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The Odds of Staying on Budget

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Book cover Automata, Languages, and Programming (ICALP 2015)

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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.

C. Haase—Supported by Labex Digicosme, Univ. Paris-Saclay, project VERICONISS.

S. Kiefer—Supported by a Royal Society University Research Fellowship.

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Author information

Authors and Affiliations

  1. Laboratoire Spécification et Vérification (LSV), CNRS and ENS de Cachan, Cachan Cedex, France

    Christoph Haase

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Stefan Kiefer

Authors
  1. Christoph Haase
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  2. Stefan Kiefer
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Corresponding author

Correspondence to Christoph Haase .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Haase, C., Kiefer, S. (2015). The Odds of Staying on Budget. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_19

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  • DOI: https://doi.org/10.1007/978-3-662-47666-6_19

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  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

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