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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)
The next larger step in automotive development will be towards autonomously driving cars. Autonomous driving will be a highly complex and safety-related function in future vehicles, and current software platforms are not adequate for this function. We present our ongoing research on an open-source software platform for autonomous driving software systems.(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 expressible 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)
The complex anatomy of the sacrum makes surgical fracture fixation challenging. We developed statistical models to investigate sacral anatomy with special regard to trans-sacral implant fixation. We used computed tomographies of 20 intact adult pelves to establish 3D statistical models: a surface model of the sacrum and the trans-sacral corridor S1,(More)
Fragility fractures of the pelvic ring (FFP) are increasing in frequency and require challenging treatment. A new comprehensive classification considers both fracture morphology and degree of instability. The classification system also provides recommendations for type and invasiveness of treatment. In this article, a literature review of treatment(More)
Trans-sacral implants can be used alternatively to sacro-iliac screws in the treatment of osteoporosis-associated fragility fractures of the pelvis and the sacrum. We investigated trans-sacral corridor dimensions, the number of individuals amenable to trans-sacral fixation, as well as the osseous boundaries and shape of the S1 corridor. 3D models were(More)