Verification of randomized distributed algorithms
Lectures on formal methods and performance analysis
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
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This dissertation presents methods for the formal modeling and specification of probabilistic systems, and algorithms for the automated verification of these systems. Our system models describe the behavior of a system in terms of probability, nondeterminism, fairness and time. The formal specification languages we consider are based on extensions of branching-time temporal logics, and enable the expression of single-event and long-run average system properties. This latter class of properties, not expressible with previous formal languages, includes most of the performance properties studied in the field of performance evaluation, such as system throughput and average response time. Our choice of system models and specification languages has been guided by the goal of providing efficient verification algorithms. The algorithms rely on the theory of Markov decision processes, and exploit a connection between the graph-theoretical and probabilistic properties of these processes. This connection also leads to new results about classical problems, such as an extension to the solvable cases of the stochastic shortest path problem, an improved algorithm for the computation of reachability probabilities, and new results on the average reward problem for semi-Markov decision processes.