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International Symposium on Mathematical Foundations of Computer Science

MFCS 2015: Mathematical Foundations of Computer Science 2015 pp 344–356Cite as

Ratio and Weight Quantiles

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9234))

Abstract

Several types of weighted-automata models and formalisms to specify and verify constraints on accumulated weights have been studied in the past. The lack of monotonicity for weight functions with positive and negative values as well as for ratios of the accumulated values of non-negative weight functions renders many verification problems to be undecidable or computationally hard. Our contribution comprises polynomial-time algorithms for computing ratio and weight quantiles in Markov chains, which provide optimal bounds guaranteed almost surely or with positive probability on, e.g., cost-utility ratios or the energy conversion efficiency.

The authors are supported by the DFG through the collaborative research centre HAEC (SFB 912), the Excellence Initiative by the German Federal and State Governments (cluster of excellence cfAED and Institutional Strategy), the Graduiertenkolleg QuantLA (1763), Deutsche Telekom Stiftung, the EU-FP-7 grant MEALS (295261).

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Acknowledgements

We thank Stefan Kiefer for pointing us to the continued-fraction method and its application [20].

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Authors and Affiliations

  1. Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany

    Daniel Krähmann, Jana Schubert, Christel Baier & Clemens Dubslaff

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  1. Daniel Krähmann
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  2. Jana Schubert
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  3. Christel Baier
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  4. Clemens Dubslaff
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Correspondence to Daniel Krähmann .

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Editors and Affiliations

  1. Università di Roma "Tor Vergata", Rome, Italy

    Giuseppe F Italiano

  2. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  3. University of Edinburgh, Edinburgh, United Kingdom

    Donald T. Sannella

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Krähmann, D., Schubert, J., Baier, C., Dubslaff, C. (2015). Ratio and Weight Quantiles. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_27

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  • DOI: https://doi.org/10.1007/978-3-662-48057-1_27

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  • Online ISBN: 978-3-662-48057-1

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