In this paper we consider the model of single insertion-deletion systems that at each step insert or delete a single symbol in a context-free manner (i.e. at any position in the word). The corresponding operation is performed if the word contains a set of permitting (that have to be present in the word) and/or forbidding (that must not be present in the word) strings of some size. The main result of this paper states that if forbidding strings of size 2 and permitting strings of size 1 are used then computational completeness can be achieved; moreover, checking for a single permitting symbol is sufficient. We also show that in the case of systems having rules with forbidding conditions only, all regular languages can be obtained. Finally, we show the computational non-completeness in the case of systems using rules with forbidding strings of size 1 (single symbols) and permitting strings of any finite size.

在本文中，我们考虑单插​​入-删除系统的模型，该模型在每一步以上下文无关的方式插入或删除单个符号（即在词中的任何位置）。如果单词包含一组具有某种大小的允许（必须出现在单词中）和/或禁止（不能出现在单词中）字符串，则执行相应的操作。本文的主要结果表明，如果使用大小为 2 的禁止字符串和大小为 1 的允许字符串，则可以实现计算完整性；此外，检查单个允许符号就足够了。我们还表明，在系统只有禁止条件的规则的情况下，可以获得所有常规语言。最后，我们展示了在系统使用规则的情况下的计算非完整性，该规则禁止大小为 1 的字符串（单个符号）并允许任何有限大小的字符串。