Document Open Access Logo

Linear Distances between Markov Chains

Authors Przemyslaw Daca, Thomas A. Henzinger, Jan Kretinsky, Tatjana Petrov

PDF
Thumbnail PDF

File

LIPIcs.CONCUR.2016.20.pdf
  • Filesize: 490 kB
  • 15 pages

Document Identifiers

Author Details

Przemyslaw Daca
Thomas A. Henzinger
Jan Kretinsky
Tatjana Petrov

Cite As Get BibTex

Przemyslaw Daca, Thomas A. Henzinger, Jan Kretinsky, and Tatjana Petrov. Linear Distances between Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CONCUR.2016.20

Abstract

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.

Subject Classification

Keywords
  • probabilistic systems
  • verification
  • statistical model checking
  • temporal logic
  • behavioural equivalence

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Alessandro Abate. Approximation metrics based on probabilistic bisimulations for general state-space Markov processes: A survey. Electr. Notes Theor. Comput. Sci., 297:3-25, 2013. Google Scholar
  2. Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. The BisimDist library: Efficient computation of bisimilarity distances for Markovian models. In QEST, pages 278-281, 2013. Google Scholar
  3. Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. Computing behavioral distances, compositionally. In MFCS, pages 74-85, 2013. Google Scholar
  4. Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. On-the-fly exact computation of bisimilarity distances. In TACAS, pages 1-15, 2013. Google Scholar
  5. Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. Converging from branching to linear metrics on Markov chains. In ICTAC, pages 349-367, 2015. Google Scholar
  6. Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. On the total variation distance of semi-Markov chains. In FoSSaCS, pages 185-199, 2015. Google Scholar
  7. Paul Caspi and Albert Benveniste. Toward an approximation theory for computerised control. In EMSOFT, pages 294-304, 2002. Google Scholar
  8. Taolue Chen and Stefan Kiefer. On the total variation distance of labelled Markov chains. In CSL-LICS, pages 33:1-33:10, 2014. Google Scholar
  9. Przemyslaw Daca, Thomas A. Henzinger, Jan Křetínský, and Tatjana Petrov. Linear distances between Markov chains. Technical Report abs/1605.00186, arXiv.org, 2014. Google Scholar
  10. Przemyslaw Daca, Thomas A. Henzinger, Jan Křetínský, and Tatjana Petrov. Faster statistical model checking for unbounded temporal properties. TACAS, pages 112-129, 2016. Google Scholar
  11. Luca de Alfaro, Marco Faella, and Mariëlle Stoelinga. Linear and branching metrics for quantitative transition systems. In ICALP, pages 97-109, 2004. Google Scholar
  12. Luca de Alfaro, Rupak Majumdar, Vishwanath Raman, and Mariëlle Stoelinga. Game relations and metrics. In LICS, pages 99-108, 2007. Google Scholar
  13. Josee Desharnais, Vineet Gupta, Radha Jagadeesan, and Prakash Panangaden. Metrics for labeled Markov systems. In CONCUR, pages 258-273, 1999. Google Scholar
  14. Jyotirmoy V. Deshmukh, Rupak Majumdar, and Vinayak S. Prabhu. Quantifying conformance using the Skorokhod metric. In CAV, pages 234-250, 2015. Google Scholar
  15. Laurent Doyen, Thomas A. Henzinger, and Jean-François Raskin. Equivalence of labeled Markov chains. Int. J. Found. Comput. Sci., 19(3):549-563, 2008. Google Scholar
  16. Norm Ferns, Prakash Panangaden, and Doina Precup. Metrics for finite Markov decision processes. In AAAI, pages 950-951, 2004. Google Scholar
  17. Nathanaël Fijalkow, Stefan Kiefer, and Mahsa Shirmohammadi. Trace refinement in labelled Markov decision processes. In FOSSACS, pages 303-318, 2016. Google Scholar
  18. Antoine Girard and George J. Pappas. Approximate bisimulation: A bridge between computer science and control theory. Eur. J. Control, 17(5-6):568-578, 2011. Google Scholar
  19. Leo A Goodman. Simultaneous confidence intervals for contrasts among multinomial populations. The Annals of Mathematical Statistics, pages 716-725, 1964. Google Scholar
  20. Manfred Jaeger, Hua Mao, Kim G. Larsen, and Radu Mardare. Continuity properties of distances for Markov processes. In QEST, pages 297-312, 2014. Google Scholar
  21. Stefan Kiefer and A. Prasad Sistla. Distinguishing hidden markov chains. In 31th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, 2016. Google Scholar
  22. Kim G. Larsen and Arne Skou. Bisimulation through probabilistic testing. In POPL, pages 344-352, 1989. Google Scholar
  23. Rupak Majumdar and Vinayak S. Prabhu. Computing the Skorokhod distance between polygonal traces. In HSCC, pages 199-208, 2015. Google Scholar
  24. Ilya Tkachev and Alessandro Abate. On approximation metrics for linear temporal model-checking of stochastic systems. In HSCC, pages 193-202, 2014. Google Scholar
  25. Franck van Breugel, Babita Sharma, and James Worrell. Approximating a behavioural pseudometric without discount for probabilistic systems. In FOSSACS, pages 123-137, 2007. Google Scholar
  26. Franck van Breugel and James Worrell. Approximating and computing behavioural distances in probabilistic transition systems. Theor. Comput. Sci., 360(1-3):373-385, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact