University, Diss., 2003--Saarbrücken.

Probabilistic model checking is a powerful formal verification method that can ensure the correctness of real-life systems that exhibit stochastic behaviour. The work presented in this thesis aims to solve the scalability challenge of probabilistic model checking, by developing, for the first time, fully-automated compositional verification techniques for probabilistic systems. The contributions are novel approaches for automatically learning probabilistic assumptions for three different compositional verification frameworks. The first framework considers systems that are modelled as Segala probabilistic automata, with assumptions captured by probabilistic safety properties. A fully-automated approach is developed to learn assumptions for various assume-guarantee rules, including an asymmetric rule Asym for two-component systems, an asymmetric rule Asym-N for n-component systems, and a circular rule Circ. This approach uses the L* and NL* algorithms for automata learning. The second framework considers systems where the components are modelled as probabilistic I/O systems (PIOSs), with assumptions represented by Rabin probabilistic automata (RPAs). A new (complete) assume-guarantee rule Asym-Pios is proposed for this framework. In order to develop a fully-automated approach for learning assumptions and performing compositional verification based on the rule Asym-Pios, a (semi-)algorithm to check language inclusion of RPAs and an L*-style learning method for RPAs are also proposed. The third framework considers the compositional verification of discrete-time Markov chains (DTMCs) encoded in Boolean formulae, with assumptions represented as Interval DTMCs (IDTMCs). A new parallel operator for composing an IDTMC and a DTMC is defined, and a new (complete) assume-guarantee rule Asym-Idtmc that uses this operator is proposed. A fully-automated approach is formulated to learn assumptions for rule Asym-Idtmc, using the CDNF learning algorithm and a new symbolic reachability analysis algorithm for IDTMCs. All approaches proposed in this thesis have been implemented as prototype tools and applied to a range of benchmark case studies. Experimental results show that these approaches are helpful for automating the compositional verification of probabilistic systems through learning small assumptions, but may suffer from high computational complexity or even undecidability. The techniques developed in this thesis can assist in developing scalable verification frameworks for probabilistic models.

Feature-oriented software architecture is a way of organizing code around the features that the program provides instead of the program's objects and components. In the development of a feature-oriented software system, the developers, supplied with a set of features, select and organize features to construct the desired system. This approach, by better aligning the implementation of a system with the external view of users, is believed to have many potential benefits such as feature reuse and easy maintenance. However, there are challenges in the formal verification of feature-oriented systems: first, the product may grow very large and complicated. As a result, it's intractable to apply the traditional formal verification techniques such as model checking on such systems directly; second, since the number of feature-oriented products the developers can build is exponential in the number of features available, there may be redundant verification work if doing verification on each product. For example, developers may have shared specifications on different products built from the same set of features and hence doing verification on these features many times is really unnecessary. All these drive the need for modular verifications for feature-oriented architectures. Assume-guarantee reasoning as a modular verification technique is believed to be an effective solution. In this thesis, I compare two verification methods of this category on feature-oriented systems and analyze the results. Based on their pros and cons, I propose a new modular model checking method to accomplish verification for sequential feature compositions with cyclic connections between the features. This method first builds an abstract finite state machine, which summarizes the information related to checking the property/specification from the concrete feature design, and then applies a revised CTL model checker to decide whether the system design can preserve the property or not. Proofs of the soundness of my method are also given in this thesis.