Abstract
This paper presents a library for exactly computing the bisimilarity Kantorovich-based pseudometrics between Markov chains and between Markov decision processes. These are distances that measure the behavioral discrepancies between non-bisimilar systems. They are computed by using an on-the-fly greedy strategy that prevents the exhaustive state space exploration and does not require a complete storage of the data structures. Tests performed on a consistent set of (pseudo)randomly generated instances show that our algorithm improves the efficiency of the previously proposed iterative algorithms, on average, with orders of magnitude. The tool is available as a Mathematica package library.
Work supported by the VKR Center of Excellence MT-LAB and the Sino-Danish Basic Research Center IDEA4CPS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bacci, G., Bacci, G., Larsen, K.G., Mardare, R.: Computing behavioral distances, compositionally. In: Chatterjee, K., Sgall, J. (eds.) MFCS 2013. LNCS, vol. 8087, pp. 74–85. Springer, Heidelberg (2013)
Bacci, G., Bacci, G., Larsen, K.G., Mardare, R.: On-the-Fly Exact Computation of Bisimilarity Distances. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 1–15. Springer, Heidelberg (2013)
Chen, D., van Breugel, F., Worrell, J.: On the Complexity of Computing Probabilistic Bisimilarity. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 437–451. Springer, Heidelberg (2012)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. Theoretical Computer Science 318(3), 323–354 (2004)
Ferns, N., Panangaden, P., Precup, D.: Metrics for finite Markov Decision Processes. In: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence, UAI, pp. 162–169. AUAI Press (2004)
Givan, R., Dean, T., Greig, M.: Equivalence notions and model minimization in Markov decision processes. Artificial Intelligence 147(1-2), 163–223 (2003)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)
van Breugel, F., Sharma, B., Worrell, J.: Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems. Logical Methods in Computer Science 4(2), 1–23 (2008)
van Breugel, F., Worrell, J.: Approximating and computing behavioural distances in probabilistic transition systems. Theoretical Computer Science 360(1-3), 373–385 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bacci, G., Bacci, G., Guldstrand Larsen, K., Mardare, R. (2013). The BisimDist Library: Efficient Computation of Bisimilarity Distances for Markovian Models. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds) Quantitative Evaluation of Systems. QEST 2013. Lecture Notes in Computer Science, vol 8054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40196-1_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-40196-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40195-4
Online ISBN: 978-3-642-40196-1
eBook Packages: Computer ScienceComputer Science (R0)