… erties of probabilistic systems, and we present veri cation and speci cation methods that
overcome … To complete our review of related work, we mention the use of formal methods for the …

… Our model for probabilistic systems is a Markov decision process (MDP). An MDP is a
generalization of a Markov chain in which a set of possible actions is associated with each state. …

… for probabilistic systems, and we provide algorithms that solve the verification problem for
various classes of probabilistic … of formal methods for the analysis and verification of systems re…

… that arise as model for distributed probabilistic systems. We present efficient methods for
solving these two classes of … Technical Report CSR-99-1, University of Birmingham, 1999. …

… To be able to relate the behavior of abstract and concrete systems, we equip the notion of
ab… probabilistic systems (abstract Markov chains) with respect to specifications in probabilistic …

… the probabilistic component of the behavior described the system’… for concurrent probabilistic
systems, probabilistic systems … ], and under-specified probabilistic systems [BdA95, dA97a]. …

… and distributed systems. Model checking is a push-button technique to check properties
about the behaviour of probabilistic systems. Given a property and a model of the system, model …

… can ask two kinds of verification questions: quantitative and … probability with which the
property holds in the system; qualitative questions ask whether the property holds with probability …

… in the specification of probabilistic properties is given… system and the structured English
grammar captures expert knowledge and helps practitioners to correctly apply formal verification …

… breaks down as soon as we consider both probabilistic systems and quantitative valuations.
Since discounting plays no role in the proof of the theorem, an analogous result holds also …