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Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems

Published:14 January 2015Publication History
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Abstract

We propose the first sound and complete learning-based compositional verification technique for probabilistic safety properties on concurrent systems where each component is an Markov decision process. Different from previous works, weighted assumptions are introduced to attain completeness of our framework. Since weighted assumptions can be implicitly represented by multi-terminal binary decision diagrams (MTBDD's), we give an L*-based learning algorithm for MTBDD's to infer weighted assumptions. Experimental results suggest promising outlooks for our compositional technique.

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References

  1. IEEE standard for a high-performance serial bus. IEEE Std 1394--2008, pages 1--954, Oct 2008.Google ScholarGoogle Scholar
  2. IEEE standard for information technology--telecommunications and information exchange between systems local and metropolitan area networks--specific requirements part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications. IEEE Std 802.11--2012 (Revision of IEEE Std 802.11--2007), pages 1--2793, March 2012.Google ScholarGoogle Scholar
  3. D. Angluin. Learning regular sets from queries and counterexamples. Information and Computation, 75(2):87--106, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. J. Aspnes and M. Herlihy. Fast randomized consensus using shared memory. Journal of Algorithms, 11(3):441--460, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. C. Baier and J.-P. Katoen. Principles of model checking. MIT Press, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. C. Baier, E. M. Clarke, V. Hartonas-Garmhausen, M. Kwiatkowska, and M. Ryan. Symbolic model checking for probabilistic processes. In ICALP, volume 1256 of LNCS, pages 430--440. Springer, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. A. Beimel, F. Bergadano, N. H. Bshouty, E. Kushilevitz, and S. Varricchio. Learning functions represented as multiplicity automata. Journal of ACM, 47(3):506--530, May 2000. . Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. A. Bianco and L. de Alfaro. Model checking of probabalistic and nondeterministic systems. In FSTTCS, volume 1026 of LNCS, pages 499--513. Springer, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. B. Bollig, J.-P. Katoen, C. Kern, M. Leucker, D. Neider, and D. R. Piegdon. libalf: The automata learning framework. In CAV, volume 6174 of LNCS, pages 360--364. Springer, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Y. Chen, H. Mao, M. Jaeger, T. Nielsen, K. Guldstrand Larsen, and B. Nielsen. Learning Markov models for stationary system behaviors. In NASA Formal Methods, volume 7226 of LNCS, pages 216--230. Springer, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Y.-F. Chen, E. M. Clarke, A. Farzan, M.-H. Tsai, Y.-K. Tsay, and B.- Y. Wang. Automated assume-guarantee reasoning through implicit learning. In CAV, volume 6174 of LNCS, pages 511--526. Springer, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. E. Clarke, O. Grumberg, S. Jha, Y. Lu, and H. Veith. Counterexample-guided abstraction refinement. In CAV, volume 1855 of LNCS, pages 154--169. Springer, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. J. M. Cobleigh, D. Giannakopoulou, and C. S. Păsăreanu. Learning assumptions for compositional verification. In TACAS, volume 2619 of LNCS, pages 331--346. Springer, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. J. M. Cobleigh, G. S. Avrunin, and L. A. Clarke. Breaking up is hard to do: An evaluation of automated assume-guarantee reasoning. ACM Transactions on Software Engineering and Methodology (TOSEM), 17 (2):7, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. L. De Alfaro, M. Kwiatkowska, G. Norman, D. Parker, and R. Segala. Symbolic model checking of probabilistic processes using MTBDDs and the Kronecker representation. In TACAS, volume 1758 of LNCS, pages 395--410. Springer, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. L. Feng, M. Kwiatkowska, and D. Parker. Compositional verification of probabilistic systems using learning. In QEST, pages 133--142. IEEE, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. L. Feng, T. Han, M. Kwiatkowska, and D. Parker. Learning-based compositional verification for synchronous probabilistic systems. In ATVA, volume 6996 of LNCS, pages 511--521. Springer-Verlag, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. M. Fujita, P. C. McGeer, and J.-Y. Yang. Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Formal Methods in System Design, 10(2/3):149--169, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. R. Gavaldà and D. Guijarro. Learning ordered binary decision diagrams. In ALT, volume 997 of LNCS, pages 228--238. Springer, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. M. Gheorghiu, D. Giannakopoulou, and C. S. Păsăreanu. Refining interface alphabets for compositional verification. In TACAS, volume 4424 of LNCS, pages 292--307. Springer, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. M. Gheorghiu Bobaru, C. S. Păsăreanu, and D. Giannakopoulou. Automated assume-guarantee reasoning by abstraction refinement. In CAV, volume 5123 of LNCS, pages 135--148. Springer, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. A. Gupta, K. L. McMillan, and Z. Fu. Automated assumption generation for compositional verification. In CAV, volume 4590 of LNCS, pages 420--432. Springer, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. T. Han, J.-P. Katoen, and D. Berteun. Counterexample generation in probabilistic model checking. IEEE Transactions on Software Engineering, 35(2):241--257, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal aspects of computing, 6(5):512--535, 1994.Google ScholarGoogle Scholar
  25. F. He, B.-Y. Wang, L. Yin, and L. Zhu. Symbolic assume-guarantee reasoning through BDD learning. In ICSE, pages 1071--1082. ACM, 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. A. Hinton, M. Kwiatkowska, G. Norman, and D. Parker. PRISM: A tool for automatic verification of probabilistic systems. In TACAS, volume 3920 of LNCS, pages 441--444. Springer, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. J.-P. Katoen, L. Song, and L. Zhang. Probably safe or live. In Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 55:1--55:10. ACM, 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. S. Kimura and E. M. Clarke. A parallel algorithm for constructing binary decision diagrams. In ICCD, pages 220--223. IEEE, 1990.Google ScholarGoogle ScholarCross RefCross Ref
  29. A. Komuravelli, C. S. Păsăreanu, and E. M. Clarke. Assume-guarantee abstraction refinement for probabilistic systems. In CAV, volume 7358 of LNCS, pages 310--326. Springer, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. A. Komuravelli, C. S. Păsăreanu, and E. M. Clarke. Learning probabilistic systems from tree samples. In LICS, pages 441--450. IEEE, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. M. Kwiatkowska, G. Norman, and D. Parker. Probabilistic symbolic model checking with PRISM: A hybrid approach. International Journal on Software Tools for Technology Transfer, 6(2):128--142, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. M. Kwiatkowska, G. Norman, D. Parker, and H. Qu. Assume-guarantee verification for probabilistic systems. In TACAS, volume 6015 of LNCS, pages 23--37. Springer, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. D. Lehmann and M. O. Rabin. On the advantage of free choice: A symmetric and fully distributed solution to the dining philosophers problem (extended abstract). In POPL, pages 133--138. ACM, 1981. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. H. Mao, Y. Chen, M. Jaeger, T. D. Nielsen, K. G. Larsen, and B. Nielsen. Learning probabilistic automata for model checking. In QEST, pages 111--120. IEEE, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. H. Mao, Y. Chen, M. Jaeger, T. D. Nielsen, K. G. Larsen, and B. Nielsen. Learning Markov decision processes for model checking. arXiv preprint arXiv:1212.3873, 2012.Google ScholarGoogle Scholar
  36. R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. A. Nakamura. An efficient query learning algorithm for ordered binary decision diagrams. Information and Computation, 201(2):178--198, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. D. A. Parker. Implementation of symbolic model checking for probabilistic systems. PhD thesis, University of Birmingham, 2002.Google ScholarGoogle Scholar
  39. R. Segala and N. Lynch. Probabilistic simulations for probabilistic processes. In CONCUR, volume 836 of LNCS, pages 481--496. Springer, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. W.-G. Tzeng. Learning probabilistic automata and Markov chains via queries. Machine Learning, 8(2):151--166, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. R. Wimmer, N. Jansen, E. Ábrahám, B. Becker, and J.-P. Katoen. Minimal critical subsystems for discrete-time Markov models. In TACAS, volume 7214 of LNCS, pages 299--314. Springer, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. R. Wimmer, N. Jansen, A. Vorpahl, E. Ábrahám, J.-P. Katoen, and B. Becker. High-level counterexamples for probabilistic automata. In QEST, pages 39--54. IEEE, 2013. Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. H. Zhu, F. He, W. N. Hung, X. Song, and M. Gu. Data mining based decomposition for assume-guarantee reasoning. In FMCAD, pages 116--119. IEEE, 2009.Google ScholarGoogle ScholarCross RefCross Ref

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      • Published in

        cover image ACM SIGPLAN Notices
        ACM SIGPLAN Notices  Volume 50, Issue 1
        POPL '15
        January 2015
        682 pages
        ISSN:0362-1340
        EISSN:1558-1160
        DOI:10.1145/2775051
        • Editor:
        • Andy Gill
        Issue’s Table of Contents
        • cover image ACM Conferences
          POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
          January 2015
          716 pages
          ISBN:9781450333009
          DOI:10.1145/2676726

        Copyright © 2015 ACM

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        • Published: 14 January 2015

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