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Differential BDDs

  • Anuchit Anuchitanukul
  • Zohar Manna
  • Tomás E. Uribe
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1000)

Abstract

We present a class of Ordered Binary Decision Diagrams, Differential BDDs (δBDDs), and transformations Push-up (↑) and Delta (δ) over them. In addition to the ordinary node-sharing in normal BDDs, isomorphic substructures can be collapsed further in δBDDs and their derived classes, forming a more compact representation of boolean functions. The elimination of isomorphic substructures coincides with the repetitive occurrences of small components in many applications of BDDs. The reduction is potentially exponential in the number of nodes and proportional to the number of variables, while operations on δBDDs remain efficient.

Keywords

Model Check Boolean Function Directed Acyclic Graph Hash Table Node Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Akers, S.. Binary decision diagrams. IEEE Transactions on Computers 6, 27 (June 1978), 509–516.Google Scholar
  2. 2.
    Ashar, P., Ghosh, A., and Devadas, S. Boolean satisfiability and equivalence checking using general binary decision diagrams. In IEEE International Conf. on Computer Design: VLSI in Computers and Processors (1991), pp. 259–264.Google Scholar
  3. 3.
    Bani-Eqbal, B. Exclusive normal form of boolean circuits. Tech. Rep. UMCS-92-4-1, Department of Computer Science, University of Manchester, 1992.Google Scholar
  4. 4.
    Becker, B., Bryant, R., Coudert, O., and Meinel, C., Eds. Report on the Third Workshop on Computer Aided Design and Test (Feb. 1995). http: //www. informatik. uni-trier. de/Design_and_Test/.Google Scholar
  5. 5.
    Becker, B., Drechsler, R., and Theobald, M. OKFDDs versus OBDDs and OFDDs. In International Colloquium on Automata, Languages and Programming (July 1995), LNCS. To appear.Google Scholar
  6. 6.
    Bern, J., Meinel, C., and Slobodová, A. Efficient OBDD-based boolean manipulation in CAD beyond current limits. In 32ndDesign Automation Conf. (1995).Google Scholar
  7. 7.
    Bitner, J., Jain, J., Abadir, M., Abraham, J., and Fussell, D. Efficient algorithmic computation using indexed BDDs. In 24thIntl. Symposium on Fault-Tolerant Computing (1994), pp. 266–275.Google Scholar
  8. 8.
    Brace, K. S., Rudell, R. L., and Bryant, R. E. Efficient implementation of a BDD package. In 27thDesign Automation Conf. (1990), pp. 40–45.Google Scholar
  9. 9.
    Bryant, R. E. Graph-based algorithms for Boolean function manipulation. IEEE Trans. on Computers 35, 8 (Aug. 1986), 677–691.Google Scholar
  10. 10.
    Bryant, R. E. On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. on Computers 40, 2 (Feb. 1991), 205–213.CrossRefGoogle Scholar
  11. 11.
    Bryant, R. E. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24, 3 (Sept. 1992), 293–318.CrossRefGoogle Scholar
  12. 12.
    Bryant, R. E., And Chen, Y.-A. Verification of arithmetic circuits with Binary Moment Diagrams. In 32nd Design Automation Conf. (June 1995). To appear.Google Scholar
  13. 13.
    Burch, J., Clarke, E., McMillan, K., Dill, D., and Hwang, L. Symbolic modelchecking: 1020 states and beyond. Information and Computation 98, 2 (June 1992), 142–170.CrossRefGoogle Scholar
  14. 14.
    Clarke, E. M., McMillan, K., Zhao, X., Fujita, M., and Yang, J. Spectral transforms for large Boolean functions with applications to technology mapping. In 30thDesign Automation Conf. (June 1993).Google Scholar
  15. 15.
    Jeong, S., Plessier, B., Hachtel, G., and Somenzi, F. Extended BDD's: Trading off canonicity for structure in verification algorithms. In IEEE Intl. Conf. on Computer-Aided Design (1991), pp. 464–467.Google Scholar
  16. 16.
    Kam, T. Y. K., and Brayton, R. K. Multi-valued decision diagrams. Technical Report UCB/ERL M90/125, University of California, Berkeley, Dec. 1990.Google Scholar
  17. 17.
    Karplus, K. Using if-then-else DAGs for multi-level logic minimization. In Advance Research in VLSI (1989), C. Seitz, Ed., MIT Press, pp. 101–118.Google Scholar
  18. 18.
    Lai, Y.-T., AND Sastry, S. Edge-valued binary decision diagrams for multi-level hierarchical verification. In 29thDesign Automation Conf. (1992), pp. 608–613.Google Scholar
  19. 19.
    Madre, J., and Billon, J. Proving circuit correctness using formal comparison between expected and extracted behaviour. In 25thDesign Automation Conf. (June 1988), pp. 205–210.Google Scholar
  20. 20.
    McMillan, K. L. Hierarchical representations of discrete functions, with application to model checking. In Proc. 6th Intl. Conf. on Computer-Aided Verification (June 1994), vol. 818 of LNCS, Springer-Verlag, pp. 41–54.Google Scholar
  21. 21.
    Minato, S. Zero-supressed BDDs for set manipulation in combinatorial problems. In 30thDesign Automation Conf. (1993), pp. 272–277.Google Scholar
  22. 22.
    Minato, S., Ishiura, N., and Jajima, S. Shared binary decision diagram with attributed edges for efficient boolean function manipulation. In 27thDesign Automation Conf. (1990), pp. 52–57.Google Scholar
  23. 23.
    Possega, J., AND Ludäscher, B. Towards first-order deduction based on Shannon graphs. In Proc. 16thGerman Conf. on AI (GWAI-92) (1992), vol. 671 of LNAI, Springer-Verlag, pp. 67–76.Google Scholar
  24. 24.
    Sieling, D., AND Wegener, I. Graph driven BDDs—a new data structure for boolean functions. Theoretical Comput. Sci. 141, 2 (Apr. 1995).Google Scholar
  25. 25.
    Uribe, T. E., and Stickel, M. E. Ordered binary decision diagrams and the Davis-Putnam procedure. In Proc. 1stIntl. Conf. on Constraints in Computational Logics(Sept. 1994), vol. 845 of LNCS, pp. 34–49Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Anuchit Anuchitanukul
    • 1
  • Zohar Manna
    • 1
  • Tomás E. Uribe
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanford

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