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Minimization of Probabilistic Models of Programs

Abstract

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 the concept of equivalence of states of a PTS and present an algorithm for removing equivalent states. A result of this algorithm is a PTS such that all of its properties expressed by formulas of PCTL coincide with those of the original PTS.

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Correspondence to A. M. Mironov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 1, pp. 121–163, 2014.

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Mironov, A.M., Frenkel, S.L. Minimization of Probabilistic Models of Programs. J Math Sci 211, 381–412 (2015). https://doi.org/10.1007/s10958-015-2611-2

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Keywords

  • Model Check
  • Random Function
  • Reduction Algorithm
  • Atomic Proposition
  • State Formula