An algebraic approach to communication complexity

  • Jean-FranÇois Raymond
  • Pascal Tesson
  • Denis Thérien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)


Let M be a finite monoid: define C(k)(M) to be the maximum number of bits that need to be exchanged in the k-party communication game to decide membership in any language recognized by M. We prove the following:
  1. a)

    If M is a group then, for any k, C(k)(M) = O(1) if M is nilpotent of class k − 1 and C(k)(M) = θ(n) otherwise.

  2. b)

    If M is aperiodic, then C(2)(M) = O(1) if M is commutative, C(2)(M) = θ(log n) if M belongs to the variety DA but is not commutative and C(2)(M) = θ(n) otherwise.


We also show that when M is in DA, C(k)(M) = O(1) for some k and conjecture that this algebraic condition is also necessary.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jean-FranÇois Raymond
    • 1
  • Pascal Tesson
    • 1
  • Denis Thérien
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontréal (PQ)Canada

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