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Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1738))

Abstract

It is well-known that an arbitrary nondeterministic Turing machine can be simulated with polynomial overhead by a so-called guess-and- verify machine. It is an open question whether an analogous simulation exists in the context of space-bounded computation. In this paper, a negative answer to this question is given for nondeterministic OBDDs. If we require that all nondeterministic variables are tested at the top of the OBDD, i. e., at the beginning of the computation, this may blow-up the size exponentially.

This is a consequence of the following main result of the paper. There is a sequence of Boolean functions f n : {0, 1}n → {0, 1} such that f n has nondeterministic OBDDs of polynomial size with O(n 1/3 log n) nondeterministic variables, but f n requires exponential size if only at most O(log n) nondeterministic variables may be used.

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References

  1. F. Ablayev. Randomization and nondeterminism are incomparable for polynomial ordered binary decision diagrams. In Proc. of the 24th Int. Coll. on Automata, Languages, and Programming (ICALP), LNCS 1256, 195–202. Springer, 1997. 344

    Google Scholar 

  2. R. E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Trans. Computers, C-35(8):677–691, Aug. 1986. 344

    Article  Google Scholar 

  3. K. Hosaka, Y. Takenaga, and S. Yajima. On the size of ordered binary decision diagrams representing threshold functions. In Proc. of the 5th Int. Symp. on Algorithms and Computation (ISAAC), LNCS 834, 584–592. Springer, 1994. 344

    Google Scholar 

  4. J. Hromkovič. Communication Complexity and Parallel Computing. EATCS Texts in Theoretical Computer Science. Springer, Berlin, 1997. 345

    Google Scholar 

  5. J. Hromkovič and M. Sauerhoff. Communication with restricted nondeterminism and applications to branching program complexity. Manuscript, 1999. 345, 346, 350

    Google Scholar 

  6. J. Hromkovič and G. Schnitger. Nondeterministic communication with a limited number of advice bits. In Proc. of the 28th Ann. ACM Symp. on Theory of Computing (STOC), 551–560, 1996. 344, 347

    Google Scholar 

  7. S. P. Jukna. Entropy of contact circuits and lower bounds on their complexity. Theoretical Computer Science, 57:113–129, 1988. 344

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Krause. Lower bounds for depth-restricted branching programs. Information and Computation, 91(1):1–14, Mar. 1991. 344

    Article  MATH  MathSciNet  Google Scholar 

  9. I. Kremer, N. Nisan, and D. Ron. On randomized one-round communication complexity. In Proc. of the 27th Ann. ACM Symp. on Theory of Computing (STOC), 596–605, 1995. 346

    Google Scholar 

  10. E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, Cambridge, 1997. 345

    MATH  Google Scholar 

  11. I. Newman. Private vs. common random bits in communication complexity. Information Processing Letters, 39:67–71, 1991. 344

    Article  MATH  MathSciNet  Google Scholar 

  12. A. A. Razborov. Lower bounds for deterministic and nondeterministic branching programs. In Proc. of Fundamentals of Computation Theory (FCT), LNCS 529, 47–60. Springer, 1991. 343

    Google Scholar 

  13. M. Sauerhoff. Complexity Theoretical Results for Randomized Branching Programs. PhD thesis, Univ. of Dortmund. Shaker, 1999. 344, 344, 344

    Google Scholar 

  14. M. Sauerhoff. On the size of randomized OBDDs and read-once branching programs for k-stable functions. In Proc. of the 16th Ann. Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 1563, 488–499. Springer, 1999. 344, 347

    Google Scholar 

  15. I. Wegener. The Complexity of Boolean Functions. Wiley-Teubner, 1987. 343

    Google Scholar 

  16. I. Wegener. Branching Programs and Binary Decision Diagrams-Theory and Applications. Monographs on Discrete and Applied Mathematics. SIAM, 1999. To appear. 343

    Google Scholar 

  17. A. C. Yao. Lower bounds by probabilistic arguments. In Proc. of the 24th IEEE Symp. on Foundations of Computer Science (FOCS), 420–428, 1983. 347

    Google Scholar 

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Sauerhoff, M. (1999). Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1999. Lecture Notes in Computer Science, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46691-6_28

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  • DOI: https://doi.org/10.1007/3-540-46691-6_28

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  • Print ISBN: 978-3-540-66836-7

  • Online ISBN: 978-3-540-46691-8

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