On the descriptive power of term rewriting systems
Journal of Symbolic Computation
Divergence phenomena during completion
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
It is undecidable whether a finite special string-rewriting system presents a group
Discrete Mathematics
String-rewriting systems
Some properties of finite special string-rewriting systems
Journal of Symbolic Computation
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Following the course set by A. Markov (1951), S. Adjan (1958), and M. Rabin (1958), C. Ó'Dúnlaing (1983) has shown that certain properties of finitely generated Thue congruences are undecidable in general. Here we prove that many of these undecidability results remain valid even when only finitely generated Thue congruences on a fixed two-letter alphabet Σ 2 are considered. In contrast to a construction given by P. Schupp (1976) which applies to groups only, we use a modified version of a technical lemma from A. Markov's original paper. Based on this technical result we can carry the result of A. Sattler-Klein (1996), which says that certain Markov properties remain undecidable even when they are restricted to finitely generated Thue congruences that are decidable, over to the alphabet Σ 2.