发表机构
Akita University; Loughborough University（秋田大学; 拉夫堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二元语言（固定a、b及ab子序列数量）的存在与全称子序列普适性，给出精确算术刻画，并证明固定模式出现概率有多项式时间加法近似方案。
AI 中文摘要
与一个单词对应的普适性指数是最大的整数k，使得给定字母表上的每个长度为k的单词都作为该单词的子序列出现。相对于语言，这个概念可以从存在量词和全称量词两个方面进行研究，前者对应于语言中存在一个单词其普适性指数至少为k，而后者则考虑语言所包含的所有单词的指数。在这项工作中，我们研究了二元语言的存在性（存在-普适性）和全称性（全称-普适性）子序列普适性（如[Adamson et al., ISAAC 2023]所引入的），这些语言由具有固定数量的字母a、字母b和子序列ab的所有单词组成。我们证明了存在-普适性和全称-普适性对于这些语言都具有精确的算术刻画。扩展上述概念，我们在论文结尾开始了对固定单词作为此类语言中单词的子序列出现概率的分析。为此，我们证明了对于每个固定的模式单词w和误差容限，给定描述语言的子序列计数作为输入，语言中具有模式w作为子序列的单词比例允许一个加法近似方案，该方案在输入计数的二进制编码上是多项式时间的。
英文摘要
The universality index corresponding to a word is the largest integer k such that every word of length k over the given alphabet occurs in it as a subsequence. Relative to languages this notion can be investigated with respect to both existential and universal quantifiers, with the former corresponding to the existence of a word in the language with universality index at least k, while the latter considers the index across all words that the language contains. In this work we study the existential (exists-universality) and universal (forall-universality) subsequence universality (as introduced in [Adamson et al., ISAAC 2023]) for binary languages consisting of all words with a fixed number of letters a, letters b, and subsequences ab. We prove that both exists- and forall-universality admit exact arithmetic characterizations for these languages. Extending the above notions, we end the paper by initiating the analysis of the probability of a fixed word occurring as subsequence of the words in such a language. To this end, we prove that, for every fixed pattern word w and an error tolerance, given as input the subsequence counts describing a language, the ratio of words in the language having the pattern w as a subsequence admits an additive approximation scheme that is polynomial-time in the binary encoding of the input counts.
CommentsIn Proceedings AFL 2026, arXiv:2608.23071
Journal refEPTCS 451, 2026, pp. 140-154
