Highly dynamic and complex computing systems are increasingly needed and are relied upon in daily life. One such system is the dynamic network, particularly in communication, in which it has widespread applications, such as: Internet, peer-to-peer networks, mobile networks and wireless networks. Dynamic networks consist of nodes and edges whose operating status may change over time; the edges may be unreliable and operate intermittently. Message-passing in such networks is inherently difficult and reasoning about the behaviour of message-passing algorithms is also difficult and hard to analyse. Their behaviour and correctness are hard to formulate and establish. To undertake formal reasoning about such systems, abstract models are essential in order to separate the general reasoning about message routing and the updating of routing tables from the details of how these are implemented in particular networks. This thesis proposes a new approach to modelling and reasoning about dynamic networks as follows. It develops a series of abstract models which makes it possible to focus on the correctness of routing methods. It models the dynamic network as a “demonic” process which runs concurrently with routing updates and message-passing, to express dynamic networks as concurrent systems. This allows the use of temporal logic and fairness constraints to reason about dynamic networks. To do so, it introduces a modal logic and formulates concepts of fairness which capture network properties. The correctness of dynamic networks means that under certain conditions, all messages will eventually be delivered. Formulating networks as concurrent systems means can establish the correctness for networks that never cease to change. Modelling at that one level of abstraction means being able to prove the properties of networks independently of the mechanisms in actual networks. Therefore, it provides “a factorisation” of proofs of correctness for actual dynamic networks. The models are implemented as multi-threaded programs, and then adopted an experimental runtime verification tool called RULER to test whether model instances satisfy the modal correctness for message delivery.

Models of true concurrency have gained a lot of interest over the last decades as models of concurrent or distributed systems which avoid the well-known problem of state space explosion of the interleaving models. In this thesis, we study such models from two perspectives. Firstly, we study the relation between Petri nets and stable event structures. Petri nets can be considered as one of the most general and perhaps wide-spread models of true concurrency. Event structures on the other hand, are simpler models of true concurrency with explicit causality and conflict relations. Stable event structures expand the class of event structures by allowing events to be enabled in more than one way. While the relation between Petri nets and event structures is well understood, the relation between Petri nets and stable event structures has not been studied explicitly. We define a new and more compact unfoldings of safe Petri nets which is directly translatable to stable event structures. In addition, the notion of complete finite prefix is defined for compact unfoldings, making the existing model checking algorithms applicable to them. We present algorithms for constructing the compact unfoldings and their complete finite prefix. Secondly, we study probabilistic models of true concurrency. We extend the definition of probabilistic event structures as defined by Abbes and Benveniste to a newly defined class of stable event structures, namely, jump-free stable event structures arising from Petri nets (characterised and referred to as net-driven). This requires defining the fundamental concept of branching cells in probabilistic event structures, for jump-free net-driven stable event structures, and by proving the existence of an isomorphism among the branching cells of these systems, we show that the latter benefit from the related results of the former models. We then move on to defining a probabilistic logic over probabilistic event structures (PESL). To our best knowledge, this is the first probabilistic logic of true concurrency. We show examples of expressivity achieved by PESL, which in particular include properties related to synchronisation in the system. This is followed by the model checking algorithm for PESL for finite event structures. Finally, we present a logic over stable event structures (SEL) along with an account of its expressivity and its model checking algorithm for finite stable event structures.

Formal methods provide means for rigorously specifying the desired behaviour of a hardware or software system, making a precise model of its actual behaviour, and then verifying whether that actual behaviour corresponds to the specification.<br><br> My habiliation thesis reports on various contributions to this realm, where my main interest has been on algorithmic aspects. This is motivated by the observation that asymptotic worst-case complexity, often used to characterize the difficulty of algorithmic problems, is only loosely related to the difficulty encountered in solving those problems in practice.<br><br> The two main types of system I have been working on are pushdown systems and Petri nets. Both are fundamental notions of computation, and both offer, in my opinion, particularly nice opportunities for combining theory and algorithmics.<br><br> Pushdown systems are finite automata equipped with a stack; since the height of the stack is not bounded, they represent a class of infinite-state systems that model programs with (recursive) procedure calls. Moreover, we shall see that specifying authorizations is another, particularly interesting application of pushdown systems.<br><br> While pushdown systems are primarily suited to express sequential systems, Petri nets model concurrent systems. My contributions in this area all concern unfoldings. In a nutshell, the unfolding of a net N is an acyclic version of N in which loops have been unrolled. Certain verification problems, such as reachability, have a lower complexity on unfoldings than on general Petri nets.

<p> This thesis presents a new modelling technique for the complex current system. It integrates object-oriented methodology into Petri Nets formalism.</p> <p> Petri Nets are used for modelling concurrent systems. They have natural graphical representation as well as formal specifications. They have been successfully used in various industrial applications. But with the development of distributed and network systems, their traditional weakness, namely their inadequate support for compositionality, is a big obstacle to their practical use for large, complex systems. To address this problem, we introduce the Object-Oriented Coloured Petri Nets (OO-CPN), which integrates the powerful modularity of an object-oriented paradigm into Petri Nets formalism. OO-CPN is based on Coloured Petri Nets and supports the concepts of object, class, inheritance and polymorphism.</p> / Thesis / Master of Science (MSc)

Well-behaved SNC covers well-behaved and various classes of FC (free-choice) and is not included in AC (asymmetric choice). An SNC allows internal choices and concurrency and hence is powerful for irodeling. Any SNC is bounded and its liveness conditions are simple. An integrated algorithm, has been presented for verification of a net being SNC and its liveness with polynomial time complexity. Scholars often need to verify properties on nets appearing in literatures. Verification by CAD tool is less desirable than that by hand due to the extra efforts to input the model aid learn to use the tool. We propose to manually search the maximum SNC component followed by locating bad siphons in an incremental manner. We then apply Lautenback's Maridng Condition (MC) for liveness to berify the property of liveness. But there are two drawbacks associated with the above MC. First, it guarantees only deadlock-freeness, and not necessary liveness. We have identified the structure cause for this and developed its livess conditions correspondingly. Second a net may be live even if the MC is not satisfied. We have identified the structure cause for this. The MC has been readjusted based on our proposed new theorey.

The factored state representation and concurrency semantics of Petri nets are closely related to those of classical planning models, yet automated planning and Petri net analysis have developed independently, with minimal and mainly unconvincing attempts at crossfertilisation. This thesis exploits the relationship between the formal reachability problem, and the automated planning problem, via Petri net unfolding, which is an attractive reachability analysis method for highly concurrent systems as it facilitates reasoning about independent sub-problems. The first contribution of this thesis is the theory of directed unfolding: controlling the unfolding process with informative strategies, for the purpose of optimality and increased efficiency. The second contribution is the application of directed unfolding to automated planning. Inspired by well-known planning heuristics, this thesis shows how problem specific information can be employed to guide unfolding, in response to the formal problem of developing efficient, directed reachability analysis methods for concurrent systems. Complimenting this theoretical work, this thesis presents a new forward search method for partial order planning which can be exponentially more efficient than state space search. Our suite of planners based on directed unfolding can perform optimal and suboptimal classical planning subject to arbitrary action costs, optimal temporal planning with respect to arbitrary action durations, and address probabilistic planning via replanning for the most likely path. Empirical results reveal directed unfolding is competitive with current state of the art automated planning systems, and can solve Petri net reachability problems beyond the reach of the original “blind” unfolding technique. / Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2008

This work presents a method to perform formal and dynamic verification of concurrent software. The objective is to provide a method capable of identifying problems in programs whose execution is based on multiple threads, and analyze behavioral properties. The method is able to detect problems in concurrent software, as well as check conformity of the concurrent software with desirable behavior, based on information collected dynamically, i.e. at runtime. The information collected consists of the software execution flow as well as data about the way communicate the software components during this run. The data collected reflect the software's execution, which ensures greater confidence to the information collected. This information is analyzed to identify deadlocks and race conditions in a process called Dynamic Analysis. In addition, this information is also used to automatically generate a model that describes the behavior of a software, which is used for verification of behavioral properties. This process is called Formal Verification. The automatic model generation eliminates the need for manual construction of the model, which requires much effort and knowledge of formal methods, this can increase costs and development time software. However, the dynamic analysis is known to only perform coverage of the current behavior of competing software systems. Current behavior is one that occurs only during an execution of concurrent software systems, without considering all other possible behaviors from the non-determinism. Due to the non-determinism, concurrent software can produce different results for the same input to each execution of software. Therefore reproduce the behavior that leads to competitive software failure is a complex task. This paper proposes a method to perform formal verification and dynamic concurrent software capable of capturing the non-deterministic behavior of these systems and provide reduced development costs by eliminating the need for manual construction of concurrent software system models. The method is validated by a case study consists of three test software systems. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Neste trabalho é apresentado um método para verificação formal e dinâmica de software concorrentes. O objetivo é oferecer um método capaz de identificar problemas inerentes a programas cuja execução baseia-se em múltiplas threads, além de analisar propriedades comportamentais descritas com base nos preceitos da lógica temporal. Propõe-se um método capaz de detectar problemas e verificar formalmente a adequação da execução de sistemas de software concorrentes com relação ao comportamento desejável a tais sistemas, baseando-se em informações coletadas dinamicamente, ou seja, em tempo de execução. As informações coletadas correspondem às sequências de execução de sistemas de software, bem como dados sobre a maneira como se comunicam seus componentes durante sua execução. Os dados colhidos refletem a execução do sistema de software propriamente dito, o que garante maior confiança às informações coletadas. Tais informações são analisadas de modo a identificar impasses e condições de corrida em um processo denominado Análise Dinâmica. Ademais, estas informações também são utilizadas para geração automática de um modelo que descreve o comportamento do sistema de software, o qual é utilizado para verificação de propriedades comportamentais. A este processo de verificação dá-se o nome de Verificação Formal. A geração automática do modelo elimina a necessidade de construção manual do mesmo, que requer muito esforço e conhecimento acerca de métodos formais, isso pode aumentar custos e tempo de desenvolvimento do sistema de software. Entretanto, a análise dinâmica é conhecida por apenas realizar cobertura sobre o comportamento atual de sistemas de software concorrentes, sem considerar a análise de todas as outras possíveis sequências de execuções devido ao não determinismo. Em razão do comportamento não determinístico, sistemas de software concorrentes são capazes de produzir resultados diferentes para a mesma entrada a cada nova execução. Deste modo, reproduzir o comportamento que leva sistemas de software concorrente à falha é uma tarefa complexa. O presente trabalho propõe um método para realizar verificação formal e dinâmica de sistemas de software concorrente capaz de capturar o comportamento não determinístico desses sistemas, além de proporcionar a redução de custos de desenvolvimento através da eliminação da necessidade de construção manual de modelos de sistemas de software concorrente. O método é validado através de um estudo de caso composto por testes em três sistemas de software.

[pt] Atualmente, podemos observar uma clara tendência na direção de sistemas cada vez maiores e mais complexos quanto às suas partes e formas de interconexão. Num cenário como este, torna-se imperativa a preocupação com a modelagem da estrutura, organização geral e formas de interação presentes nesses sistemas, assim como com as garantias de que certos requisitos críticos sejam atendidos. O contexto de nosso trabalho engloba disciplinas de Engenharia de Software, como Arquitetura de Software e Técnicas de Modelagem, e disciplinas mais formais como Verificação de Modelos, Lógicas Modais e Álgebras de Processos. Nosso trabalho tem inspirações nestas disciplinas mas apresenta, de fato, um cunho metodológico, localizando-se nas fronteiras da ES com Métodos Formais, onde buscamos investigar e estabelecer uma forma sistemática para utilização efetiva de métodos formais logo nas etapas iniciais do desenvo lvimento. Mais especificamente, mostramos como é possível, a partir de modelos baseados em abstrações arquiteturais, obter-se sistematicamente um modelo formal sobre o qual possamos realizar certos tipos de análise comportamental. Nossa proposta inclui um sistema notacional básico para expressar modelos arquiteturais, junto com sua semântica formal, e um protótipo construído para dar suporte a tarefas de especificação e análise formal orientadas por abstrações arquiteturais. Com isto, pretendemos abordar alguns dos aspectos essenciais de uma metodologia de desenvolvimento que integre ferramentas e técnicas formais na etapa de modelagem arquitetural. / [en] There is a trend nowadays towards bigger and more complex systems concerning their parts and interconnectivity. In such scenario, modeling structure, overall organization and interaction have become a main concern, as well as fulfillment of mission critical requirements. The scope of our work encompasses Software Engineering related subjects such as Software Architecture, Modeling Techniques and more formal disciplines like Model Checking, Modal Logics and Process Algebra. Although inspired by such techniques, there is, indeed a methodological orientation in our work, traversing the boundaries of Software Engineering with Formal Methods, through which we seek to investigate and establish a systematic way for the effective utilization of formal methods in the first steps of software development. Still, more specifically, we show how it is possible, starting from models based on architectural abstractions, to systematically produce a formal model upon which we can execute certain forms of behavior analysis. Our proposal includes a basic notational system to express architectural models along with their formal semantics and a prototype built to support specification and formal analysis tasks oriented by architectural abstractions. With this, we intend to stress some essential aspects of a development methodology which aims to integrate tools and formal techniques to software modeling.

Cette thèse développe des techniques à base d'automates pour la vérification formelle de systèmes physiquement distribués communiquant via des canaux fiables de tailles non bornées. Chaque machine peut exécuter localement plusieurs programmes récursifs (multi-threading). Un programme récursif peut également utiliser pour ses calculs locaux des structures de données non bornées, comme des files ou des piles. Ces systèmes, utilisés en pratique, sont si puissants que tous leurs problèmes de vérification deviennent indécidables. Nous introduisons et étudions un nouveau paramètre, appelé largeur de coupe (split-width), pour l'analyse de ces systèmes. Cette largeur de coupe est définie comme le nombre minimum de scissions nécessaires pour partitioner le graphe d'une exécution en parties sur lesquelles on pourra raisonner de manière indépendante. L'analyse est ainsi réalisée avec une approche diviser pour régner. Lorsqu'on se restreint à la classe des comportements ayant une largeur de coupe bornée par une constante, on obtient des procédures de décision optimales pour divers problèmes de vérification sur ces systèmes tels que l'accessibilité, l'inclusion, etc. ainsi que pour la satisfaisabilité et le model checking par rapport à divers formalismes comme la logique monadique du second ordre, la logique dynamique propositionnelle et des logiques temporelles. On montre aussi que les comportements d'un système ont une largeur de coupe bornée si et seulement si ils ont une largeur de clique bornée. Ainsi, grâce aux résultats de Courcelle sur les graphes de degré uniformément borné, la largeur de coupe est non seulement suffisante, mais aussi nécessaire pour obtenir la décidabilité du problème de satisfaisabilité d'une formule de la logique monadique du second ordre. Nous étudions ensuite l'existence de contrôleurs distribués génériques pour nos systèmes distribués. Nous proposons plusieurs contrôleurs, certains ayant un nombre fini d'états et d'autres étant déterministes, qui assurent que les comportements du système sont des graphes ayant une largeur de coupe bornée. Un système ainsi contrôlé de manière distribuée hérite des procédures de décision optimales pour les différents problèmes de vérification lorsque la largeur de coupe est bornée. Cette classe décidable de système généralise plusieurs sous-classes décidables étudiées précédemment. / This thesis investigates automata-theoretic techniques for the verification of physically distributed machines communicating via unbounded reliable channels. Each of these machines may run several recursive programs (multi-threading). A recursive program may also use several unbounded stack and queue data-structures for its local-computation needs. Such real-world systems are so powerful that all verification problems become undecidable. We introduce and study a new parameter called split-width for the under-approximate analysis of such systems. Split-width is the minimum number of splits required in the behaviour graphs to obtain disjoint parts which can be reasoned about independently. Thus it provides a divide-and-conquer approach for their analysis. With the parameter split-width, we obtain optimal decision procedures for various verification problems on these systems like reachability, inclusion, etc. and also for satisfiability and model checking against various logical formalisms such as monadic second-order logic, propositional dynamic logic and temporal logics. It is shown that behaviours of a system have bounded split-width if and only if they have bounded clique-width. Thus, by Courcelle's results on uniformly bounded-degree graphs, split-width is not only sufficient but also necessary to get decidability for MSO satisfiability checking. We then study the feasibility of distributed controllers for our generic distributed systems. We propose several controllers, some finite state and some deterministic, which ensure that the behaviours of the system have bounded split-width. Such a distributedly controlled system yields decidability for the various verification problems by inheriting the optimal decision procedures for split-width. These also extend or complement many known decidable subclasses of systems studied previously.

This thesis investigates automata-theoretic techniques for the verification of physically distributed machines communicating via unbounded reliable channels. Each of these machines may run several recursive programs (multi-threading). A recursive program may also use several unbounded stack and queue data-structures for its local-computation needs. Such real-world systems are so powerful that all verification problems become undecidable. We introduce and study a new parameter called split-width for the under-approximate analysis of such systems. Split-width is the minimum number of splits required in the behaviour graphs to obtain disjoint parts which can be reasoned about independently. Thus it provides a divide-and-conquer approach for their analysis. With the parameter split-width, we obtain optimal decision procedures for various verification problems on these systems like reachability, inclusion, etc. and also for satisfiability and model checking against various logical formalisms such as monadic second-order logic, propositional dynamic logic and temporal logics. It is shown that behaviours of a system have bounded split-width if and only if they have bounded clique-width. Thus, by Courcelle's results on uniformly bounded-degree graphs, split-width is not only sufficient but also necessary to get decidability for MSO satisfiability checking. We then study the feasibility of distributed controllers for our generic distributed systems. We propose several controllers, some finite state and some deterministic, which ensure that the behaviours of the system have bounded split-width. Such a distributedly controlled system yields decidability for the various verification problems by inheriting the optimal decision procedures for split-width. These also extend or complement many known decidable subclasses of systems studied previously.