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Annual Asian Computing Science Conference

ASIAN 1996: Concurrency and Parallelism, Programming, Networking, and Security pp 23–32Cite as

Relations among parallel and sequential computation models

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1179))

Abstract

This paper relates uniform small-depth circuit families as a parallel computation model with the complexity of polynomial time Turing machines. Among the consequences we obtain are: (a) a collapse of two circuit classes is equivalent to a relativizable collapse of the two corresponding polynomial time classes; and (b) a collapse of uniformity conditions for small depth circuits is equivalent to a related absolute (i.e., unrelativized) collapse in the polynomial time world.

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References

  1. E. Allender and V. Gore. On strong separations from AC0. In Proceedings 8th Fundmentals of Computation Theory, volume 529 of Springer Lecture Notes in Computer Science, pages 1–15, 1991.

    Google Scholar 

  2. E. Allender and U. Hertrampf. Depth reduction for circuits of unbounded fan-in. Information & Computation, 112:217–238, 1994.

    Google Scholar 

  3. E. Allender. P-uniform circuit complexity. Journal of the Association for Computing Machinery, 36:912–928, 1989.

    Google Scholar 

  4. E. Allender and K. W. Wagner. Counting hierarchies: polynomial time and constant depth circuits. Bulleting of the EATCS, 40:182–194, 1990.

    Google Scholar 

  5. D. A. Mix Barrington. Quasipolynomial size circuit classes. In Proceedings 7th Structure in Complexity Theory, pages 86–93. IEEE Computer Society Press, 1992.

    Google Scholar 

  6. D. P. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. International Series in Computer Science. Prentice Hall, 1994.

    Google Scholar 

  7. D. P. Bovet, P. Crescenzi, and R. Silvestri. A uniform approach to define complexity classes. Theoretical Computer Science, 104:263–283, 1992.

    Article  Google Scholar 

  8. J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I. Springer Verlag, 2nd edition, 1995.

    Google Scholar 

  9. R. Beigel, J. Gill, and U. Hertrampf. Counting classes: thresholds, parity, mods, and fewness. In Proceedings 7th Symposium on Theoretical Aspects of Computer Science, volume 415 of Lecture Notes in Computer Science, pages 49–57. Springer-Verlag, 1990.

    Google Scholar 

  10. D. A. Mix Barrington, N. Immerman, and H. Straubing. On uniformity within NC1. Journal of Computer and System Sciences, 41:274–306, 1990.

    Article  Google Scholar 

  11. R. V. Book. Tally languages and complexity classes. Information and Control, 26:186–194, 1974.

    Article  Google Scholar 

  12. A. K. Chandra, D. Kozen, and L. J. Stockmeyer. Alternation. Journal of the ACM, 28:114–133, 1981.

    Article  Google Scholar 

  13. H. Caussinus, P. McKenzie, D. Thérien, and H. Vollmer. Nondeterministic NC1 computation. In Proceedings 11th Computational Complexity, pages 12–21. IEEE Computer Society Press, 1996.

    Google Scholar 

  14. M. Furst, J. B. Saxe, and M. Sipser. Parity, circuits, and the polynomialtime hierarchy. Mathematical Systems Theory, 17:13–27, 1984.

    Article  Google Scholar 

  15. J. Håstad. Computational Limitations of Small Depth Circuits. MIT Press, Cambridge, 1988.

    Google Scholar 

  16. U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer, and K. W. Wagner. On the power of polynomial time bit-reductions. In Proceedings 8th Structure in Complexity Theory, pages 200–207, 1993.

    Google Scholar 

  17. U. Hertrampf, H. Vollmer, and K. W. Wagner. On balanced vs. unbalanced computation trees. Mathematical Systems Theory, 29:411–421, 1996.

    Google Scholar 

  18. B. Jenner, P. McKenzie, and D. Thérien. Logspace and logtime leaf languages. In 9th Annual Conference Structure in Complexity Theory, pages 242–254, 1994.

    Google Scholar 

  19. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  20. W. L. Ruzzo. On uniform circuit complexity. Journal of Computer and Systems Sciences, 21:365–383, 1981.

    Article  Google Scholar 

  21. K. Regan and H. Vollmer. Gap-languages and log-time complexity classes. Technical report, Department of Computer Science, SUNY Buffalo, 1995. Submitted for publication.

    Google Scholar 

  22. J. Toran. Complexity classes defined by counting quantifiers. Journal of the ACM, 38:753–774, 1991.

    Google Scholar 

  23. N. Vereshchagin. Relativizable and non-relativizable theorems in the polynomial theory of algorithms. Izvestija Rossijskoj Akademii Nauk, 57:51–90, 1993.

    Google Scholar 

  24. K. W. Wagner. Some observations on the connection between counting and recursion. Theoretical Computer Science, 47:131–147, 1986.

    Article  Google Scholar 

  25. C. Wrathall. Complete sets and the polynomial-time hierarchy. Theoretical Computer Science, 3:23–33, 1977.

    Article  Google Scholar 

  26. A. C. C. Yao. Separating the polynomial-time hierarchy by oracles. In Proceedings 26th Foundations of Computer Science, pages 1–10. IEEE Computer Society Press, 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Würzburg, Am Exerzierplatz 3, D-97072, Würzburg, Germany

    Heribert Vollmer

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  1. Heribert Vollmer
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Joxan Jaffar Roland H. C. Yap

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© 1996 Springer-Verlag Berlin Heidelberg

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Vollmer, H. (1996). Relations among parallel and sequential computation models. In: Jaffar, J., Yap, R.H.C. (eds) Concurrency and Parallelism, Programming, Networking, and Security. ASIAN 1996. Lecture Notes in Computer Science, vol 1179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027776

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  • DOI: https://doi.org/10.1007/BFb0027776

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62031-0

  • Online ISBN: 978-3-540-49626-7

  • eBook Packages: Springer Book Archive

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