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In this thesis, we study two fundamental problems that arise in the modeling of stochastic systems: (i) Validation of stochastic models against behavioral specifications such as temporal logics, and (ii) Discovery of kinetic parameters of stochastic biochemical models from behavioral specifications. We present a new Bayesian algorithm for Statistical Model Checking of stochastic systems based on a sequential version of Jeffreys’ Bayes Factor test. We argue that the Bayesian approach is more suited for application do- mains like systems biology modeling, where distributions on nuisance parameters and priors may be known. We prove that our Bayesian Statistical Model Checking algorithm terminates for a large subclass of prior probabilities. We also characterize the Type I/II errors associated with our algorithm. We experimentally demonstrate that this algorithm is suitable for the analysis of complex biochemical models like those written in the BioNetGen language. We then argue that i.i.d. sampling based Statistical Model Checking algorithms are not an effective way to study rare behaviors of stochastic models and present another Bayesian Statistical Model Checking algorithm that can incorporate non-i.i.d. sampling strategies. We also present algorithms for synthesis of chemical kinetic parameters of stochastic biochemical models from high level behavioral specifications. We consider the setting where a modeler knows facts that must hold on the stochastic model but is not confident about some of the kinetic parameters in her model. We suggest algorithms for discovering these kinetic parameters from facts stated in appropriate formal probabilistic specification languages. Our algorithms are based on our theoretical results characterizing the probability of a specification being true on a stochastic biochemical model. We have applied this algorithm to discover kinetic parameters for biochemical models with as many as six unknown parameters.

Il s'agit d'une étude menée sur les systèmes cyber-physiques sur trois aspects principaux: la vérification de la stabilité, l'ordonnancement et la synthèse des paramètres. Les systèmes de contrôle embarqués (ECS) agissant dans le cadre de contrats temporels sont la classe considérée de systèmes cyber-physiques dans la thèse. ECS fait référence à des intégrations d'un dispositif informatique avec le système physique. En ce qui concerne les contrats temporels, ils sont des contraintes de temps sur les instants où se produisent certains événements tels que l'échantillonnage, l'actionnement et le calcul. Ces contrats sont utilisés pour modéliser les problèmes qui se posent dans les systèmes de contrôle modernes: incertitudes sur les retards d'actionnement, les périodes d'échantillonnage incertaines et l'interaction de plusieurs systèmes physiques avec des ressources informatiques partagées (CPUs). Maintenant, compte tenu d'un ECS et d'un contrat temporel, nous reformulons le système de manière impulsionnelle et vérifions la stabilité du système, sous toutes les incertitudes bornées et données par le contrat, en utilisant des techniques d'approximation convexe et de nouveaux résultats généralisés pour le problème sur une classe de systèmes modélisés dans le cadre des inclusions différentielles. Deuxièmement, compte tenu d'un ensemble de contrôleurs implémentés sur une plate-forme de calcul commune (CPUs), dont chacun est soumis à un contrat de synchronisation, et à son meilleur et son plus mauvais cas d'exécution dans chaque CPU, nous synthétisons une politique d’ordonnancement dynamique qui garantit que chaque contrat temporel est satisfait et que chacun des CPU partagés est attribué à au plus un contrôleur à tout moment. L'approche est basée sur une reformulation qui nous permet d'écrire le problème d’ordonnancement comme un jeu temporelle avec spécification de sureté. Ensuite, en utilisant l'outil UPPAAL-TIGA, une solution au jeu fournit une politique d’ordonnancement appropriée. En outre, nous fournissons une nouvelle condition nécessaire et suffisante pour l’ordonnancement des tâches de contrôle en fonction d’un jeu temporisé simplifiés. Enfin, nous résolvons un problème de synthèse de paramètres qui consiste à synthétiser une sous-approximation de l'ensemble des contrats de synchronisation qui garantissent en même temps l’ordonnancement et la stabilité des contrôleurs intégrés. La synthèse est basée sur un nouveau paramétrage du contrat temporel pour les rendre monotones, puis sur un échantillonnage à plusieurs reprises de l'espace des paramètres jusqu'à atteindre une précision d'approximation prédéfinie. / This is a study conducted on cyber-physical systems on three main aspects: stability verification, scheduling, and parameter synthesis. Embedded control systems (ECS) acting under timing contracts are the considered class of cyber-physical systems in the thesis. ECS refers to integrations of a computing device with the physical system. As for timing contracts they are time constraints on the instants where some events happen such as sampling, actuation, and computation. These contracts are used to model issues that arise in modern embedded control systems: uncertain sampling to actuation delays, uncertain sampling periods, and interaction of several physical systems with shared computational resources (CPUs). Now given an ECS and a timing contract we reformulate the system into an impulsive one and verifies stability of the system, under all possible bounded uncertainties given by the contract, using safe convex approximation techniques and new generalized results for the problem on a class of systems modeled in the framework of difference inclusions. Second given a set of controllers implemented on a common computational platform (CPUs), each of which is subject to a timing contract, and best and worst case execution times on each CPU, we synthesize a dynamic scheduling policy, which guarantees that each timing contract is satisfied and that each of the shared CPUs are allocated to at most one embedded controller at any time. The approach is based on a timed game formulation that allows us to write the scheduling problem as a timed safety game. Then using the tool UPPAAL-TIGA, a solution to the safety game provides a suitable scheduling policy. In addition, we provide a novel necessary and sufficient condition for schedulability of the control tasks based on a simplified timed game automaton. Last, we solve a parameter synthesis problem which consists of synthesizing an under-approximation of the set of timing contracts that guarantee at the same time the schedulability and stability of the embedded controllers. The synthesis is based on a re-parameterization of the timing contract to make them monotonic, and then on a repeatedly sampling of the parameter space until reaching a predefined precision of approximation.

DNA nanotechnology is a rapidly developing field that creates nanoscale devices from DNA, which enables novel interfaces with biological material. Their therapeutic use is envisioned and applications in other areas of basic science have already been found. These devices function at physiological conditions and, owing to their molecular scale, are subject to thermal fluctuations during both preparation and operation of the device. Troubleshooting a failed device is often difficult and we develop models to characterise two separate devices: DNA walkers and DNA origami. Our framework is that of continuous-time Markov chains, abstracting away much of the underlying physics. The resulting models are coarse but enable analysis of system-level performance, such as ‘the molecular computation eventually returns the correct answer with high probability’. We examine the applicability of probabilistic model checking to provide guarantees on the behaviour of nanoscale devices, and to this end we develop novel model checking methodology. We model a DNA walker that autonomously navigates a series of junctions, and we derive design principles that increase the probability of correct computational output. We also develop a novel parameter synthesis method for continuous-time Markov chains, for which the synthesised models guarantee a predetermined level of performance. Finally, we develop a novel discrete stochastic assembly model of DNA origami from first principles. DNA origami is a widespread method for creating nanoscale structures from DNA. Our model qualitatively reproduces experimentally observed behaviour and using the model we are able to rationally steer the folding pathway of a novel polymorphic DNA origami tile, controlling the eventual shape.