generation mobile communication paradigms, such as the Mobile Ad-hoc NETworks (MANETs). MANETs are differentiated from traditional mobile systems by their unique properties, e. g. unpredictable nodal location, unstable topology and multi-hop packet relay. The success of on-going research in communications involving MANETs has encouraged their applications in areas with stringent performance requirements such as the e-healthcare, e. g. to connect them with existing systems to deliver e-healthcare services anytime anywhere. However, given that the capacity of mobile devices is restricted by their resource constraints (e. g. computing power, energy supply and bandwidth), a fundamental challenge in MANETs is how to realize the crucial performance/Quality of Service (QoS) expectations of communications in a network of high dynamism without overusing the limited resources. A variety of networking technologies (e. g. routing, mobility estimation and connectivity prediction) have been developed to overcome the topological instability and unpredictability and to enable communications in MANETs with satisfactory performance or QoS. However, these technologies often feature a high consumption of power and/or bandwidth, which makes them unsuitable for resource constrained handheld or embedded mobile devices. In particular, existing strategies of routing and mobility characterization are shown to achieve fairly good performance but at the expense of excessive traffic overhead or energy consumption. For instance, existing hybrid routing protocols in dense MANETs are based in two-dimensional organizations that produce heavy proactive traffic. In sparse MANETs, existing packet delivery strategy often replicates too many copies of a packet for a QoS target. In addition, existing tools for measuring nodal mobility are based on either the GPS or GPS-free positioning systems, which incur intensive communications/computations that are costly for battery-powered terminals. There is a need to develop economical networking strategies (in terms of resource utilization) in delivering the desired performance/soft QoS targets. The main goal of this project is to develop new networking strategies (in particular, for routing and mobility characterization) that are efficient in terms of resource consumptions while being effective in realizing performance expectations for communication services (e. g. in the scenario of e-healthcare emergency) with critical QoS requirements in resource-constrained MANETs. The main contributions of the thesis are threefold: (1) In order to tackle the inefficient bandwidth utilization of hybrid service/routing discovery in dense MANETs, a novel "track-based" scheme is developed. The scheme deploys a one-dimensional track-like structure for hybrid routing and service discovery. In comparison with existing hybrid routing/service discovery protocols that are based on two-dimensional structures, the track-based scheme is more efficient in terms of traffic overhead (e. g. about 60% less in low mobility scenarios as shown in Fig. 3.4). Due to the way "provocative tracks" are established, the scheme has also the capability to adapt to the network traffic and mobility for a better performance. (2) To minimize the resource utilization of packet delivery in sparse MANETs where wireless links are intermittently connected, a store-and-forward based scheme, "adaptive multicopy routing", was developed for packet delivery in sparse mobile ad-hoc networks. Instead of relying on the source to control the delivery overhead as in the conventional multi-copy protocols, the scheme allows each intermediate node to independently decide whether to forward a packet according to the soft QoS target and local network conditions. Therefore, the scheme can adapt to varying networking situations that cannot be anticipated in conventional source-defined strategies and deliver packets for a specific QoS targets using minimum traffic overhead. ii (3) The important issue of mobility measurement that imposes heavy communication/computation burdens on a mobile is addressed with a set of resource-efficient "GPS-free" soluti ons, which provide mobility characterization with minimal resource utilization for ranging and signalling by making use of the information of the time-varying ranges between neighbouring mobile nodes (or groups of mobile nodes). The range-based solutions for mobility characterization consist of a new mobility metric for network-wide performance measurement, two velocity estimators for approximating the inter-node relative speeds, and a new scheme for characterizing the nodal mobility. The new metric and its variants are capable of capturing the mobility of a network as well as predicting the performance. The velocity estimators are used to measure the speed and orientation of a mobile relative to its neighbours, given the presence of a departing node. Based on the velocity estimators, the new scheme for mobility characterization is capable of characterizing the mobility of a node that are associated with topological stability, i. e. the node's speeds, orientations relative to its neighbouring nodes and its past epoch time. iiiBIOPATTERN EU Network of Excellence (EU Contract 508803

Models, Algorithms, and Architectures for Scalable Packet Classification

The growth and diversification of the Internet imposes increasing demands on the performance and functionality of network infrastructure. Routers, the devices responsible for the switch-ing and directing of traffic in the Internet, are being called upon to not only handle increased volumes of traffic at higher speeds, but also impose tighter security policies and provide support for a richer set of network services. This dissertation addresses the searching tasks performed by Internet routers in order to forward packets and apply network services to packets belonging to defined traffic flows. As these searching tasks must be performed for each packet traversing the router, the speed and scalability of the solutions to the route lookup and packet classification problems largely determine the realizable performance of the router, and hence the Internet as a whole. Despite the energetic attention of the academic and corporate research communities, there remains a need for search engines that scale to support faster communication links, larger route tables and filter sets and increasingly complex filters. The major contributions of this work include the design and analysis of a scalable hardware implementation of a Longest Prefix Matching (LPM) search engine for route lookup, a survey and taxonomy of packet classification techniques, a thorough analysis of packet classification filter sets, the design and analysis of a suite of performance evaluation tools for packet classification algorithms and devices, and a new packet classification algorithm that scales to support high-speed links and large filter sets classifying on additional packet fields