Geodesic
Minimization of probabilistic models of programs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 121-163

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In this paper, we consider a problem of reduction of probabilistic transition systems (PTS) in order to reduce the complexity of model checking of such systems. The problem of model checking of a PTS is to calculate truth values of formulas of the probabilistic temporal logic PCTL in an initial state of the PTS. We introduce a concept of equivalence of states of a PTS, and represent an algorithm for removing equivalent states. A result of this algorithm is a PTS such that all its properties expressed by formulas of PCTL coincide with those of the original PTS. 
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A. M. Mironov; S. L. Frenkel. Minimization of probabilistic models of programs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 121-163. http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a6/