论文标题
风格单体的热带表示和身份
Tropical Representations and Identities of the Stylic Monoid
论文作者
论文摘要
我们表现出每个有限级别等级的风格单体的忠实表示，是在热带半段上的上元素矩阵的单体。因此，我们表明，有限等级$ n $的风格单型生成伪库$ \ boldsymbol {\ Mathcal {j}} _ n $，它与Eilenberg的框架中的所有高度$ n $的分段测试语言相对应。由此，我们获得了有限等级的风格单体的方程理论，表明当且仅当$ n \ leq 3 $时，它们是有限的，并且它们的身份检查问题在线性时间内可以决定。我们还建立了风格单体和其他类似型的单素之间的连接，并解决了与造型单体的有限基础问题。
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank $n$ generates the pseudovariety $\boldsymbol{\mathcal{J}}_n$, which corresponds to the class of all piecewise testable languages of height $n$, in the framework of Eilenberg's correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if $n \leq 3$, and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution.
