论文标题
一个单词hyperbolic特殊的单鞋，有不可证明的二芬太丁问题
A word-hyperbolic special monoid with undecidable Diophantine problem
论文作者
论文摘要
MONOID $ M $的Diophantine问题是决定任何给定方程式是否具有$ M $的解决方案的决策问题。在本说明中，我们给出了一个简单的示例，说明了一个无上文，有限的，特殊的单型$ m $，带有微不足道的单位，因此在$ m $中不可发现的二只问题。这回答了Garreta＆Gray在2019年提出的两个问题，并表明Dahmani＆Guirardel所证明的双曲线群中二磷酸群问题的可决定性并未推广到Word-Hyperbolic Monoids。
The Diophantine problem for a monoid $M$ is the decision problem to decide whether any given system of equations has a solution in $M$. In this note, we give a simple example of a context-free, word-hyperbolic, finitely presented, special monoid $M$ with trivial group of units, and such that the Diophantine problem is undecidable in $M$. This answers two questions asked by Garreta & Gray in 2019, and shows that the decidability of the Diophantine problem in hyperbolic groups, as proved by Dahmani & Guirardel, does not generalise to word-hyperbolic monoids.
