Abstract
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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References
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© 1987 Springer-Verlag Berlin Heidelberg
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Diekert, V. (1987). Some remarks on presentations by finite Church-Rosser Thue systems. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds) STACS 87. STACS 1987. Lecture Notes in Computer Science, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039612
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DOI: https://doi.org/10.1007/BFb0039612
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