In this paper, we show that pure insertion grammars of size 2 (i.e., inserting two symbols in a left and right context, each consisting of two symbols) can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular $LOC(2)$ language, or an intersection with a $LOC(2)$ language and a weak coding. The obtained results improve the descriptional complexity of insertion grammars and complete the picture of known results on insertion-deletion systems that are motivated from the DNA computing area.

中文翻译：

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大小为2的通用插入语法

在本文中，我们证明了大小为2的纯插入语法（即，在左右上下文中插入两个符号，每个符号由两个符号组成）可以表征所有递归可枚举的语言。这可以通过应用逆态射和弱编码，或使用左（右）商和正则来实现$\mathrm{大号}ØC（2）$ 语言，或与 $\mathrm{大号}ØC（2）$语言和较弱的编码。获得的结果改善了插入语法的描述复杂性，并完成了由DNA计算领域推动的插入删除系统上已知结果的描述。