分散的单计数器语言的秩小于$ω^2$
Scattered one-counter languges have rank less than $ω^2$
摘要：
如果线性排序是某些上下文无关语言的字典排序，则称为上下文无关;如果线性排序没有稠密的子排序，则称为分散的。每一个离散排序都有一个相关的序数，称为它的秩。已知的是，分散的上下文无关（分别是规则的）排序的秩小于$ω^ω$（分别为$ω$）。本文证实了一计数器语言的秩小于$ω^2$的猜想。
英文摘要：
A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is known that scattered context-free (regular, resp.) orderings have rank less than $ω^ω$ ($ω$, resp). In this paper we confirm the conjecture that one-counter languages have rank less than $ω^2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
