Learning ordered binary decision diagrams

  • Ricard Gavaldà
  • David Guijarro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 997)


This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that finds the minimum obdd for the target respecting a given ordering. We also prove that both types of queries and the restriction to a given ordering are necessary if we want minimality in the output, unless P=NP. If learning has to occur with respect to the optimal variable ordering, polynomial-time learnability implies the approximability of two NP-hard optimization problems: the problem of finding the optimal variable ordering for a given obdd and the Optimal Linear Arrangement problem on graphs.


Polynomial Time Boolean Function Binary Decision Diagram Membership Query Deterministic Finite Automaton 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Angluin: “Learning regular sets from queries and counterexamples”. Information and Computation 75 (1987), 87–106.CrossRefGoogle Scholar
  2. 2.
    D. Angluin: “Queries and concept learning”. Machine Learning 2 (1988), 319–342.Google Scholar
  3. 3.
    D. Angluin: “Negative results for equivalence queries” Machine Learning 5 (1990), 121–150.Google Scholar
  4. 4.
    B. Bollig and I. Wegener: Improving the variable ordering of OBDDs is NP-complete. Technical Report # 542, Universität Dortmund (1994).Google Scholar
  5. 5.
    R.E. Bryant: “Symbolic boolean manipulation with ordered binary decision diagrams”. ACM Computing Surveys 24 (1992), 293–318.CrossRefGoogle Scholar
  6. 6.
    S. Fortune, J. Hopcroft, and E. Schmidt: “The complexity of equivalence and containment for free single variable program schemes”. Proc. 5th Intl. Colloquium on Automata, Languages, and Programming. Springer-Verlag Lecture Notes in Computer Science 62 (1978), 227–240.Google Scholar
  7. 7.
    M. Garey and D. Johnson: Computers and intractability: a guide to the theory of NP-completeness. Freeman 1979.Google Scholar
  8. 8.
    J. Gergov and C. Meinel: “On the complexity of analysis and manipulation of Boolean functions in terms of decision graphs”. Information Processing Letters 50 (1994), 317–322.Google Scholar
  9. 9.
    V. Raghavan and D. Wilkins: “Learning μ-branching programs with queries”. Proc. 6th COLT (1993), 27–36.Google Scholar
  10. 10.
    R.E. Schapire: The Design and Analysis of Efficient Learning Algorithms. MIT Press, 1992.Google Scholar
  11. 11.
    S. Tani, K. Hamaguchi, and S. Yajima: “The complexity of the optimal variable ordering problems for shared binary decision diagrams”, Proc. 4th Intl. Symposium ISAAC'93. Springer Verlag Lecture Notes in Computer Science 762 (1993), 389–398.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Ricard Gavaldà
    • 1
  • David Guijarro
    • 1
  1. 1.Department of Software (LSI)Universitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations