Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the “splicing operation”, a cut-and-paste binary string operation defined by a set of “splicing rules”, quadruples r = (u1,u2; u3,u4) where u1,u2,u3,u4 are words over an alphabet Σ. For two strings x1u1u2y1 and x2u3u4y2, applying the splicing rule r produces the string x1u1u4y2. In this paper we focus on a particular type of splicing systems, called (i,j) semi-simple splicing systems, i = 1, 2 and j = 3, 4, wherein all splicing rules r have the property that the two strings in positions i and j in r are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called “axiom set”, by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

中文翻译：

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半简单拼接系统的描述复杂性

剪接系统是 Tom Head 在 1987 年引入的生成机制，用于模拟 DNA 重组的生物学过程。拼接系统的计算引擎是“拼接操作”，由一组“拼接规则”定义的剪切和粘贴二进制字符串操作，四元组r = (你1,你2; 你3,你4)在哪里你1,你2,你3,你4是字母表上的单词Σ. 对于两个字符串X1你1你2是的1和X2你3你4是的2, 应用拼接规则r产生字符串X1你1你4是的2. 在本文中，我们专注于一种特定类型的拼接系统，称为(一世,j)半简单拼接系统，一世 = 1, 2和j = 3, 4, 其中所有拼接规则r具有两个字符串在位置上的属性一世和j在r是单例字母，而其他两个字符串为空。这种系统生成的语言由一组单词组成，这些单词从称为“公理集”的初始集合开始，通过迭代地将拼接规则应用于公理集中的字符串以及中间生成的字符串。我们考虑公理集是常规语言的半简单拼接系统，并根据识别它们生成的语言的最小确定性有限自动机的大小来研究此类系统的描述复杂性。