Theory of Computing Systems

, Volume 30, Issue 3, pp 249–283 | Cite as

A characterization and nearly linear-time equivalence test forμ-branching programs

  • V. Raghavan
  • D. Wilkins


We present a characterization ofμ-branching programs and a decomposition tree data structure which results from the characterization. We then show how the data structure can be used to test the equivalence of a pair ofn-nodeμ-branching programs inO((n)) time, whereα(n) is a functional inverse of the Ackermann function. In addition, we show that equivalence testing of-branching programs fork≥3 is co-NP-complete.


Boolean Function Equivalent Representation Equivalence Testing Decomposition Tree Block Tree 
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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  1. [1]
    S. B. Akers. Binary Decision Diagrams.IEEE Transaction on Computers, 27(6):509–516, 1978.zbMATHCrossRefGoogle Scholar
  2. [2]
    D. Angluin. Queries and Concept Learning.Machine Learning, 2:319–342, 1988.Google Scholar
  3. [3]
    D. Barrington. Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages inNC 1.Journal of Computer and System Sciences, 38:150–164, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    M. Blum, A. Chandra, and M. Wegman. Equivalence of Free Boolean Graphs can be Decided Probabilistically in Polynomial Time.Information Processing Letters, 10:80–82, 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    R. Bryant. Symbolic Boolean Manipulation with Ordered Binary-Decision Diagrams.ACM Computing Surveys, 24(3):293–318, 1992.CrossRefGoogle Scholar
  6. [6]
    R. L. Constable, H. B. Hunt, III, and S. Sahni. On the Computational Complexity of Scheme Equivalence.Proceedings of the 8th Princeton Conference on Information Sciences and Systems, pages 15–20, 1974.Google Scholar
  7. [7]
    S. Fortune, J. Hopcroft, and E. Schmidt. The Complexity of Equivalence and Containment for Free Single Variable Program Schemes.Lecture Notes in Computer Science: Automata, Languages Programming, 62:227–240, 1978.MathSciNetGoogle Scholar
  8. [8]
    J. Gergov and C. Meinel. Analysis and Manipulation of Boolean Functions in Terms of Decision Graphs.Graph-Theoretic Concepts in Computer Science. LNCS, volume 657, pages 310–320. Springer-Verlag, Berlin, 1992.CrossRefGoogle Scholar
  9. [9]
    J. Gergov and C. Meinel. Frontiers of Feasible and Probabilistic Feasible Boolean Manipulation with Branching Programs.STACS ’93. LNCS, volume 665, pages 576–585. Springer-Verlag, Berlin, 1993.CrossRefGoogle Scholar
  10. [10]
    T. Hancock. Identifyingμ-Formula Decision Trees with Queries.Proceedings of the Third Annual Workshop on Computational Learning Theory, pages 23–37, 1990.Google Scholar
  11. [11]
    C. Y. Lee. Representation of Switching Circuits by Binary-Decision Programs.Bell System Technical Journal, 38(4):985–999, 1959.MathSciNetGoogle Scholar
  12. [12]
    C. Meinel.Modified Branching Programs and Their Computational Power. LNCS, volume 370. Springer-Verlag, Berlin, 1989.zbMATHGoogle Scholar
  13. [13]
    S. Ponzio. A Lower Bound for Integer Multiplication with Read-Once Branching Programs.Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pages 130–139, 1995.Google Scholar
  14. [14]
    V. Raghavan and D. Wilkins. Learningμ-Branching Programs with Queries.Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory, pages 27–36, 1993.Google Scholar
  15. [15]
    R. E. Tarjan.Data Structures and Network Algorithms. SIAM, Philadelphia, PA, 1983.CrossRefGoogle Scholar
  16. [16]
    I. Wegener.The Complexity of Boolean Functions. Wiley, New York, 1987.zbMATHGoogle Scholar
  17. [17]
    D. Wilkins. Learning Restricted-Read Branching Programs with Queries. Ph.D. thesis, Vanderbilt University, 1995.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • V. Raghavan
    • 1
  • D. Wilkins
    • 2
  1. 1.Department of Computer ScienceVanderbilt UniversityNashvilleUSA
  2. 2.Department of Computer and Information ScienceUniversity of MississippiUniversityUSA

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