On the insertion of n-powers
On the insertion of n-powers
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关于n次幂的插入
DOI：
10.23638/dmtcs-21-3-5
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
O. Klíma
中科院分区：
文献类型：
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作者：
J. Almeida;O. Klíma
在代数方面，在单词中插入$n$幂可以在语言水平上通过考虑由不等式$1\le x^n$定义的有序模群的伪变来建模。我们将这个伪变种与其他几个有序半群的自然伪变种以及与由单位x^n=1$定义的群的Burnside伪变种相关的半群的自然伪变种进行了比较。特别地，我们感兴趣的是确定它生成的一元群的伪变种，这可以看作是确定在$n$幂插入下封闭的正则语言类的布尔闭包的问题。我们给出了一个简单上界，并证明了它满足所有伪恒等式，这些伪恒等式可以从$1\le x^n$证明，其中两边都是关于上界的正则元素。
In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other natural pseudovarieties of ordered monoids and of monoids associated with the Burnside pseudovariety of groups defined by the identity $x^n=1$. In particular, we are interested in determining the pseudovariety of monoids that it generates, which can be viewed as the problem of determining the Boolean closure of the class of regular languages closed under $n$-power insertions. We exhibit a simple upper bound and show that it satisfies all pseudoidentities which are provable from $1\le x^n$ in which both sides are regular elements with respect to the upper bound.