Communication Gap for Finite Memory Devices

  • Tomasz Jurdziński
  • Mirosław Kutyłowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)


So far, not much is known on communication issues for computations on distributed systems, where the components are weak and simultaneously the communication bandwidth is severely limited. We consider synchronous systems consisting of finite automata which communicate by sending messages while working on a shared read-only data. We consider the number of messages necessary to recognize a language as a its complexity measure.

We present an interesting phenomenon that the systems described require either a constant number of messages or at least Ω((log log log n)c) of them (in the worst case) for input data of length n and some constant c. Thus, in the hierarchy of message complexity classes there is a gap between the languages requiring only O(1) messages and those that need a non-constant number of messages. We show a similar result for systems of one-way automata. In this case, there is no language that requires ω(1) and o(log n) messages (in the worst case). These results hold for any fixed number of automata in the system.

The lower bound arguments presented in this paper depend very much on results concerning solving systems of diophantine equations and in- equalities.


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  1. 1.
    P. Beame, M. Tompa, P. Yan, Communication-Space Tradeoffs for Unrestricted Protocols, SICOMP 23 (1994), 652–661.zbMATHMathSciNetGoogle Scholar
  2. 2.
    P. J. Cohen, Decision procedures for real and p-adic fields, Comm. on Pure and Applied Math. 22 (1969), 131–151.zbMATHCrossRefGoogle Scholar
  3. 3.
    E. Contejean, H. Devie, An efficient algorithm for solving systems of diophantine equations, Information and Computation 113 (1994), 143–172.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    J. von zur Gathen, M. Sieveking, A bound on solutions of linear integer equalities and inequalities, Proc. of the AMS 72(1) (1978), 155–158.zbMATHCrossRefGoogle Scholar
  5. 5.
    M. Holzer, Multi-Head Finite Automata: Data-Independent Versus Data-Dependent Computations, Proc. MFCS’97, LNCS 1295, Springer Verlag, Berlin, 1997, 299–309.Google Scholar
  6. 6.
    J. Hopcroft, J.D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979.Google Scholar
  7. 7.
    T. Jurdziński, Communication Aspects of Computation of Systems of Finite Automata, Wrocław University, 2000. (
  8. 8.
    T. Jurdziński, M. Kutyłowski, K. Loryś, Multiparty finite computations, in Computing and Combinatorics, Proc. COCOON’99, LNCS 1627, Springer Verlag, Berlin, 1999, 318–329.CrossRefGoogle Scholar
  9. 9.
    L. Lipshitz, The diophantine problem for addition and divisibility, J. AMS 235 (1978), 271–283.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    L. Lipshitz, Some remarks on the diophantine problem for addition and divisibility, Bull. Soc. Math Belg. 33 (1981), 41–52.zbMATHMathSciNetGoogle Scholar
  11. 11.
    Ju. Matijasevič, Hilbert’s tenth problem, Foundations in Computing Series, MIT Press, Cambridge, 1993.Google Scholar
  12. 12.
    V. Mitrana, On the degree of communication in parallel communicating finite automata systems, Journal of Automata, Languages and Computation Vol. 5, 3(2000), 301–314.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tomasz Jurdziński
    • 1
    • 2
  • Mirosław Kutyłowski
    • 3
    • 4
  1. 1.Institute of Computer ScienceWrocław UniversityGermany
  2. 2.Department of Computer ScienceTechnical University of ChemnitzGermany
  3. 3.Department of Mathematics and Computer SciencePoznań UniversityPoland
  4. 4.Institute of MathematicsWrocław University of TechnologyGermany

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