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Don’t know in probabilistic systems. (English) Zbl 1178.68341
Valmari, Antti (ed.), Model checking software. 13th international SPIN workshop, Vienna, Austria, March 30 – April 1, 2006. Proceedings. Berlin: Springer (ISBN 3-540-33102-6/pbk). Lecture Notes in Computer Science 3925, 71-88 (2006).
Summary: 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 (abstract Markov chains) with respect to specifications in probabilistic temporal logics, interpreted over a 3-valued domain. More specifically, we introduce a 3-valued version of probabilistic computation-tree logic (PCTL) and give a model checking algorithm w.r.t. abstract Markov chains.
For the entire collection see [Zbl 1103.68011].

MSC:
68Q60 Specification and verification (program logics, model checking, etc.)
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