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Communication Complexity and Lower Bounds for Sequential Computation

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Informatik

Part of the book series: TEUBNER-TEXTE zur Informatik ((TTZI,volume 1))

Abstract

Information-theoretic approaches for lower bound problems are discussed and two applications of Communication Complexity are presented.

The first application concerns one-tape Turing machines with an additional oneway input tape. It is shown that lower bounds on the Communication Complexity of a given language immediately imply lower bounds on the running time for this Turing machine model. Consequently, lower bounds for the Turing machine complexity of specific languages are derived. Emphasis is given to bounded-error probabilistic Turing machines, since no previous lower bounds have been obtained for this computation mode.

The second application concerns a real-time comparison between Schoenhage’s Storage Modification machines and the machine model of Kolmogorov and Uspen-skii. A non-standard model of Communication Complexity is defined. It is shown that non-trivial lower bounds for this communication model will imply that Storage Modification machines cannot be simulated in real time by Kolmogorov-Uspenskii machines.

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Bibliography

  1. H. Abelson, “Lower Bounds on Information Transfer in Distributed Computations”, Proc. 19th IEEE Symp. on Foundations of Computer Science, 1978, pp. 151–158.

    Google Scholar 

  2. L. Babai, P. Frankl and J. Simon, “BPP and the Polynomial Time Hierarchy in Communication Complexity Theory”, Proc. 27th Annual IEEE Symp. on Foundations of Computer Science, 1986, pp. 337–347.

    Google Scholar 

  3. L. Babai, N. Nisan and M. Szegedy, “Multiparty Protocols and Logspace-hard Pseudorandom Sequences”, Proc. 21st Annual ACM Symp. on Theory of Computing, 1989, pp. 1–11.

    Google Scholar 

  4. A.K. Chandra, M.L. Furst and R.J. Lipton, “Multi-party protocols”, Proc. 15th Annual ACM Symp. on Theory of Computing, 1983, pp. 94–99.

    Google Scholar 

  5. Y. Gurevich, “On Kolmogorov machines and related issues”, Bull, of EATCS, 1988.

    Google Scholar 

  6. Z. Galil, R. Kannan and E. Szemeredi, “On Nontrivial Separators for k-Page Graphs and Simulations by Nondeterministic One-Tape Turing Machines”, Proc. 18th Annual ACM Symp. on Theory of Computing, 1986, pp. 39–49.

    Google Scholar 

  7. J. Hastad and M. Goldmann, “On the Power of Small Depth Threshold Circuits”, Proc. Slst Annual IEEE Symp. on Foundations of Computer Science, 1990, pp. 610–618.

    Google Scholar 

  8. J.Y. Halpern, M.C. Loui, A.R. Meyer and D. Weise, “On Time Versus Space IIP”, Math. Systems Theory 19, 1986, pp. 13–28.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Hartmanis and R.E. Stearns, “On the Computational Complexity of Algorithms”, Trans. Amer. Math. Soc. , Vol. 117, 1965, pp. 285–306.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Kalyanasundaram, “Lower Bounds on Time, Space and Communication”, Ph. D. Dissertation, The Pennsylvania State University, Dec. 1988.

    Google Scholar 

  11. D. E. Knuth, “The Art of Computer Programming”, vol. 1, Addison-Wesley, Reading Ma., 1968, pp. 462–463.

    MATH  Google Scholar 

  12. B. Kalyanasundaram and G. Schnitger, “The Probabilistic Communication Complexity of Set Intersection”, Proc. 2nd Annual Conference on Structure in Complexity Theory, 1987, pp. 41–47. To appear in SIAM J. Disc. Math.

    Google Scholar 

  13. B. Kalyanasundaram and G. Schnitger, “On the Power of One-Tape Probabilistic Turing Machines”, Proc. 24th Annual Allerton Conference on Communication, Control and Computation, 1986, pp. 749–757.

    Google Scholar 

  14. A. N. Kolmogorov and V. A. Uspenskii, “On the Definition of an Algorithm”, AMS Transi 2nd series, vol. 29, 1963, pp. 217–245.

    MathSciNet  Google Scholar 

  15. M. Karchmer and A. Wigderson, “Monotone Circuits for Connectivity Require Superlogarithmic Depth”, SI AM J. Disc. Math 3, 1990, pp. 255–265.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. Lovasz, “Communication Complexity: A Survey”, Tech. Report CS-TR-204–89, Princeton University, 1989.

    Google Scholar 

  17. D.R. Luginbuhl and M.C. Loui, “Hierarchies and Space measures for pointer machines”, University of Illinois at Urbana Champaign, Tech. Rep. UILU-ENG-88–22445.

    Google Scholar 

  18. M. Li, L. Longpre and P.M.B. Vitanyi, “On the Power of the Queue”, Structure in Complexity Theory, Lecture Notes in Computer Science, Vol. 223, 1986, pp. 219–223.

    Article  MathSciNet  Google Scholar 

  19. M. Li and P.M.B Vitanyi, “Kolmogorov Complexity and its Applications”, in J. van Leeuwen ed., Handbook of Theoretical Computer Science, vol. A,

    Google Scholar 

  20. W. Maass, “Quadratic Lower Bounds for Deterministic and Nondeterminis-tic One-Tape Turing Machines”, Proc. 16th Annual ACM Symp. on Theory of Computing, 1984, pp. 401–408.

    Google Scholar 

  21. W. Maass, G. Schnitger and E. Szemeredi, “Two Tapes are Better than One for Off-line Turing Machines”, Proc. 19th Annual ACM Symp. on Theory of Computing, 1987, 94–100.

    Google Scholar 

  22. W. Maass, G. Schnitger, E. Szemeredi and G. Turan, “Two Tapes are Better than One for Off-line Turing Machines”, Tech. Report CS-90–30, Department of Computer Science, The Pennsylvania State University, 1990.

    Google Scholar 

  23. A. Orlitsky and A. El Gamal, “Communication Complexity”, in Y. Abu-Mostafa ed. Complexity in Information Theory, Springer Verlag, 1988.

    Google Scholar 

  24. W.J. Paul, “Kolmogorov’s Complexity and Lower Bounds”, in L. Budach ed., Proc. 2nd Internat. Conf. on Fundamentals of Computation Theory, Akademie Verlag, Berlin, 1979, pp. 325–334.

    Google Scholar 

  25. W.J. Paul, N. Pippenger, E. Szemeredi and W.T. Trotter, “On Determinism versus Nondeterminism and related Problems”, Proc. 24th Annual IEEE Symp. on Foundations of Computer Science 1983, pp. 429–438.

    Google Scholar 

  26. R. Paturi and J. Simon, “Lower Bounds on the Time of Probabilistic On-line Simulations”, Proc. 2th Annual IEEE Symp. on Foundations of Computer Science, 1983, pp. 343–350.

    Google Scholar 

  27. W.J. Paul, J.I. Seiferas and J. Simon, “An Information Theoretic Approach to to Time Bounds for On-line Computation”, J. Comput. System Sci. 23, 1981, pp. 108–126.

    Article  MathSciNet  MATH  Google Scholar 

  28. A.A. Razborov, “On the Distributional Complexity of Disjointness”, Proc. 17th ICALP, 1990, pp. 249–253.

    Google Scholar 

  29. R. Raz and A. Wigderson, “Monotone Circuits for Matching Require Linear Depth”, Proc. 22nd Annual ACM Symp. on Theory of Computing, 1990, pp. 287–292.

    Google Scholar 

  30. A. Schoenhage, “Storage Modification Machines”, SIAM J. Comput., 9, 1980, pp. 490–508.

    Article  MathSciNet  MATH  Google Scholar 

  31. C. P. Schnorr, “Rekursive Funktionen und ihre Komplexitaet”, Teubner, Stuttgart, 1974.

    MATH  Google Scholar 

  32. R. E. Tarjan, “A Class of Algorithms Which Require Nonlinear Time to Maintain Disjoint Sets”, J. Comput. System Sci. 18, 1979, pp. 110–127.

    Article  MathSciNet  MATH  Google Scholar 

  33. R. E. Tarjan, “Data Structures and Network Algorithms”, SIAM, 1983, page 2.

    Book  Google Scholar 

  34. C. D. Thompson, “Area-Time Complexity for VLSI”, Proc. 11th Annual ACM Symp. on Theory of Computing 1979, pp. 81–88.

    Google Scholar 

  35. P. Van Emde Boas, “Space Measures for Storage Modification Machines”, University of Amsterdam, Tech. Rep. FVI-UVA-87–16. To appear in Information Processing Letters.

    Google Scholar 

  36. A.C. Yao, “Some Complexity Questions Related to Distributed Computing”, Proc. 11th Annual ACM Symp. on Theory of Computing, 1979, pp. 209–213.

    Google Scholar 

  37. A.C. Yao, “Lower Bounds by Probabilistic Arguments”, Proc. 24th Annual IEEE Symp. on Foundations of Computer Science, 1983, pp. 420–428.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Pittsburgh, USA

    Bala Kalyanasundaram

  2. Dept. of Computer Science, Pennsylvania State University, USA

    Georg Schnitger

Authors
  1. Bala Kalyanasundaram
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  2. Georg Schnitger
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Editor information

Editors and Affiliations

  1. Universität Saarbrücken, Deutschland

    Johannes Buchmann , Harald Ganzinger  & Wolfgang J. Paul ,  & 

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© 1992 B. G. Teubner Verlagsgesellschaft, Leipzig

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Kalyanasundaram, B., Schnitger, G. (1992). Communication Complexity and Lower Bounds for Sequential Computation. In: Buchmann, J., Ganzinger, H., Paul, W.J. (eds) Informatik. TEUBNER-TEXTE zur Informatik, vol 1. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-95233-2_15

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  • DOI: https://doi.org/10.1007/978-3-322-95233-2_15

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-8154-2033-1

  • Online ISBN: 978-3-322-95233-2

  • eBook Packages: Springer Book Archive

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