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Multi-party Finite Computations

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Computing and Combinatorics (COCOON 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

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Abstract

We consider systems consisting of a finite number of finite automata which communicate by sending messages. We consider number of messages necessary to recognize a language as a complexity measure of the language. We feel that these considerations give a new insight into computational complexity of problems computed by read-only devices in multiprocessor systems. Our considerations are related to multi-party communication complexity, but we make a realistic assumption that each party has a limited memory.

We show a number of hierarchy results for this complexity measure: for each constant k there is a language, which may be recognized with k + 1 messages and cannot be recognized with k − 1 messages. We give an example of a language that requires Θ(log log n) messages and claim that 03A9;(log log(n)) messages are necessary, if a language requires more than a constant number of messages. We present a language that requires Θ(n) messages. For a large family of functions f, f(n) = ω(log log n), f(n) = o(n), we prove that there is a language which requires Θ(f(n)) messages. Finally, we present functions that require ω(n) messages.

partially supported by Komitet Badaffin Naukowych, grant 8 T11C 032 15

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Wrocław University, Wrocław

    Tomasz Jurdziński, Mirosław Kutyłowski & Krzysztof Loryś

  2. Department of Mathematics and Computer Science, Poznań University, Poznań

    Mirosław Kutyłowski

Authors
  1. Tomasz Jurdziński
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  2. Mirosław Kutyłowski
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  3. Krzysztof Loryś
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Jurdziński, T., Kutyłowski, M., Loryś, K. (1999). Multi-party Finite Computations. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_32

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  • DOI: https://doi.org/10.1007/3-540-48686-0_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

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