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On the influence of the state encoding on OBDD-representations of finite state machines

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Mathematical Foundations of Computer Science 1997 (MFCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1295))

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Abstract

Ordered binary decision diagrams are an important data structure for the representation of Boolean functions. Typically, the underlying variable ordering is used as an optimization parameter. When finite state machines are represented by OBDDs the state encoding can be used as an additional optimization parameter. In this paper, we analyze the influence of the state encoding on the OBDD-representations of counter-type finite state machines. In particular, we prove lower bounds, derive exact sizes for important encodings and construct a worst-case encoding which leads to exponential-size OBDDs.

Supported by DFG-Graduiertenkolleg “Mathematische Optimierung”.

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References

  1. A. Aziz, S. Taziran, and R. K. Brayton. BDD variable ordering for interacting finite state machines. In Proc. 31st ACMIIEEE Design Automation Conference, 283–288, 1994.

    Google Scholar 

  2. J. R. Burch, E. M. Clarke, D. E. Long, K. L. McMillan, and D. L. Dill. Symbolic model checking for sequential circuit verification. IEEE Transactions on CAD, 13:401–424, 1994.

    Google Scholar 

  3. J. Bern, Ch. Meinel, and A. Slobodova. Global rebuilding of OBDDs-avoiding memory requirement maxima. In Proc. Computer-Aided Verification, Lecture Notes in Computer Science 939, 4-15. Springer, 1995.

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. O. Coudert, C. Berthet, and J. C. Madre. Verification of synchronous sequential machines using symbolic execution. In Proc. Workshop on Automatic Verification Methods for Finite State Machines, Lecture Notes in Computer Science 407, 365–373. Springer, 1989.

    Google Scholar 

  8. O. Coudert and J. C. Madre. The implicit set paradigm: A new approach to finite state system verification. Formal Methods in System Design, 6(2):133–145, 1995.

    Article  Google Scholar 

  9. A. Ghosh, S. Devadas, and A. R. Newton. Sequential Logic Testing and Verification. Kluwer Academic Publishers, 1992.

    Google Scholar 

  10. Ch. Meinel and A. Slobodova. On the complexity of constructing optimal ordered binary decision diagrams. In Proc. Mathematical Foundations in Computer Science, Lecture Notes in Computer Science 841, 515–524, 1994.

    Google Scholar 

  11. Ch. Meinel, F. Somenzi, and T. Theobald. Linear sifting of decision diagrams. To appear at 34th ACM/IEEE Design Automation Conference (Anaheim, CA), 1997.

    Google Scholar 

  12. Ch. Meinel and T. Theobald. Local encoding transformations for optimizing OBDD-representations of finite state machines. In Proc. International Conference on Formal Methods in CAD (Palo Alto, CA), Lecture Notes in Computer Science 1166, 404–418. Springer, 1996.

    Google Scholar 

  13. R. Rudell. Dynamic variable ordering for ordered binary decision diagrams. In Proc. IEEE International Conference on CAD, 42–47, 1993.

    Google Scholar 

  14. S. Tani, K. Hamaguchi, and S. Yajima.The complexity of the optimal variable ordering problems of shared binary decision diagrams. In Proc. International Symposium on Algorithms and Computation '93, Lecture Notes in Computer Science 762, 389–398. Springer, 1993.

    Google Scholar 

  15. I. Wegener. Efficient data structures for Boolean functions. Discrete Mathematics, 136:347–372, 1994.

    Article  Google Scholar 

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Authors and Affiliations

  1. FB IV — Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel & Thorsten Theobald

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  1. Christoph Meinel
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  2. Thorsten Theobald
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Igor Prívara Peter Ružička

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© 1997 Springer-Verlag Berlin Heidelberg

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Meinel, C., Theobald, T. (1997). On the influence of the state encoding on OBDD-representations of finite state machines. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029984

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  • DOI: https://doi.org/10.1007/BFb0029984

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63437-9

  • Online ISBN: 978-3-540-69547-9

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