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Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

Extended Abstract
  • Beate Bollig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

Branching programs are a well established computation model for Boolean functions, especially read-once branching programs have been studied intensively. In this paper the expressive power of nondeterministic read-once branching programs, i.e., the class of functions representable in polynomial size, is investigated. For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented. Furthermore, the first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven.

Keywords

Boolean Function Turing Machine Communication Complexity Expressive Power Boolean Variable 
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References

  1. 1.
    Ajtai, M. (1999). A non-linear time lower bound for Boolean branching programs. Proc. of 40th FOCS, 60–70.Google Scholar
  2. 2.
    Alon, N. and Maass, W. (1988). Meanders and their applications in lower bound arguments. Journal of Computer and System Sciences 37, 118–129.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bollig, B., Sauerhoff, M., Sieling, D., and Wegener, I. (1993). Read-k times ordered binary decision diagrams. Efficient algorithms in the presence of null chains. Tech. Report 474, Univ. Dortmund.Google Scholar
  4. 4.
    Bollig, B. and Wegener, I. (1998). Completeness and non-completeness results with respect to read-once projections. Information and Computation 143, 24–33.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bollig, B. and Wegener, I. (1999). Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory of Computing Systems 32, 487–503.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Borodin, A., Razborov, A., and Smolensky, R. (1993). On lower bounds for read-k-times branching programs. Comput. Complexity 3, 1–18.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bryant, R. E. (1986). Graph-based algorithms for Boolean manipulation. IEEE Trans. on Computers 35, 677–691.zbMATHCrossRefGoogle Scholar
  8. 8.
    Bryant, R. E. (1991). On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. on Computers 40, 205–213.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Gergov, J. (1994). Time-space trade-offs for integer multiplication on various types of input oblivious sequential machines. Information Processing Letters 51, 265–269.CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gergov, J. and Meinel, C. (1994). Efficient Boolean manipulation with OBDDs can be extended to FBDDs. IEEE Trans. on Computers 43, 1197–1209.zbMATHCrossRefGoogle Scholar
  11. 11.
    Hromkovič, J. (1997). Communication Complexity and Parallel Computing. Springer.Google Scholar
  12. 12.
    Hromkovič, J. and Sauerhoff, M. (2000). Communications with restricted nondeterminism and applications to branching program complexity. Proc. of 17th STACS, Lecture Notes in Computer Science 1770, 145–156.Google Scholar
  13. 13.
    Jain, J., Abadir, M., Bitner, J., Fussell, D. S., and Abraham, J. A. (1992). Functional partitioning for verification and related problems. Brown/MIT VLSI Conference, 210–226.Google Scholar
  14. 14.
    Kushilevitz, E. and Nisan, N. (1997). Communication Complexity. Cambridge University Press.Google Scholar
  15. 15.
    Meinel, C. (1990). Polynomial size Ω-branching programs and their computational power. Information and Computation 85, 163–182.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Ponzio, S. (1998). A lower bound for integer multiplication with read-once branching programs. SIAM Journal on Computing 28, 798–815.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Sauerhoff, M. (1999). Computing with restricted nondeterminism: The dependence of the OBDD size on the number of nondeterministic variables. Proc. of 19th FST & TCS, Lecture Notes in Computer Science 1738, 342–355.Google Scholar
  18. 18.
    Savický, P. and Sieling, D. (2000). A hierarchy result for read-once branching programs with restricted parity nondeterminism. Preprint.Google Scholar
  19. 19.
    Sieling, D. and Wegener, I. (1995). Graph driven BDDs-a new data structure for Boolean functions. Theoretical Computer Science 141, 283–310.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Thathachar, J. (1998). On separating the read-k-times branching program hierarchy. Proc. of 30th Ann. ACM Symposium on Theory of Computing (STOC), 653–662.Google Scholar
  21. 21.
    Wegener, I. (1987). The Complexity of Boolean Functions Wiley-Teubner.Google Scholar
  22. 22.
    Wegener, I. (2000). Branching Programs and Binary Decision Diagrams-Theory and Applications SIAM Monographs on Discrete Mathematics and Applications. In print.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Beate Bollig
    • 1
  1. 1.FB Informatik, LS2Univ. DortmundDortmundGermany

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