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Randomized Branching Programs

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Stochastic Algorithms: Foundations and Applications (SAGA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2264))

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Abstract

Branching programs are a graphical representation of Boolean functions which are considered as a nonuniform model of computation in complexity theory and are also used as a data structure in practice. The talk discusses randomized variants of branching programs which allow to study the relative power of deterministic, nondeterministic, and randomized algorithms in a scenario where space is the primary resource.

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References

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

    Google Scholar 

  2. F. Ablayev and M. Karpinski. On the power of randomized branching programs. In Proc. of the 23rd Int. Coll. on Automata, Languages, and Programming (ICALP), LNCS 1099, 348–356. Springer, 1996.

    Google Scholar 

  3. M. Ajtai. Determinism versus non-determinism for linear time RAMs with memory restrictions. In Proc. of the 31st Ann. ACM Symp. on Theory of Computing (STOC), 632–641, 1999.

    Google Scholar 

  4. M. Ajtai. A non-linear time lower bound for Boolean branching programs. In Proc. of the 40th IEEE Symp. on Foundations of Computer Science (FOCS), 60–70, 1999.

    Google Scholar 

  5. A. E. Andreev, A. E. F. Clementi, J. D. P. Rolim, and L. Trevisan. Weak random sources, hitting sets, and BPP simulations. In Proc. of the 38th IEEE Symp. on Foundations of Computer Science (FOCS), 264–272, 1997.

    Google Scholar 

  6. A. E. Andreev, A. E. F. Clementi, J. D. P. Rolim, and L. Trevisan. Weak random sources, hitting sets, and BPP simulations. SIAM J. Comp., 28(6):2103–2116, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Beame, M. Saks, X. Sun, and E. Vee. Super-linear time-space tradeoff lower bounds for randomized computation. In Proc. of the 41st IEEE Symp. on Foundations of Computer Science (FOCS), 2000.

    Google Scholar 

  8. P. Beame, M. Saks, and J. S. Thathachar. Time-space tradeoffs for branching programs. In Proc. of the 39th IEEE Symp. on Foundations of Computer Science (FOCS), 254–263, 1998.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Cobham. The recognition problem for the set of perfect squares. In Proc. of the 7th Symposium on Switching an Automata Theory (SWAT), 78–87, 1966.

    Google Scholar 

  11. R. Impagliazzo and A. Wigderson. P = BPP if E requires exponential circuits: Derandomizing the XOR lemma. In Proc. of the 29th Ann. ACM Symp. on Theory of Computing (STOC), 220–228, 1997.

    Google Scholar 

  12. K.-I. Ko. Some observations on the probabilistic algorithms and NP-hard problems. Information Processing Letters, 14(1):39–43, Mar. 1982.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. A. Okol’nishnikova. On lower bounds for branching programs. Siberian Advances in Mathematics, 3(1):152–166, 1993.

    MathSciNet  Google Scholar 

  14. P. Pudlák and S. Zák. Space complexity of computations. Technical report, Univ. Prague, 1983.

    Google Scholar 

  15. M. Sauerho.. Lower bounds for randomized read-k-times branching programs. In Proc. of the 15th Ann. Symp. on Theoretical Aspects of Computer Science (STACS), LNCS 1373, 105–115. Springer, 1998.

    Google Scholar 

  16. M. Sauerho.. Complexity Theoretical Results for Randomized Branching Programs. PhD thesis, Univ. of Dortmund. Shaker, Aachen, 1999.

    Google Scholar 

  17. M. Sauerho.. 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. To appear in Computational Complexity.

    Google Scholar 

  18. M. Sauerho.. Approximation of Boolean functions by combinatorial rectangles. Technical Report 58, Electr. Coll. on Comp. Compl., 2000.

    Google Scholar 

  19. J. Thathachar. On separating the read-k-times branching program hierarchy. In Proc. of the 30th Ann. ACM Symp. on Theory of Computing (STOC), 653–662, 1998.

    Google Scholar 

  20. I. Wegener. On the complexity of branching programs and decision trees for clique functions. Journal of the ACM, 35(2):461–471, Apr. 1988.

    Article  MATH  MathSciNet  Google Scholar 

  21. I. Wegener. Branching Programs and Binary Decision Diagrams—Theory and Applications. Monographs on Discrete and Applied Mathematics. SIAM, Philadelphia, PA, 2000.

    Google Scholar 

  22. A. Wigderson. De-randomizing BPP: The state of the art. In Proc. of the 14th IEEE Int. Conf. on Computational Complexity, 1999.

    Google Scholar 

  23. S. Žák. An exponential lower bound for one-time-only branching programs. In Proc. of the 11th Int. Symp. on Mathematical Foundations of Computer Science (MFCS), LNCS 176, 562–566. Springer, 1984.

    Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Sauerho., M. (2001). Randomized Branching Programs. In: Steinhöfel, K. (eds) Stochastic Algorithms: Foundations and Applications. SAGA 2001. Lecture Notes in Computer Science, vol 2264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45322-9_4

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  • DOI: https://doi.org/10.1007/3-540-45322-9_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43025-4

  • Online ISBN: 978-3-540-45322-2

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