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VSOP (Valued-Sum-of-Products) Calculator for Knowledge Processing Based on Zero-Suppressed BDDs

  • Shin-ichi Minato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3847)

Abstract

Recently, Binary Decision Diagrams (BDDs) are widely used for efficiently manipulating large-scale Boolean function data. BDDs are also applied for handling combinatorial item set data. Zero-suppressed BDDs (ZBDDs) are special type of BDDs which are suitable for implicitly handling large-scale combinatorial item set data. In this paper, we present VSOP program developed for calculating combinatorial item set data specified by symbolic expressions based on ZBDD techniques. Our program supports not only combinatorial set operations but also numerical arithmetic operations based on Valued-Sum-Of-Products algebra, such as addition, subtraction, multiplication, division, numerical comparison, etc. We discuss the data structures and algorithms in our program, and show some typical applications. VSOP calculator will be useful for solving many problems in Computer Science. We show one of the promising application to find a hidden data group related each other under the huge amount of web space. Our method will facilitates knowledge federation over the web, and also useful for many other applications in computer science.

Keywords

Boolean Function Product Term Knowledge Processing Reduction Rule Binary Decision Diagram 
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.B.: Binary decision diagrams. IEEE Trans. Comput., C-27(6), 509–516 (1978)Google Scholar
  2. 2.
    Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast Discovery of Association Rules. In: Advances in Knowledge Discovery and Data Mining, pp. 307–328. MIT Press, Cambridge (1996)Google Scholar
  3. 3.
    Brayton, R.K., Rudell, R., Sangiovnni-Vincentelli, A., Wang, A.R.: MIS: A multiple-level logic optimization system. In: IEEE Trans. on CAD, vol. CAD-6, pp. 1062–1081 (November 1987)Google Scholar
  4. 4.
    Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput., C-35(8), 677–691 (1986)Google Scholar
  5. 5.
    Bryant, R.E., Chen, Y.-A.: Verification of arithmetic functions with binary moment diagrams. In: Proc. of 32nd ACM/IEEE Design Automation Conference (DAC 1995), session 32.1 (June 1995)Google Scholar
  6. 6.
    Coudert, O.: Solving graph optimization problems with ZBDDs. In: Proc. of IEEE The European Design and Test Conference (ED&TC 1997), pp. 244–248 (March 1997)Google Scholar
  7. 7.
    Goethals, B., Javeed Zaki, M. (eds.): Frequent Itemset Mining Dataset Repository, Frequent Itemset Mining Implementations (FIMI 2003) (2003), http://fimi.cs.helsinki.fi/data/
  8. 8.
    Hayashi, Y., Matsuki, J.: Determination of Optimal System Configuration in Japanese Secondary Power Systems. IEEE Trans. on Power Systems 18(1), 394–399 (2003)CrossRefGoogle Scholar
  9. 9.
    Minato, S.: BEM-II: An Arithmetic Boolean Expression Manipulator Using BDDs. IEICE Trans. Fundamentals E76-A(10), 1721–1729 (1993)Google Scholar
  10. 10.
    Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proc. 30th ACM/IEEE Design Automation Conf (DAC 1993), pp. 272–277 (1993)Google Scholar
  11. 11.
    Minato, S.: Calculation of Unate Cube Set Algebra Using Zero-Suppressed BDDs. In: Proc. of 31st ACM/IEEE Design Automation Conference (DAC 1994), pp. 420–424 (June 1994)Google Scholar
  12. 12.
    Minato, S.: Implicit Manipulation of Polynomials Using Zero-Suppressed BDDs. In: Proc. of IEEE The European Design and Test Conference (ED&TC 1995), pp. 449–454 (March 1995)Google Scholar
  13. 13.
    Minato, S.: Binary Decision Diagrams and Applications for VLSI CAD. Kluwer Academic Publishers, Dordrecht (November 1996)Google Scholar
  14. 14.
    Minato, S.: Fast Factorization Method for Implicit Cube Set Representation. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 15(4), 377–384 (1996)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Minato, S.: Zero-suppressed BDDs and Their Applications. International Journal on Software Tools for Technology Transfer (STTT) 3(2), 156–170 (2001)zbMATHGoogle Scholar
  16. 16.
    Minato, S., Arimura, H.: Efficient Combinatorial Item Set Analysis Based on Zero-Suppressed BDDs. In: IEEE/IEICE/IPSJ International Workshop on Challenges in Web Information Retrieval and Integration (WIRI 2005), pp. 3–10 (April 2005)Google Scholar
  17. 17.
    Miyazaki, T.: Boolean-based formulation for data path synthesis. In: IEEE Asia-Pasific Conference on Circuits and Systems APCCAS 1992, pp. 201–205 (December 1992)Google Scholar
  18. 18.
    Okuno, H.G.: Reducing Combinatorial Explosions in Solving Search-Type Combinatorial Problems with Binary Decision Diagram. Trans of Information Processing Soc. Japan (IPSJ) (in Japanese) 35(5), 739–753 (1994)Google Scholar
  19. 19.
    Okuno, H.G., Minato, S., Isozaki, H.: On the properties of combination set operations. Information Processing Letters 66, 195–199 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Zheng, Z., Kohavi, R., Mason, L.: Real World Performance of Association Rule Algorithms. In: Proc. of ACM SIGKDD conference KDD 2001, pp. 401–406 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shin-ichi Minato
    • 1
  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

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