When an Ornstein-Uhlenbeck (or CAR(1)) process is observed at discrete times 0, h, 2h,··· [T/h]h, the unobserved driving process can be approximated from the ob- served process. Approximated increments of the driving process are used to test the assumption that the process is L\'evy-driven. Asymptotic behavior of the test statis- tic at high sampling frequencies is developed assuming that the model parameters are known. The behavior of the test statistics using an estimated parameter is also studied. If it can be concluded that the driving process is L\'evy, the empirical process of the approximated increments can then be used to carry out more precise tests of goodness-of-fit. For example, one can test whether the driving process can be modeled as a Brownian motion or a gamma process. In each case, performance of the proposed test is illustrated through simulation.

This thesis presents our method to integrate formal methods with model-driven engineering. Although a large amount of literature exists with the goal of facilitating the adoption of formal methods for educational and industrial practice, yet the adoption of formal methods in academia and industry is poor. The goal of this research is to improve the adoption of formal methods by automating the generation of formal methods code while maintaining scalability and bridging the gaps between formal analysis and actual implementation of the complete system. Our approach is based on generating formal representations of software abstractions expressed in a textual language, called Umple, which is derived from UML. Software abstractions of interest include class models and state machines. For state machines, we address concerns such as composite and concurrent states separately. The resulting systems are analyzable by back-end analysis engines such as Alloy and nuXmv or NuSMV for model checking. To ensure correctness of our approach, we have adopted simulation, empirical studies and rigorous test-driven development (TDD) methodologies. To guarantee correctness of state machine systems under analysis (SSUAs), we present methods to automatically generate specifications to analyze domain-independent properties such as non-determinism and reachability analysis. We apply these methods in various case studies; certify their conformance with sets of requirements and uncover certain flaws. Our contributions include a) The overall approach, involving having the developer write the system in Umple and generating both the formal system for analysis and the final code from the same model; b) a novel approach to encode SSUAs even in the presence of and-cross transitions; c) a fully automated approach to certify an SSUA to be free from nondeterminism even in the presence of unbounded domains and multiple and-cross transitions within the same enclosing orthogonal state; d) an empirical study of the impact of abstraction on some performance parameters; and e) a translator from Umple to Alloy and SMV.

Les systèmes à canaux non fiables ont été introduits à l'origine comme un modèle de communication. Ils ont donné naissance à une classe de complexité restée mal comprise pendant longtemps. Dans cette thèse, nous étudions et comblons certaines des plus importantes lacunes dans la connaissance de cette classe. Nous fournissons entre autres des bornes inférieure et supérieure qui se rejoignent pour la complexité en temps. Puis nous proposons un nouvel outil de preuve : le Problème de Sous Mot de Post (PEP). C'est un problème simple, inspiré du Problème de Correspondance de Post, et complet pour cette classe de complexité. Nous étudions ensuite PEP et ses variantes, ainsi que les langages de solutions de PEP sur lesquels nous avons fourni des résultats de complexité et des outils de preuve tels que des lemmes de pompage. / Lossy channel systems were originally introduced to model communication protocols. It gave birth to a complexity class wich remained scarcely undersood for a long time. In this thesis we study some of the most important gaps. In particular, we bring matching upper and lower bounds for the time complexity. Then we describe a new proof tool : the Post Embedding Problem (PEP) which is a simple problem, closely related to the Post Correspondence Problem, and complete for this complexity class. Finally, we study PEP, its variants and the languages of solutions of PEP on which we provide complexity results and proof tools like pumping lemmas.

Concurrent software executes multiple threads or processes to achieve high performance. However, concurrency results in a huge number of different system behaviors that are difficult to test and verify. The aim of this dissertation is to develop new methods and tools for modeling and analyzing concurrent software systems at design and code levels. This dissertation consists of several related results. First, a formal model of Mondex, an electronic purse system, is built using Petri nets from user requirements, which is formally verified using model checking. Second, Petri nets models are automatically mined from the event traces generated from scientific workflows. Third, partial order models are automatically extracted from some instrumented concurrent program execution, and potential atomicity violation bugs are automatically verified based on the partial order models using model checking. Our formal specification and verification of Mondex have contributed to the world wide effort in developing a verified software repository. Our method to mine Petri net models automatically from provenance offers a new approach to build scientific workflows. Our dynamic prediction tool, named McPatom, can predict several known bugs in real world systems including one that evades several other existing tools. McPatom is efficient and scalable as it takes advantage of the nature of atomicity violations and considers only a pair of threads and accesses to a single shared variable at one time. However, predictive tools need to consider the tradeoffs between precision and coverage. Based on McPatom, this dissertation presents two methods for improving the coverage and precision of atomicity violation predictions: 1) a post-prediction analysis method to increase coverage while ensuring precision; 2) a follow-up replaying method to further increase coverage. Both methods are implemented in a completely automatic tool.

Uma importante etapa do desenvolvimento de software é o de levantamento e análise dos requisitos. Porém, durante esta etapa podem ocorrer inconsistências que prejudicarão o andamento do projeto. Além disso, após finalizada a especificação, o cliente pode querer acrescentar ou modificar as funcionalidades do sistema. Tudo isso requer que a especificação do software seja revista, mas isso é altamente custoso, tornando necessário um processo automatizado para simplificar tal revisão. Para lidar com este problema, uma das abordagens utilizadas tem sido o processo de Revisão de Crenças, juntamente com o processo de Verificação de Modelos. O objetivo deste trabalho é utilizar o processo de revisão de crenças e verificação de modelos para avaliar especificações de um projeto procurando inconsistências, utilizando o fragmento universal da Computation Tree Logic (CTL), conhecido como ACTL, e revisá-las gerando sugestões de mudanças na especificação. A nossa proposta é traduzir para lógica clássica tanto o modelo (especificação do software) quanto a propriedade a ser revisada, e então aplicar um resolvedor SAT para verificar a satisfazibilidade da fórmula gerada. A partir da resposta do resolvedor SAT, iremos gerar sugestões válidas de mudanças para a especificação, fazendo o processo de tradução reversa da lógica clássica para o modelo original. / The objective of this work is to join the proccess of belief revision and model checking to evaluate project specifications looking for inconsistences, using the universal fragment of Computation Tree Logic (CTL), known as ACTL, and revise them generating changes suggestions in the specification. Our approach will translate the model (software specification) and the property to be revised to classical logic. Then we will apply a SAT solver to verify the generated formulas satsifability. From the SAT solver answer, we will create changes valid suggestions to the specification making the translation back from classical logic to the original model. To generate the changes suggestions, we proposed a framework based on heuristics where different approaches and decisions can be implemented, aiming a better application for each project scope. We implemented a basic heuristic as an example and used it to test the implementation to analise the proposed algorithm

Neste trabalho apresentamos uma implementação de revisão de crenças baseada em comparação de modelos (estados) em uma ferramenta de verificação automática de sistemas de estados finitos. Dada uma fórmula (na lógica CTL) inconsistente com o modelo do sistema, revisamos esse modelo de tal maneira que essa fórmula temporal se torne verdadeira. Como temos oito operadores temporais (AG, AF, AX, AU, EG, EF, EX e EU), foram criados algoritmos especícos para cada um deles. Como o modelo do sistema deriva do seu código na linguagem SMV, a sua revisão passa obrigatoriamente por mudanças na sua descrição. A nossa implementação contempla três tipos de mudanças: acréscimo de linhas, eliminação de linhas e mudança no estado inicial, sendo que as duas primeiras provocam modicações nas transições entre os estados que compõe o modelo. Alguns testes foram aplicados para comprovar a contribuição da revisão de crenças (revisão de modelos) como ferramenta de auxílio ao usuário durante o processo de modelagem de sistemas. / In this work we present an implementation of belief revision based on comparison of models (states) in a tool for automatic verication of nite state systems. Given a formula (in the language of CTL) inconsistent with the model of the system, we revise this model in such way that the temporal formula becomes valid. As we have eight temporal operators (AG, AF, AX, AU, EG, EF, EX and EU), specic algorithms for each one of them have been created. As the model of the system is related with its code in SMV language, its revision forces changes in its description. Our implementation contemplates three types of change: addition of lines, elimination of lines and change in the initial state, where the rst two cause modications in the transitions between the states of the model. Some tests were applied to prove the contribution of the belief revision (model revision) as aid-tool to the user during the process of systems modeling.

Verificação de modelos é uma das mais eficientes técnicas de verificação automática de sistemas. No entanto, apesar de poder lidar com verificações complexas, as ferramentas de verificação de modelos usualmente não fornecem informação alguma sobre como reparar inconsistências nestes modelos. Nesta dissertação, mostramos que abordagens desenvolvidas para a atualização de modelos CTL inconsistentes não são capazes de lidar com todos os tipos de alterações em modelos. Introduzimos então o conceito de revisão de modelos: uma abordagem baseada em revisão de crenças para o reparo de modelos inconsistentes em um contexto estático. Relacionamos nossa proposta com trabalhos clássicos em revisão de crenças. Definimos um operador de revisão de modelos e mostramos que este obedece postulados de racionalidade clássico de revisão de crenças. Propomos um algoritmo de revisão com base no algoritmo utilizado pela abordagem de atualização de modelos. Discutimos sobre problemas e limites do algoritmo proposto, e mostramos que essa estratégia de adaptação não é uma solução apropriada. / Model checking is one of the most robust techniques in automated system verification. But, although this technique can handle complex verifications, model checking tools usually do not give any information on how to repair inconsistent system models. In this dissertation, we show that approaches developed for CTL model update cannot deal with all kinds of model changes. We introduce the concept of CTL model revision: an approach based on belief revision to handle system inconsistency in a static context. We relate our proposal to classical works on belief revision. We define an operator for model revision and we show that it obeys the classical rationality postulates of belief revision. We propose an algorithm for model revision based on the algorithm used by the model update approach. We discuss problems and limitations of our proposed algorithm and show that this strategy of adaptation is not an appropriate solution.

Cette thèse s'attaque au problème de détection de malware en utilisant des techniques de model-checking: les automates à pile sont utilisés pour modéliser les programmes binaires, et la logique CARET (et ses variantes) sont utilisées pour représenter les comportements malicieux. La détection de malware est alors réduite au problème de model-checking des automates à pile par rapport à ces logiques CARET. Cette thèse propose alors différents algorithmes de model-checking des automates à pile par rapport à ces logiques CARET et montre comment ceci peut s'appliquer pour la détection de malware. / The number of malware is growing significantly fast. Traditional malware detectors based on signature matching or code emulation are easy to get around. To overcome this problem, model-checking emerges as a technique that has been extensively applied for malware detection recently. Pushdown systems were proposed as a natural model for programs, since they allow to keep track of the stack, while extensions of LTL and CTL were considered for malicious behavior specification. However, LTL and CTL like formulas don't allow to express behaviors with matching calls and returns. In this thesis, we propose to use CARET (a temporal logic of calls and returns) for malicious behavior specification. CARET model checking for Pushdown Systems (PDSs) was never considered in the literature. Previous works only dealt with the model checking problem for Recursive State Machine (RSMs). While RSMs are a good formalism to model sequential programs written in structured programming languages like C or Java, they become non suitable for modeling binary or assembly programs, since, in these programs, explicit push and pop of the stack can occur. Thus, it is very important to have a CARET model checking algorithm for PDSs. We tackle this problem in this thesis. We reduce it to the emptiness problem of Büchi Pushdown Systems. Since CARET formulas for malicious behaviors are huge, we propose to extend CARET with variables, quantifiers and predicates over the stack. This allows to write compact formulas for malicious behaviors. Our new logic is called Stack linear temporal Predicate logic of CAlls and RETurns (SPCARET). We reduce the malware detection problem to the model checking problem of PDSs against SPCARET formulas, and we propose efficient algorithms to model check SPCARET formulas for PDSs. We implemented our algorithms in a tool for malware detection. We obtained encouraging results. We then define the Branching temporal logic of CAlls and RETurns (BCARET) that allows to write branching temporal formulas while taking into account the matching between calls and returns and we proposed model-checking algorithms of PDSs for BCARET formulas. Finally, we consider Dynamic Pushdown Networks (DPNs) as a natural model for multithreaded programs with (recursive) procedure calls and thread creation. We show that the model-checking problem of DPNs against CARET formulas is decidable.

Since the mid-1990s, formal verification has become increasingly important because it can provide guarantees that a software system is free of bugs and working correctly based on a provided model. Verification of biological and medical systems is a promising application of formal verification. Human neural networks have recently been emulated and studied as a biological system. Some recent research has been done on modelling some crucial neuronal circuits and using model checking techniques to verify their temporal properties. In large case studies, model checkers often cannot prove the given property at the desired level of generality. In this thesis, we provide a model using the Coq proof assistant and prove some properties concerning the dynamic behavior of some basic neuronal structures. Understanding the behavior of these modules is crucial because they constitute the elementary building blocks of bigger neuronal circuits. By using a proof assistant, we guarantee that the properties are true in the general case, that is, true for any input values, any length of input, and any amount of time. In this thesis, we define a model of human neural networks. We verify some properties of this model starting with properties of neurons. Neurons are the smallest unit in a human neuronal network. In the next step, we prove properties about functional structures of human neural networks which are called archetypes. Archetypes consist of two or more neurons connected in a suitable way. They are known for displaying some particular classes of behaviours, and their compositions govern several important functions such as walking, breathing, etc. The next step is verifying properties about structures that couple different archetypes to perform more complicated actions. We prove a property about one of these kinds of compositions. With such a model, there is the potential to detect inactive regions of the human brain and to treat mental disorders. Furthermore, our approach can be generalized to the verification of other kinds of networks, such as regulatory, metabolic, or environmental networks.

Mnoho aplikací přijímá, odesílá a zpracovává data v textové podobě. Správné a bezpečné zpracování těchto dat je typicky zajištěno tzv. ošetřením řetězců (string sanitization). Pomocí metod formální verifikace je možné analyzovat takovéto operace s řetězci a prověřit, zda jsou správně navržené či implementované.  Naším cílem je vytvořit obecný nástroj pro analýzu systémů jejichž konfigurace lze kódovat pomocí slov z vhodné abecedy, a také jeho specializaci pro analýzu programů pracujících s řetězci. Nejprve jsou popsaný konečné automaty a převodníky a poté různé třídy a podtřídy symbolických převodníků, zejména pak jejich omezení. Na základě těchto informací je pak pro použití v analýze programů navržen nový typ symbolických převodníků. Dále je popsán regulární model checking, speciálně pak jeho variantu založenou na abstrakci automatů, tzv. ARMC, u kterého je známo že dokáže velmi úspěšně překonat problém stavové exploze u automatů a umožňuje nám tzv. dosáhnout pevného bodu v analýze. Poté je navržena vlastní analýza programů psaných v imperativním paradigmatu, a to zejména programů manipulujících s řetězci, založená na principech ARMC. Následuje popis vlastní implementace nástroje s důrazem na jeho praktické vlastnosti. Rovněž jsou popsaný důležité části knihovny AutomataDotNet, na které nástroj staví. Práci je uzavřena diskuzí experimentů s nástrojem provedených na příkladech z knihovny LibStranger.