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Specification and verification of quantitative properties : expressions, logics, and automata / Spécification et vérification de propriétés quantitatives : expressions, logiques et automatesMonmege, Benjamin 24 October 2013 (has links)
La vérification automatique est aujourd'hui devenue un domaine central de recherche en informatique. Depuis plus de 25 ans, une riche théorie a été développée menant à de nombreux outils, à la fois académiques et industriels, permettant la vérification de propriétés booléennes - celles qui peuvent être soit vraies soit fausses. Les besoins actuels évoluent vers une analyse plus fine, c'est-à-dire plus quantitative. L'extension des techniques de vérification aux domaines quantitatifs a débuté depuis 15 ans avec les systèmes probabilistes. Cependant, de nombreuses autres propriétés quantitatives existent, telles que la durée de vie d'un équipement, la consommation énergétique d'une application, la fiabilité d'un programme, ou le nombre de résultats d'une requête dans une base de données. Exprimer ces propriétés requiert de nouveaux langages de spécification, ainsi que des algorithmes vérifiant ces propriétés sur une structure donnée. Cette thèse a pour objectif l'étude de plusieurs formalismes permettant de spécifier de telles propriétés, qu'ils soient dénotationnels - expressions régulières, logiques monadiques ou logiques temporelles - ou davantage opérationnels, comme des automates pondérés, éventuellement étendus avec des jetons. Un premier objectif de ce manuscript est l'étude de résultats d'expressivité comparant ces formalismes. En particulier, on donne des traductions efficaces des formalismes dénotationnels vers celui opérationnel. Ces objets, ainsi que les résultats associés, sont présentés dans un cadre unifié de structures de graphes. Ils peuvent, entre autres, s'appliquer aux mots et arbres finis, aux mots emboîtés (nested words), aux images ou aux traces de Mazurkiewicz. Par conséquent, la vérification de propriétés quantitatives de traces de programmes (potentiellement récursifs, ou concurrents), les requêtes sur des documents XML (modélisant par exemple des bases de données), ou le traitement des langues naturelles sont des applications possibles. On s'intéresse ensuite aux questions algorithmiques que soulèvent naturellement ces résultats, tels que l'évaluation, la satisfaction et le model checking. En particulier, on étudie la décidabilité et la complexité de certains de ces problèmes, en fonction du semi-anneau sous-jacent et des structures considérées (mots, arbres...). Finalement, on considère des restrictions intéressantes des formalismes précédents. Certaines permettent d'étendre l'ensemble des semi-anneau sur lesquels on peut spécifier des propriétés quantitatives. Une autre est dédiée à l'étude du cas spécial de spécifications probabilistes : on étudie en particulier des fragments syntaxiques de nos formalismes génériques de spécification générant uniquement des comportements probabilistes. / Automatic verification has nowadays become a central domain of investigation in computer science. Over 25 years, a rich theory has been developed leading to numerous tools, both in academics and industry, allowing the verification of Boolean properties - those that can be either true or false. Current needs evolve to a finer analysis, a more quantitative one. Extension of verification techniques to quantitative domains has begun 15 years ago with probabilistic systems. However, many other quantitative properties are of interest, such as the lifespan of an equipment, energy consumption of an application, the reliability of a program, or the number of results matching a database query. Expressing these properties requires new specification languages, as well as algorithms checking these properties over a given structure. This thesis aims at investigating several formalisms, equipped with weights, able to specify such properties: denotational ones - like regular expressions, first-order logic with transitive closure, or temporal logics - or more operational ones, like navigating automata, possibly extended with pebbles. A first objective of this thesis is to study expressiveness results comparing these formalisms. In particular, we give efficient translations from denotational formalisms to the operational one. These objects, and the associated results, are presented in a unified framework of graph structures. This permits to handle finite words and trees, nested words, pictures or Mazurkiewicz traces, as special cases. Therefore, possible applications are the verification of quantitative properties of traces of programs (possibly recursive, or concurrent), querying of XML documents (modeling databases for example), or natural language processing. Second, we tackle some of the algorithmic questions that naturally arise in this context, like evaluation, satisfiability and model checking. In particular, we study some decidability and complexity results of these problems depending on the underlying semiring and the structures under consideration (words, trees...). Finally, we consider some interesting restrictions of the previous formalisms. Some permit to extend the class of semirings on which we may specify quantitative properties. Another is dedicated to the special case of probabilistic specifications: in particular, we study syntactic fragments of our generic specification formalisms generating only probabilistic behaviors.
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Specification and verification of quantitative properties : expressions, logics, and automataMonmège, Benjamin 24 October 2013 (has links) (PDF)
Automatic verification has nowadays become a central domain of investigation in computer science. Over 25 years, a rich theory has been developed leading to numerous tools, both in academics and industry, allowing the verification of Boolean properties - those that can be either true or false. Current needs evolve to a finer analysis, a more quantitative one. Extension of verification techniques to quantitative domains has begun 15 years ago with probabilistic systems. However, many other quantitative properties are of interest, such as the lifespan of an equipment, energy consumption of an application, the reliability of a program, or the number of results matching a database query. Expressing these properties requires new specification languages, as well as algorithms checking these properties over a given structure. This thesis aims at investigating several formalisms, equipped with weights, able to specify such properties: denotational ones - like regular expressions, first-order logic with transitive closure, or temporal logics - or more operational ones, like navigating automata, possibly extended with pebbles. A first objective of this thesis is to study expressiveness results comparing these formalisms. In particular, we give efficient translations from denotational formalisms to the operational one. These objects, and the associated results, are presented in a unified framework of graph structures. This permits to handle finite words and trees, nested words, pictures or Mazurkiewicz traces, as special cases. Therefore, possible applications are the verification of quantitative properties of traces of programs (possibly recursive, or concurrent), querying of XML documents (modeling databases for example), or natural language processing. Second, we tackle some of the algorithmic questions that naturally arise in this context, like evaluation, satisfiability and model checking. In particular, we study some decidability and complexity results of these problems depending on the underlying semiring and the structures under consideration (words, trees...). Finally, we consider some interesting restrictions of the previous formalisms. Some permit to extend the class of semirings on which we may specify quantitative properties. Another is dedicated to the special case of probabilistic specifications: in particular, we study syntactic fragments of our generic specification formalisms generating only probabilistic behaviors.
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