发表机构
University of Catania（卡塔尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过改进自顶向下转换方法，将任意拼贴系统转换为内部拼贴系统的大小上界从 9m 降至 5m，证明内部拼贴系统的最小规模不超过一般拼贴系统的五倍。
AI 中文摘要
拼贴系统是一种基于文法的压缩模型，它通过重复和子串截断扩展了直线程序。内部拼贴系统额外要求每个非终结符在结构上可从起始符号到达。Migita、Uehata 和我（CPM 2026）证明了任意大小为 $m$ 的拼贴系统都可以转换为生成相同字符串且大小至多为 $9m$ 的内部拼贴系统，并将改进这一常数留作开放问题。我们证明了对其自顶向下转换的一个简单改进将界限降低到 $5m$。该证明结合了三个基本思想：对生成的截断进行规范化，使其保持与目标端点对齐；一个重复分解，将重复基的每个完整副本吸收到最大核心中；以及结构可达性的单调性，它防止输入截断规则既变得结构上可达，又在之后充当端点对齐丢失的隐藏目标。在所述的单位成本随机存取机器模型中，该转换在最坏情况下以确定性 $O(m^2)$ 时间运行。因此，对于每个字符串，内部拼贴系统的最小大小至多是一般拼贴系统最小大小的五倍。
英文摘要
A collage system is a grammar-based compression model that extends straight-line programs with repetition and substring truncation. Internal collage systems additionally require every nonterminal to be structurally reachable from the start symbol. Migita, Uehata, and I (CPM 2026) showed that any collage system of size $m$ can be converted into an internal one generating the same string with size at most $9m$, and left the improvement of this constant as an open problem. We show that a simple refinement of their top-down conversion reduces the bound to $5m$. The proof combines three elementary ideas: canonicalization of generated truncations that remain aligned with a target endpoint; a repetition decomposition that absorbs every complete copy of the repetition base into a maximal core; and monotonicity of structural reachability, which prevents an input truncation rule from both becoming structurally reachable and later acting as a hidden target at which endpoint alignment is lost. The conversion runs in deterministic $O(m^2)$ worst-case time in the stated unit-cost random-access machine model. Consequently, for every string, the minimum size of an internal collage system is at most five times the minimum size of a general collage system.
