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International Symposium on Stochastic Algorithms

SAGA 2005: Stochastic Algorithms: Foundations and Applications pp 107–115Cite as

On Some Bounds on the Size of Branching Programs (A Survey)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3777))

Abstract

Previously it was shown by the author that it is possible to reduce obtaining of lower bounds on the complexity of Boolean functions for branching programs without restriction to obtaining of lower bounds on the complexity of minorants of the considered function for branching programs with restriction on the number of occurrences of a variable in a path (read-k-times branching programs). Theorems that reduce the problem of nonlinear lower bounds on the complexity of Boolean functions for branching programs to the problem of lower bounds on the complexity of covering of the set of “ones” of a Boolean function by functions of the defined type or to the problem of obtaining the upper bounds on the number of “ones” of a Boolean function in i-faces of a cube of the defined dimension are presented. A survey of bounds obtained by this method is given.

This research was supported by the Russian foundation for Basic Researches (Grant 03-01-00634) and President program for support of Leading Scientific schools (Grant 313.2003.1).

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References

  1. Babai, L., Pudlák, P., Rödl, V., Szemerédi, M.: Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science 74, 313–324 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bollig, B., Sauerhoff, M., Wegener, I.: On the nonappoximability on boolean functions by OBDD and read-k-times branching programs. Information and Computation 178, 263–278 (2002)

    MATH  MathSciNet  Google Scholar 

  3. Borodin, A., Razborov, A., Smolensky, R.: On lower bounds for read-k-times branching programs. Computational Complexity 3(1), 1–18 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. MacWilliams, F.J., Sloane, N.J.F.: The theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  5. Nečiporuk, E.: On a Boolean function. Soviet Math. Doklady 7, 999–1000 (1966)

    Google Scholar 

  6. Okol’nishnikova, E.A.: Lower bounds on complexity for the realization of characteristic functions of binary codes by binary programs. Metody Diskret. Anal. 51, 61–83 (1991) (in Russian) (see also: Siberian Adv. Math., 3(1), 152–166) (1993)

    Google Scholar 

  7. Okol’nishnikova, E.A.: On the hierarchy of nondeterministic branching k-programs. In: Chlebus, B.S., Czaja, L. (eds.) FCT 1997. LNCS, vol. 1279, pp. 376–387. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Okol’nishnikova, E.A.: On one method of obtaining of lower bounds of Boolean functions for nondeterministic branching programs. Diskretn. Anal. Issled. Oper. Ser. 1 8(4), 76–102 (2001) (in Russian) (see also: ECCC TR02-020,2002), available at http://www.eccc.uni-tri.de/eccc/ (in English)

  9. Okol’nishnikova, E.A.: On the complexity of nondeterministic branching programs for characteristic functions of Reed–Muller codes. Diskretn. Anal. Issled. Oper. Ser. 1 10(3), 67–81 (2003) (in Russian)

    Google Scholar 

  10. Pudlák, P.: A lower bound on complexity of branching programs. In: Chytil, M.P., Koubek, V. (eds.) MFCS 1984. LNCS, vol. 176, pp. 480–489. Springer, Heidelberg (1984)

    Chapter  Google Scholar 

  11. Pudlák, P.: The hierarchy of Boolean circuits. Comput. Artificial Intelligence 6(5), 449–468 (1987)

    MATH  MathSciNet  Google Scholar 

  12. Razborov, A.A.: Lower bounds on the complexity of symmetric Boolean functions by switching-rectifier circuits. Matemat. zametki 48(6), 79–90 (1990)

    MATH  MathSciNet  Google Scholar 

  13. Razborov, A.A.: Lower bounds for deterministic and nondeterministic branching program. In: Budach, L. (ed.) FCT 1991. LNCS, vol. 529, pp. 47–61. Springer, Heidelberg (1991)

    Google Scholar 

  14. Sauerhoff, M.: Randomness versus nondeterminism for read-once and read-k branching programs. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 105–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Sauerhoff, M.: Randomness versus nondeterminism for read-once and read-k branching programs. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 307–318. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. Thathachar, J.S.: On separating the read-k-times program hierarchy. In: Proc. of the 30th annual ACM Symposium on theory of computing, pp. 652–662 (1998)

    Google Scholar 

  17. Wei, V.K.: Generalized Hamming weights for linear codes. IEEE Trans. on Inform. Theory 37(5), 1412–1418 (1991)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences, prospect acad. Koptjuga, 4, Novosibirsk, 630090, Russia

    Elizaveta A. Okol’nishnikova

Authors
  1. Elizaveta A. Okol’nishnikova
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Editor information

Editors and Affiliations

  1. Department of Discrete Mathematics, Leninskie Gory, Moscow State University, 119992, Moscow, Russia

    Oleg B. Lupanov  & Oktay M. Kasim-Zade  & 

  2. Faculty of Mechanics and Mathematics, Department of Discrete Mathematics, Leninskie Gory, Moscow State University, 119992, Moscow, Russia

    Alexander V. Chaskin

  3. Department of Computer Science, King’s College London, WC2R 2LS, London, UK

    Kathleen Steinhöfel

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Okol’nishnikova, E.A. (2005). On Some Bounds on the Size of Branching Programs (A Survey). In: Lupanov, O.B., Kasim-Zade, O.M., Chaskin, A.V., Steinhöfel, K. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2005. Lecture Notes in Computer Science, vol 3777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11571155_11

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  • DOI: https://doi.org/10.1007/11571155_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29498-6

  • Online ISBN: 978-3-540-32245-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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