Abstract
For finitely presented monoids the finiteness problem, the free monoid problem, the trivial monoid problem, the group problem and the problem of commutativity are undecidable in general. On the other hand, these problems are all decidable for the class of finite presentations involving complete string rewriting systems. Thus the question arises whether these problems are also decidable for the class of finite presentations describing monoids which have decidable word problems. In this paper we present some results from the author's Doctoral Dissertation [Sa96] which answer this question in the negative and show that each of these problems is undecidable for the class of finitely presented monoids with decidable word problems admitting regular complete presentations as well as for the class of finitely presented monoids with tractable word problems.
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© 1997 Springer-Verlag Berlin Heidelberg
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Sattler-Klein, A. (1997). New undecidability results for finitely presented monoids. In: Comon, H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62950-5_62
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DOI: https://doi.org/10.1007/3-540-62950-5_62
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