关于齐次幺半群的有限完全重写系统、有限导子型和自动性
On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids
摘要：
本文从计算的角度研究了一类由齐次（保长）关系定义的保序幺半群。研究了这类幺半群的允许有限完全重写系统、有限导子型重写系统、自动重写系统和双自动重写系统的性质。第一个主要结果表明，对于这些性质和它们的否定的任何相容组合，存在一个齐次幺半群恰好具有这种性质的组合。然后，我们引入了新的概念，抽象的Rees-可扩展性（一个类似的概念，抽象的可扩展性的群体），以显示相同的声明，即使限制注意类的$n$ -ary齐次幺半群（其中每一边的每一个关系有固定的长度$n$）。然后，我们引入了一个新的编码技术，使我们能够部分地扩展结果的类的$n$ -ary multihomogeneous幺半群。
英文摘要：
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of $n$-ary homogeneous monoids (where every side of every relation has fixed length $n$). We then introduce a new encoding technique that allows us to extend the result partially to the class of $n$-ary multihomogenous monoids.
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