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On Application of Multi-Rooted Binary Decision Diagrams to Probabilistic Model Checking

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7148))

Abstract

In this paper we consider the applicability of multi-rooted binary decision diagrams for the probabilistic model checking. The symbolic probabilistic model checking involves manipulation of functions and matrices with the values in [0,1], and multi-terminal binary decision diagrams, sparse matrices, and combinations thereof are used to represent these objects. We propose algorithms for representing these objects by means of multi-rooted binary decision diagrams when a function with the values in [0,1] is approximated by a set of Boolean functions. Each Boolean function is represented by a binary decision diagram and being combined together these diagrams form a mutli-rooted binary decision diagram. Presented experimental results show that this approach allows for the model checking for large problems with a smaller memory footprint, compared to the use of the multi-terminal binary decision diagrams.

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References

  1. Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Transactions on Computers 45(9), 993–1002 (1996)

    Article  MATH  Google Scholar 

  2. Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)

    Article  MathSciNet  Google Scholar 

  3. Bugaychenko, D.: BddFunctions: Multi-rooted binary decision diagrams package, http://code.google.com/p/bddfunctions/

  4. Bugaychenko, D., Soloviev, I.: Application of multiroot decision diagrams for integer functions. Vestnik St. Petersburg University: Mathematics 43(2), 92–97 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fujita, M., McGeer, P.C., Yang, J.C.Y.: Multi-terminal binary decision diagrams: An efficient datastructure for matrix representation. Form. Methods Syst. Des. 10(2-3), 149–169 (1997)

    Article  Google Scholar 

  6. Lind-Nielsen, J.: BDD Package BuDDy, http://buddy.sourceforge.net

  7. McMillan, K.L.: Symbolic model checking. Kluwer Academic Publishers, Dordrecht (1993)

    Book  MATH  Google Scholar 

  8. Minato, S., Ishiura, N., Yajima, S.: Shared binary decision diagram with attributed edges for efficient boolean function manipulation. In: Proceedings of the 27th ACM/IEEE Design Automation Conference, pp. 52–57. ACM (1991)

    Google Scholar 

  9. Oldenkamp, H.: Probabilistic model checking. A comparison of tools. Master’s thesis, University of Twente, Niederlande (2007)

    Google Scholar 

  10. Parker, D.: Implementation of symbolic model checking for probabilistic system. Ph.D. thesis, University of Birmingham (2002)

    Google Scholar 

  11. Somenzi, F.: CUDD: Colorado University Decision Diagram package, http://vlsi.colorado.edu/~fabio/CUDD

  12. Xie, B.: Symbolic moment computation with application to statistical timing analysis. In: Asia Pacific Conference on Postgraduate Research in Microelectronics & Electronics, PrimeAsia 2009, pp. 460–463. IEEE (2009)

    Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Bugaychenko, D. (2012). On Application of Multi-Rooted Binary Decision Diagrams to Probabilistic Model Checking. In: Kuncak, V., Rybalchenko, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2012. Lecture Notes in Computer Science, vol 7148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27940-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-27940-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27939-3

  • Online ISBN: 978-3-642-27940-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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