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Bisimulation Minimisations for Boolean Equation Systems

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Hardware and Software: Verification and Testing (HVC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6405))

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Abstract

Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and idempotence-identifying bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES mostly exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem.

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References

  1. Chen, T., Ploeger, B., van de Pol, J., Willemse, T.A.C.: Equivalence checking for infinite systems using Parameterized Boolean Equation Systems. In: Caires, L., Li, L. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 120–135. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Fisler, K., Vardi, M.Y.: Bisimulation minimization and symbolic model checking. Formal Methods in System Design 21(1), 39–78 (2002)

    Article  MATH  Google Scholar 

  3. Friedmann, O., Lange, M.: Solving parity games in practice. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 182–196. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Fritz, C., Wilke, T.: Simulation relations for alternating parity automata and parity games. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 59–70. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Groote, J.F., Willemse, T.A.C.: Parameterised Boolean Equation Systems. Theor. Comput. Sci. 343(3), 332–369 (2005)

    Article  MATH  Google Scholar 

  6. Jurdziński, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Katoen, J.-P., Kemna, T., Zapreev, I.S., Jansen, D.N.: Bisimulation minimisation mostly speeds up probabilistic model checking. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 87–101. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Keiren, J., Willemse, T.A.C.: Bisimulation minimisations for boolean equation systems. Technical Report CSR09-17, Eindhoven University of Technology (2009)

    Google Scholar 

  9. Mader, A.: Verification of Modal Properties Using Boolean Equation Systems. PhD thesis, Technische Universität München (1997)

    Google Scholar 

  10. Mateescu, R., Thivolle, D.: A model checking language for concurrent value-passing systems. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 148–164. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6) (1987)

    Google Scholar 

  12. Reniers, M.A., Willemse, T.A.C.: Analysis of Boolean equation systems through structure graphs. In: Proc. of SOS 2009. EPTCS (2009) (to appear)

    Google Scholar 

  13. Blom, S., Orzan, S.: Distributed state space minimization. Int. J. STTT 7(3) (2005)

    Google Scholar 

  14. Schewe, S.: Solving parity games in big steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands

    Jeroen J. A. Keiren & Tim A. C. Willemse

Authors
  1. Jeroen J. A. Keiren
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  2. Tim A. C. Willemse
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Editor information

Editors and Affiliations

  1. Bell Laboratories, Alcatel-Lucent, 600 Mountain Ave., 2B-435, 07974, Murray Hill, NJ, USA

    Kedar Namjoshi

  2. Saarland University, Campus E1, 66123, Saarbrücken, Germany

    Andreas Zeller

  3. IBM Research Laboratory, 31905, Haifa, Mount Carmel, Israel

    Avi Ziv

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© 2011 Springer-Verlag Berlin Heidelberg

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Keiren, J.J.A., Willemse, T.A.C. (2011). Bisimulation Minimisations for Boolean Equation Systems. In: Namjoshi, K., Zeller, A., Ziv, A. (eds) Hardware and Software: Verification and Testing. HVC 2009. Lecture Notes in Computer Science, vol 6405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19237-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-19237-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19236-4

  • Online ISBN: 978-3-642-19237-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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