The Odds of Staying on Budget

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)

Abstract

Given Markov chains and Markov decision processes (MDPs) whose transitions are labelled with non-negative integer costs, we study the computational complexity of deciding whether the probability of paths whose accumulated cost satisfies a Boolean combination of inequalities exceeds a given threshold. For acyclic Markov chains, we show that this problem is PP-complete, whereas it is hard for the PosSLP problem and in PSpace for general Markov chains. Moreover, for acyclic and general MDPs, we prove PSpace- and EXP-completeness, respectively. Our results have direct implications on the complexity of computing reward quantiles in succinctly represented stochastic systems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Laboratoire Spécification et Vérification (LSV)CNRS and ENS de CachanCachan CedexFrance
  2. 2.Department of Computer ScienceUniversity of OxfordOxfordUK

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