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On the Non-deterministic Communication Complexity of Regular Languages

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Book cover Developments in Language Theory (DLT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5257))

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Abstract

In this paper we study the non-deterministic communication complexity of regular languages. We show that a regular language has either constant or at least logarithmic non-deterministic communication complexity. We prove several linear lower bounds which we know cover a wide range of regular languages with linear complexity. Furthermore we find evidence that previous techniques (Tesson and Thérien 2005) for proving linear lower bounds, for instance in deterministic and probabilistic models, do not work in the non-deterministic setting.

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References

  1. Ada, A.: Non-deterministic communication complexity of regular languages. Master’s thesis (2008)

    Google Scholar 

  2. Babai, L., Frankl, P., Simon, J.: Complexity classes in communication complexity theory (preliminary version). In: FOCS 1986: Proceedings of the 27th Annual IEEE Symposium on Foundations of Computer Science, pp. 337–347 (1986)

    Google Scholar 

  3. Babai, L., Nisan, N., Szegedy, M.: Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci. 45(2), 204–232 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Beame, P., Pitassi, T., Segerlind, N.: Lower bounds for Lovasz-Schrijver systems and beyond follow from multiparty communication complexity. SIAM Journal on Computing 37(3), 845–869 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Eilenberg, S.: Automata, Languages, and Machines. Academic Press, Inc., Orlando (1974)

    MATH  Google Scholar 

  6. Grolmusz, V.: Separating the communication complexities of MOD m and MOD p circuits. In: IEEE Symposium on Foundations of Computer Science, pp. 278–287 (1992)

    Google Scholar 

  7. Halstenberg, B., Reischuk, R.: On different modes of communication. In: STOC 1988: Proceedings of the twentieth annual ACM symposium on Theory of computing, pp. 162–172. ACM, New York (1988)

    Chapter  Google Scholar 

  8. Håstad, J., Goldmann, M.: On the power of small-depth threshold circuits. Computational Complexity 1, 113–129 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  10. Pin, J.-E.: A variety theorem without complementation. Russian Mathematics (Izvestija vuzov.Matematika) 39, 80–90 (1995)

    MathSciNet  Google Scholar 

  11. Pin, J.-E.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of formal languages, ch. 10, vol. 1, pp. 679–746. Springer, Heidelberg (1997)

    Google Scholar 

  12. Pin, J.-E., Weil, P.: Polynomial closure and unambiguous product. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 348–359. Springer, Heidelberg (1995)

    Google Scholar 

  13. Raymond, J.-F., Tesson, P., Thérien, D.: An algebraic approach to communication complexity. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 29–40. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Tesson, P., Thérien, D.: Complete classifications for the communication complexity of regular languages. Theory Comput. Syst. 38(2), 135–159 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. Journal of Computer and System Sciences 43(3), 441–466 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  16. Yao, A.C.-C.: Some complexity questions related to distributive computing (pre- liminary report). In: STOC 1979: Proceedings of the eleventh annual ACM symposium on Theory of computing, pp. 209–213. ACM Press, New York (1979)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science, McGill University,  

    Anil Ada

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  1. Anil Ada
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Masami Ito Masafumi Toyama

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© 2008 Springer-Verlag Berlin Heidelberg

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Ada, A. (2008). On the Non-deterministic Communication Complexity of Regular Languages. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-85780-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85779-2

  • Online ISBN: 978-3-540-85780-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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