We are interested in developing computational tools for reducing the state space of irreducible Markov chains. As means of decreasing the dimensionality of a given Markov chain we study the concept of aggregation. The approximation error between the original and the reduced order model is captured by a metric that penalizes the asymptotic deviation of the outputs of the two systems. For the cas...

Quantum Markov chains are an extension of classical Markov chains which are labelled with super-operators rather than probabilities. They allow to faithfully represent quantum programs and quantum protocols. In this paper, we investigate model checking ω-regular properties, a very general class of properties (including, e.g., LTL properties) of interest, against this model. For classical Markov...

In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstra...

Internet browsers generate “click stream” data that supply information about the path taken through a web site. Click stream data have an interesting temporal structure in which sequences of individual page requests are nested within browsing sessions, and some users return to the web site for multiple sessions. We model sequences of page requests within a session using a hidden Markov mixture ...

The concurrent composition of Markov chains quickly leads to the notorious problem of state space explosion, also known as the largeness problem, as the number of involved Markov chains increases. In the context of Markovian Process Algebras (MPAs) this problem is of particular interest, since small and compact model descriptions in form of language terms provided by the MPA may possess huge un...

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We...

We investigate the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie. We consider two semantic interpretations for the uncertainty in the transi...

Abstract Let G be a finite group. $H, K$ subgroups of and $H \backslash / the double coset space. If Q is probability on which constant conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then random walk driven by projects to Markov chain /K$ . This allows analysis lumped using representation theory Examples include coagulation-fragmentation processes natural chains contingency tables. Our main exam...