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Construction Methods for MDD-Based State Space Representations of Unstructured Systems

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 8376)

Abstract

Multi-valued Decision Diagrams (MDDs) are used in various fields of application. In performance evaluation, a compact representation of the state space of Markovian systems can often be achieved by using MDDs. It is well known that the size of the resulting MDD representation heavily depends on the variable ordering, i.e. the arrangement of the levels within the MDD. Markov models, derived from higher level descriptions of the system, often contain structural information. This information might give hints for an optimized variable ordering a priori, i.e. before the MDD is constructed. Whenever a model is described by constraints—considering the design space of a system, for example—there is a lack of such structural information. This is the reason why the MDD representation often consumes too much memory to be handled efficiently. In order to keep the memory consumption practicable, we have developed two optimization mechanisms. The presented examples demonstrate that efficient MDD representations of the feasible design space can be obtained, even for large unstructured systems.

Keywords

  • Unstructured systems
  • Design space
  • Multi-valued decision diagram
  • Variable ordering
  • Constraint computation sequence

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References

  1. Bolch, G., Greiner, S., de Meer, H., Trivedi, K.S.: Queueing Networks and Markov Chains, 2nd edn. John Wiley and Sons, New York (2006)

    CrossRef  Google Scholar 

  2. Hillston, J., Ribaudo, M.: Stochastic process algebras: a new approach to performance modeling. In: Modeling and Simulation of Advanced Computer Systems, pp. 235–256, Gordon Breach (1998)

    Google Scholar 

  3. Hermanns, H., Herzog, U., Katoen, J.-P.: Process algebra for performance evaluation. Theoretical Computer Science 274(12), 43–87 (2002)

    MathSciNet  CrossRef  Google Scholar 

  4. Trowitzsch, J., Jerzynek, D., Zimmermann, A.: A toolkit for performability evaluation based on stochastic UML state machines. In: VALUETOOLS 2007, p. 30 (2007)

    Google Scholar 

  5. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers C-35 (8), 677–691 (1986)

    CrossRef  Google Scholar 

  6. Kam, T., Villa, T., Brayton, R.K., Sangiovanni-Vincentelli, A.: Multivalued decision diagrams: theory and applications. Multiple-Valued Logic 4(1-2), 9–62 (1998)

    MathSciNet  MATH  Google Scholar 

  7. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  8. Heiner, M., Rohr, C., Schwarick, M.: MARCIE – Model Checking and Reachability Analysis Done Efficiently. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 389–399. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  9. Ciardo, G., Jones III, R.L., Miner, A.S., Siminiceanu, R.: Logic and stochastic modeling with SMART. Perform. Eval (PE) 63(6), 578–608 (2006)

    CrossRef  Google Scholar 

  10. Mateescu, R., Marinescu, R., Dechter, R.: AND/OR Multi-valued Decision Diagrams for Constraint Optimization. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 498–513. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  11. Bollig, B., Wegener, I.: Improving the Variable Ordering of OBDDs Is NP-Complete. IEEE Transactions on Computers 45(9) (1996)

    Google Scholar 

  12. Rice, M., Kulhari, S.: A Survey of Static Variable Ordering Heuristics for Efficient BDD/MDD Construction, Technical Report, UC Riverside (2008)

    Google Scholar 

  13. Siminiceanu, R.I., Ciardo, G.: New Metrics for Static Variable Ordering in Decision Diagrams. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 90–104. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  14. Fujita, M., Matsunaga, Y., Kakuda, T.: On variable ordering of binary decision diagrams for the application of multi-level logic synthesis. In: Proceedings of the Conference on European Design Automation (EURO-DAC 1991), pp. 50–54. IEEE Computer Society Press, Los Alamitos (1991)

    CrossRef  Google Scholar 

  15. Ishiura, N., Sawada, H., Yajima, S.: Minimazation of Binary Decision Diagrams Based on Exchanges of Variables. In: ICCAD 1991, pp. 472–475 (1991)

    Google Scholar 

  16. Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: ICCAD 1993, pp. 42–47 (1993)

    Google Scholar 

  17. Somenzi, F.: CUDD: Colorado University Decision Diagram Package, Release 2.4.2. User’s Manual and Programmer’s Manual (February 2009)

    Google Scholar 

  18. Ossowski, J., Baier, C.: A uniform framework for weighted decision diagrams and its implementation. STTT 10(5), 425–441 (2008)

    CrossRef  Google Scholar 

  19. Hadzic, T., Subbarayan, S., Jensen, R.M., Andersen, H.R., Moller, J., Hulgaard, H.: Fast Backtrack-free Product Configuration using a Precompiled Solution Space Representation. In: PETO Conference, DTU-TRYK, pp. 131–138 (2004)

    Google Scholar 

  20. Eckert, J., Villanueva, F., German, R., Dressler, F.: Distributed Mass-Spring-Relaxation for Anchor-Free Self-Localization in Sensor and Actor Networks. In: Proceedings of 20th International Conference on Computer Communications and Networks (ICCCN), pp. 1–8 (2011)

    Google Scholar 

  21. Aloul, A.F., Markov, L.I., Sakallah, A.K.: FORCE: A Fast and Easy-to-Implement Variable-Ordering Heuristic. In: Great Lakes Symposium on VLSI (GLSVLSI), Washington, D.C., pp. 116–119 (2003)

    Google Scholar 

  22. Berndt, R., Bazan, P., Hielscher, K.-S.: MDD-based Verification of Car Manufacturing Data. In: 3rd International Conference on Computational Intelligence, Modelling and Simulation (CIMSiM), pp. 187–193 (2011)

    Google Scholar 

  23. Berndt, R., Bazan, P., Hielscher, K.-S., German, R., Lukasiewycz, M.: Multi-valued Decision Diagrams for the Verification of Consistency in Automotive Product Data. In: Proceedings of the 12th International Conference on Quality Software (QSIC), pp. 189–192 (2012)

    Google Scholar 

  24. Narodytska, N., Walsh, T.: Constraint and variable ordering heuristics for compiling configuration problems. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 149–154 (2007)

    Google Scholar 

  25. van Dongen, S.: A cluster algorithm for graphs, Technical Report INS-R0010, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam (May 2000)

    Google Scholar 

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Berndt, R., Bazan, P., Hielscher, KS., German, R. (2014). Construction Methods for MDD-Based State Space Representations of Unstructured Systems. In: Fischbach, K., Krieger, U.R. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2014. Lecture Notes in Computer Science, vol 8376. Springer, Cham. https://doi.org/10.1007/978-3-319-05359-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-05359-2_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05358-5

  • Online ISBN: 978-3-319-05359-2

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