Don't Know in Probabilistic Systems

Abstract

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.

@inproceedings{fecherDontKnowInProbabilistic2006,
 author = {Harald Fecher and Martin Leucker and Verena Wolf},
 booktitle = {Model Checking Software. International Symposium on Model Checking Software (SPIN-2006), 13th International SPIN Workshop, March 30 - April 1, Vienna, Austria},
 doi = {10.1007/11691617_5},
 edition = {1st},
 editor = {Antti Valmari},
 isbn = {9783540331032},
 month = {3},
 pages = {71-88},
 publisher = {Springer Berlin Heidelberg, Heidelberg},
 title = {Don't Know in Probabilistic Systems},
 year = {2006}
}