Some remarks on presentations by finite Church-Rosser Thue systems

  • Volker Diekert
Contributed Papers Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 247)


An infinite cancellative monoid where the classes of the syntactical congruence of its center form a finite group has no presentation by a finite Church-Rosser Thue System unless the monoid is isomorphic to ℤ or ℕ. This generalizes a result of Avenhaus et al. [1] on commutative monoids.

An infinite group with an abelian subgroup of finite index admits a finite Church-Rosser Thue presentation if and only if the group is isomorphic to ℤ or isomorphic to the free product ℤ / 2ℤ * ℤ / 2ℤ.

A group having a finite Church-Rosser Thue presentation is proved to be context-free.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Volker Diekert
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2

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