Oritatami is a computational model of RNA cotranscriptional folding, in which an RNA transcript is folding upon itself while being synthesized from its template DNA. This model is known to be Turing universal. Under the restriction on its parameters delay and arity both being 1, however, any deterministically foldable conformation is known to be at most ten times as large as its initial conformation (seed), and hence, the model becomes weaker. In this paper, we shall improve the size upper bound from 10n down to 4n + 5 and also provide a system that can fold into a conformation of size 3n − 20. These tighter bounds result from a novel graph representation of deterministic oritatami folding pathways. We shall also study the case in which a transcript is trapped in a region closed by a seed and show that under this confinement, the upper bound is further improved to 11 3 n − 5.

中文翻译：

---

贪婪确定性折纸中构象大小的线性界限

Oritatami 是 RNA 共转录折叠的计算模型，其中 RNA 转录物在从其模板 DNA 合成的同时折叠自身。众所周知，该模型是图灵通用的。然而，在其参数 delay 和 arity 均为 1 的限制下，已知任何确定性可折叠的构象最多为其初始构象（种子）的十倍，因此，模型变得更弱。在本文中，我们将从10n向下4n + 5并且还提供了一个可以折叠成尺寸构象的系统3n - 20. 这些更严格的界限是由确定性折纸折叠路径的新颖图形表示产生的。我们还将研究转录被困在种子封闭区域中的情况，并表明在这种限制下，上限进一步提高到11 3 n - 5.