This thesis describes a system that synthesizes regularity exposing attributes from large protein databases. After processing primary and secondary structure data, this system discovers an amino acid representation that captures what are thought to be the three most important amino acid characteristics (size, charge, and hydrophobicity) for tertiary structure prediction. A neural network trained using this 16 bit representation achieves a performance accuracy on the secondary structure prediction problem that is comparable to the one achieved by a neural network trained using the standard 24 bit amino acid representation. In addition, the thesis describes bounds on secondary structure prediction accuracy, derived using an optimal learning algorithm and the probably approximately correct (PAC) model.

A major current challenge consists in extending formal methods in order to handle infinite-state systems. Infiniteness stems from the fact that the system operates on unbounded data structure such as stacks, queues, clocks, integers; as well as parameterization. Systems with unbounded data structure are natural models for reasoning about communication protocols, concurrent programs, real-time systems, etc. While parameterized systems are more suitable if the system consists of an arbitrary number of identical processes which is the case for cache coherence protocols, distributed algorithms and so forth. In this thesis, we consider model checking problems for certain fundamental classes of probabilistic infinite-state systems, as well as the verification of safety properties in parameterized systems. First, we consider probabilistic systems with unbounded data structures. In particular, we study probabilistic extensions of Lossy Channel Systems (PLCS), Vector addition Systems with States (PVASS) and Noisy Turing Machine (PNTM). We show how we can describe the semantics of such models by infinite-state Markov chains; and then define certain abstract properties, which allow model checking several qualitative and quantitative problems. Then, we consider parameterized systems and provide a method which allows checking safety for several classes that differ in the topologies (linear or tree) and the semantics (atomic or non-atomic). The method is based on deriving an over-approximation which allows the use of a symbolic backward reachability scheme. For each class, the over-approximation we define guarantees monotonicity of the induced approximate transition system with respect to an appropriate order. This property is convenient in the sense that it preserves upward closedness when computing sets of predecessors.

This doctoral thesis considers the automatic verification of parameterized systems, i.e. systems with an arbitrary number of communicating components, such as mutual exclusion protocols, cache coherence protocols or heap manipulating programs. The components may be organized in various topologies such as words, multisets, rings, or trees. The task is to show correctness regardless of the size of the system and we consider two methods to prove safety:(i) a backward reachability analysis, using the well-quasi ordered framework and monotonic abstraction, and (ii) a forward analysis which only needs to inspect a small number of components in order to show correctness of the whole system. The latter relies on an abstraction function that views the system from the perspective of a fixed number of components. The abstraction is used during the verification procedure in order to dynamically detect cut-off points beyond which the search of the state-space need not continue. Our experimentation on a variety of benchmarks demonstrate that the method is highly efficient and that it works well even for classes of systems with undecidable property. It has been, for example, successfully applied to verify a fine-grained model of Szymanski's mutual exclusion protocol. Finally, we applied the methods to solve the complex problem of verifying highly concurrent data-structures, in a challenging setting: We do not a priori bound the number of threads, the size of the data-structure, the domain of the data to store nor do we require the presence of a garbage collector. We successfully verified the concurrent Treiber's stack and Michael & Scott's queue, in the aforementioned setting. To the best of our knowledge, these verification problems have been considered challenging in the parameterized verification community and could not be carried out automatically by other existing methods.

<p>A major current challenge consists in extending formal methods in order to handle infinite-state systems. Infiniteness stems from the fact that the system operates on unbounded data structure such as stacks, queues, clocks, integers; as well as parameterization.</p><p>Systems with unbounded data structure are natural models for reasoning about communication protocols, concurrent programs, real-time systems, etc. While parameterized systems are more suitable if the system consists of an arbitrary number of identical processes which is the case for cache coherence protocols, distributed algorithms and so forth. </p><p>In this thesis, we consider model checking problems for certain fundamental classes of probabilistic infinite-state systems, as well as the verification of safety properties in parameterized systems. First, we consider probabilistic systems with unbounded data structures. In particular, we study probabilistic extensions of Lossy Channel Systems (PLCS), Vector addition Systems with States (PVASS) and Noisy Turing Machine (PNTM). We show how we can describe the semantics of such models by infinite-state Markov chains; and then define certain abstract properties, which allow model checking several qualitative and quantitative problems.</p><p>Then, we consider parameterized systems and provide a method which allows checking safety for several classes that differ in the topologies (linear or tree) and the semantics (atomic or non-atomic). The method is based on deriving an over-approximation which allows the use of a symbolic backward reachability scheme. For each class, the over-approximation we define guarantees monotonicity of the induced approximate transition system with respect to an appropriate order. This property is convenient in the sense that it preserves upward closedness when computing sets of predecessors.</p>