Original results in computational and combinatorial theory of reset words in transition systems, road coloring in directed graphs, and discontinuous input processing in formal languages are presented, including strong lower bounds on subset synchronization thresholds, lower bounds on descriptive power of jumping finite automata, and corresponding complexity classifications.

Made available in DSpace on 2016-03-15T19:38:08Z (GMT). No. of bitstreams: 1 Guilherme Kronemberger.pdf: 1225637 bytes, checksum: 6f698faf7a8661b382c4977e4b07f631 (MD5) Previous issue date: 2008-01-28 / Cellular automata have been studied as computer models in many different areas. They have many properties, one of them being reversibility. Reversible cellular automata can be used, among other applications, for data compressing and encryption. Apparently, the reversible rules featured in the literature seem to have been derived through exhaustive searches in their corresponding spaces. However, it would be important the availability of an algorithm that would allow their direct and easy construction, different from what occurs in literature. This is the aim of this work. Along this line, we tried to come up with an algorithm to allow the identification of one-dimensional, reversible cellular automaton rules. This was based on reversible rules with 2 states and 2, 3, 4 and 5 cells per neighborhood, and on those with 3 states and 2 and 3 cells per neighborhood, all of them drawn out of exhaustive analysis and from the literature. By studying these rules it was possible to verify in each space that: all reversible rules are balanced; they are symmetrically distributed; a subset of them herein denoted primitive reversible rules, RPs have a simple formation law, defined by homogeneous blocks of states; and, if a rule is reversible, so are all its dynamically equivalent rules. In the attempt to obtain the targetted algorithm, an approach was explored in which the non-primitive reversible rules (the so-called derived rules, RDs) were supposed to be obtained from the primitives. Along this line, two ways to construct the RDs were tried out, one based upon using all RPs jointly as a group, and another, using them individually; however, neither of them led to a positive result. Additionally, relations between the properties of reversibility and conservativity of a rule have also been studied in the rule spaces considered. / Autômatos celulares têm sido estudados como modelos computacionais em diversas áreas, sendo que muitas são as suas propriedades, entre elas a reversibilidade. Autômatos celulares reversíveis podem ser usados, entre outras aplicações, para compactação ou encriptação de dados. Aparentemente, as regras reversíveis apresentadas na literatura parecem ter sido derivadas apenas através de buscas exaustivas em seus espaços correspondentes. No entanto, seria importante a existência de um algoritmo que permitisse construí-las fácil e diretamente, diferente do que acontece na literatura. Este é o objetivo deste trabalho. Neste sentido, buscou-se um algoritmo que permitesse identificar regras de autômatos celulares unidimensionais reversíveis. Para tanto, foram obtidas em análises exaustivas e na literatura todas as regras reversíveis de 2 estados e vizinhanças de 2, 3, 4 e 5 células, e de 3 estados e vizinhanças de 2 e 3 células. Com o estudo destas regras constatou-se em cada espaço que: todas as regras reversíveis são balanceadas; elas se distribuem simetricamente; um subconjunto delas aqui denominadas regras reversíveis primitivas, RPs possui lei de formação simples, definida por blocos homogêneos de estados; e, se uma regra é reversível, todas as suas equivalentes dinâmicas também o são. Na tentativa de se obter o algoritmo desejado explorou-se uma abordagem em que as regras reversíveis não primitivas (denominadas regras derivadas, RDs), seriam obtidas a partir das primitivas. Nesse sentido foram testados dois esquemas de construção das RDs, um baseado na utilização conjunta de todas as RPs, e outro, utilizando-as individualmente; entretanto, ambos não levaram a resultado positivo. Adicionalmente, estudou-se a relação entre as propriedades de reversibilidade e conservatividade de regras nos espaços considerados.

Cette thèse étudie l’enforcement de propriétés temporisées à l’exécution en présence d’évènements incontrôlables. Les travaux se placent dans le cadre plus général de la vérification à l’exécution qui vise à surveiller l’exécution d’un système afin de s’assurer qu’elle respecte certaines propriétés. Ces propriétés peuvent être spécifiées à l’aide de formules logiques, ou au moyen d’autres modèles formels, parfois équivalents, comme des automates. Nous nous intéressons à l’enforcement à l’exécution de propriétés spécifiées par des automates temporisés. Tout comme la vérification à l’exécution, l’enforcement à l’exécution surveille l’exécution d’un système, la différence étant qu’un mécanisme d’enforcement réalise certaines modifications sur l’exécution afin de la contraindre à satisfaire la propriété souhaitée. Nous étudions plus particulièrement l’enforcement à l’exécution lorsque certains évènements de l’exécution sont incontrôlables, c’est-à-dire qu’ils ne peuvent pas être modifiés par un mécanisme d’enforcement. Nous définissons des algorithmes de synthèse de mécanismes d’enforcement décrits de manières fonctionnelle puis opérationnelle, à partir de propriétés temporisées régulières (pouvant être représentées par des automates temporisés). Ainsi, deux mécanismes d’enforcement équivalents sont définis, le premier présentant une approche correcte sans considération d’implémentation, alors que le second utilise une approche basée sur la théorie des jeux permettant de précalculer certains comportements, ce qui permet de meilleures performances. Une implémentation utilisant ce précalcul est également présentée et évaluée. Les résultats sont encourageant quant à la faisabilité de l’enforcement à l’exécution en temps réel, avec des temps supplémentaires suffisamment courts sur de petites propriétés pour permettre une utilisation de tels systèmes. / This thesis studies the runtime enforcement of timed properties when some events are uncontrollable. This work falls in the domain of runtime verification, which includes all the techniques and tools based on or related to the monitoring of system executions with respect to requirement properties. These properties can be specified using different models such as logic formulae or automata. We consider timed regular properties, that can be represented by timed automata. As for runtime verification, a runtime enforcement mechanism watches the executions of a system, but instead of just outputting a verdict, it modifies the execution so that it satisfies the property. We are interested in runtime enforcement with uncontrollable events. An uncontrollable event is an event that an enforcement mechanism can not modify. We describe the synthesis of enforcement mechanisms, in both a functional and an operational way, that enforce some desired timed regular property. We define two equivalent enforcement mechanisms, the first one being simple, without considering complexity aspects, whereas the second one has a better time complexity thanks to the use of game theory; the latter being better suited for implementation. We also detail a tool that implements the second enforcement mechanism, as well as some performance considerations. The overhead introduced by the use of our tool seems low enough to be used in some real-time application scenarios.

Markov decision processes (MDPs) are finite-state probabilistic systems with both strategic and random choices, hence well-established to model the interactions between a controller and its randomly responding environment. An MDP can be mathematically viewed as a one and half player stochastic game played in rounds when the controller chooses an action, and the environment chooses a successor according to a fixed probability distribution.<p><p>There are two incomparable views on the behavior of an MDP, when the strategic choices are fixed. In the traditional view, an MDP is a generator of sequence of states, called the state-outcome; the winning condition of the player is thus expressed as a set of desired sequences of states that are visited during the game, e.g. Borel condition such as reachability. The computational complexity of related decision problems and memory requirement of winning strategies for the state-outcome conditions are well-studied.<p><p>Recently, MDPs have been viewed as generators of sequences of probability distributions over states, called the distribution-outcome. We introduce synchronizing conditions defined on distribution-outcomes, which intuitively requires that the probability mass accumulates in some (group of) state(s), possibly in limit. A probability distribution is p-synchronizing if the probability mass is at least p in some state, and a sequence of probability distributions is always, eventually, weakly, or strongly p-synchronizing if respectively all, some, infinitely many, or all but finitely many distributions in the sequence are p-synchronizing.<p><p>For each synchronizing mode, an MDP can be (i) sure winning if there is a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there is a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there is a strategy that produces a (1-epsilon)-synchronizing sequence.<p><p>We consider the problem of deciding whether an MDP is winning, for each synchronizing and winning mode: we establish matching upper and lower complexity bounds of the problems, as well as the memory requirement for optimal winning strategies.<p><p>As a further contribution, we study synchronization in probabilistic automata (PAs), that are kind of MDPs where controllers are restricted to use only word-strategies; i.e. no ability to observe the history of the system execution, but the number of choices made so far. The synchronizing languages of a PA is then the set of all synchronizing word-strategies: we establish the computational complexity of the emptiness and universality problems for all synchronizing languages in all winning modes.<p><p>We carry over results for synchronizing problems from MDPs and PAs to two-player turn-based games and non-deterministic finite state automata. Along with the main results, we establish new complexity results for alternating finite automata over a one-letter alphabet. In addition, we study different variants of synchronization for timed and weighted automata, as two instances of infinite-state systems. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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Cette thèse a pour but d’étudier des propriétés structurelles d’automates étendant celle du déterminisme, et les langages pouvant être dénotés par une expression rationnelle dont l’automate des positions présente l’une de ces propriétés. Si Book et al. ont montré que tous les langages rationnels peuvent être reconnus par un automate des positions non-ambigu, Brüggemann-Klein et Wood ont montré que ceux pouvant l’être par un automate des positions déterministe forment une famille strictement incluse dans celle des rationnels. Nous nous intéressons aux extensions de cette famille, en cherchant à caractériser leurs langages, et à étudier leur hiérarchie interne et leur inclusion entre elles. / This thesis aims to study structural properties of automata extending determinism, and the languages that can be denoted by a regular expression of which the position automaton has one such property. If Book et al. showed that all regular languages can be recognized by an unambiguous position automaton, Brüggemann-Klein and Wood showed that only a proper subset of them can be recognized by a deterministic position automaton. We focus on extensions of this subfamily, by seeking to characterize their languages, and to study their internal hierarchy and how they relate to each other.

Formal language theory, originally developed to model and study our natural spoken languages, is nowadays also put to use in many other fields. These include, but are not limited to, the definition and visualization of programming languages and the examination and verification of algorithms and systems. Formal languages are instrumental in proving the correct behavior of automated systems, e.g., to avoid that a flight guidance system navigates two airplanes too close to each other. This vast field of applications is built upon a very well investigated and coherent theoretical basis. It is the goal of this dissertation to add to this theoretical foundation and to explore ways to make formal languages and their models more expressive. More specifically, we are interested in models that are able to model quantitative features of the behavior of systems. To this end, we define and characterize weighted automata over structures with hierarchical information and over graphs. In particular, we study infinite nested words, operator precedence languages, and finite and infinite graphs. We show Büchi-like results connecting weighted automata and weighted monadic second order (MSO) logic for the respective classes of weighted languages over these structures. As special cases, we obtain Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result for graphs has been an open problem for weighted logics for some time. We conjecture that our techniques can be applied to derive similar equivalence results in other contexts like traces, texts, and distributed systems.

Der Inhalt dieser Arbeit sind jedoch nicht Quantencomputer im Allgemeinen, sondern hauptsächlich Quantenautomaten. Dies führt zu den Begriffen der „endlichen Quantenautomaten“ und der „quantenregulären“ oder „quantenerkennbaren Sprachen“, die Hauptgegenstand der vorliegenden Arbeit sind.

Formal methods play an important part in the development as well as testing stages of software and hardware systems. A significant and often overlooked part of the process is the development of specifications and correctness requirements for the system under test. Traditionally, English has been used as the specification language, which has resulted in verbose and difficult to use specification documents that are usually abandoned during product development. This research focuses on investigating the use of Live Sequence Charts (LSCs), a graphical and intuitive language directly suited for expressing communication behaviors of a system as the specification language for a system under test. The research presents two methods for using LSCs as a specification language: first, by translating LSCs to temporal logic, and second, by translating LSCs to an automaton structure that is directly suited for formal verification of systems. The research first presents the translation for each method and further, identifies the pros and cons for each verification method.

Theoretical computer science is inconceivable without the concept of finite automata. These devices and their upgraded versions, weighted automata, are widely used to implement (quantitative) evaluations of inputs in image compression, probabilistic systems or natural language processing. In particular, the handling of natural language requires more sophisticated input structures such as trees. Together with the quantitative dimension, this leads to the model of weighted tree automata and the regular weighted tree languages they recognize. From a computational point of view, regular languages have many advantages: They allow compact representations, many of their fundamental properties are decidable and they are closed under several natural operations. One exception to this, however, are tree homomorphisms. It is long known that these deterministic transformations do not necessarily preserve regularity, but for decades, it was an open problem whether regularity of the homomorphic image is decidable. In 2010, this so-called HOM-problem was solved by Godoy, Giménez, Ramos and Àlvarez. More precisely, given a tree automaton and a tree homomorphism, it can be decided in exponential time whether the homomorphic image of the recognized language is again regular. In this thesis, we approach different weighted versions of this problem, where the input automaton is a weighted device over a certain semiring. We prove the decidability of this problem, both for restricted and unrestricted input, for different classes of weight domains. For this, we introduce a novel extension of weighted tree automata with explicit constraints, which we use to represent and study the homomorphic images. Moreover, we demonstrate an additional application of this automata model as we use it to describe the ranges of bottom-up and top-down weighted tree transformations.:1 Introduction 1.1 About this Work 1.2 Publications 2 Background 2.1 Preliminaries 2.1.1 Trees 2.1.2 Semirings 2.1.3 Tree Homomorphisms 2.2 Tree Automata and the HOM-Problem 3 Weighted Tree Automata with Constraints 3.1 The Model 3.2 Closure Properties 3.3 Hom-Regular Languages and the Subclass WTAh 3.4 Recognizing Homomorphic Images 3.5 A Pumping Lemma for WTAh 3.6 Conclusion 4 Unambiguity and the Weighted HOM-Problem 4.1 Translating TAh into TAhom 4.2 Deciding Regularity for Unambiguous WTAh 4.3 Unambiguity and the Instances of the HOM-Problem 4.4 Conclusion and Perspective 5 The N-Weighted HOM-Problem 5.1 The Large Duplication Property 5.2 Deciding the N-Weighted HOM-Problem 5.3 Conclusion 6 The HOM-Problem for Fields 6.1 Relating WTAh to WTA 6.2 A Pumping Lemma for WTAh over Fields 6.3 The Tetris-Free Weighted HOM-Problem 6.4 Conclusion 7 Weighted Tree Transducers in Light of Hom-Regular Tree Languages 7.1 Preliminaries: Transformations 7.2 Weighted Bottom-up Tree Transducers 7.2.1 Separating Weighted TOP and BOT – Part I 7.2.2 The Range of a Weighted Bottom-up Tree Transducer 7.3 Weighted Top-down Tree Transducers 7.3.1 Separating Weighted TOP and BOT – Part II 7.3.2 The Range of a Weighted Top-down Tree Transducer 7.4 Conclusion 8 Conclusion 8.1 Summary 8.2 FutureWork Bibliography Lebenslauf Selbständigkeitserklärung