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We present Hintikka games for formulae of the proba-bilistic temporal logic PCTL and countable labeled Markov chains as models, giving an operational account of the de-notational semantics of PCTL on such models. Winning strategies have a decent degree of compositionality in the parse tree of a PCTL formula and express the precise evidence for truth or… (More)

Probabilistic model checking is a technique for verifying whether a model such as a Markov chain satisfies a probabilistic, behavioral property – e.g. " with probability at least 0.999, a device will be elected leader. " Such properties are express-ible in probabilistic temporal logics, e.g. PCTL, and efficient algorithms exist for checking whether these… (More)

Three-valued Markov chains and their PCTL semantics abstract – via probabilistic simulations – labeled Markov chains and their usual PCTL semantics. This abstraction framework is complete for a PCTL formula if all labeled Markov chains that satisfy said formula have a finite-state abstraction that satisfies it in its abstract semantics. We show that not all… (More)

We develop a new approach to probabilistic verification by adapting notions and techniques from alternating tree automata to the realm of Markov chains. The resulting p-automata determine languages of Markov chains which are proved to be closed under Boolean operations, to subsume bisimulation equivalence classes of Markov chains, and to subsume the set of… (More)

- Daniel Wagner
- 2011

Formal concept analysis (FCA) comprises a set of powerful algorithms which can be used for data analysis and manipulation, and a set of visualisation tools which enable the discovery of meaningful relationships between attributes of the data. We explore the potential of combining FCA and mathematical discovery tools in order to better facilitate discovery… (More)

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