反向波斯特对应问题与5'→3'字符串组装系统的不可判定性
Reverse Post Correspondence Problem and Undecidability of $5' \rightarrow 3'$ String Assembly Systems
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中文总结 AI 辅助
本文定义反向波斯特对应问题并证明其不可判定性，进而证明5'→3'字符串组装系统的空性问题不可判定，该模型具有生物动机。
中文摘要 AI 辅助
波斯特对应问题（Post Correspondence Problem）是指：给定一组多米诺骨牌，是否存在任意（可重复的）骨牌序列，使得由该序列中各骨牌上半部分组成的字符串与下半部分组成的字符串完全相同，它是最著名的算法上不可判定问题之一。本文定义了反向波斯特对应问题，即骨牌序列组装得到的两个字符串互为反转，并证明了这个新的修正问题的不可判定性。进一步地，基于该结果，本文还证明了5'→3'字符串组装系统的空性问题也是不可判定的。5'→3'字符串组装系统属于字符串组装系统类形式语言生成模型，其中5'→3'表示这类模型中生成字符串的推导从两端开始；该记号和新模型具有生物动机，因为任何双链DNA都具有两条方向相反的5'→3'链。
英文摘要
The Post Correspondence Problem is as follows: having a set of dominoes, is there any (maybe repeating) sequence of them such that the words formed by the upper parts and the lower parts by the sequence of dominoes are identical. It is one of the most known problems that is algorithmically undecidable. In this paper, the reverse Post Correspondence Problem is defined, that is, where the two assembled words of the dominos are reversals of each other. Undecidability about this new, modified problem is proven. Further, based on this result, it is also proven that the emptiness problem for 5'->3' String Assembly Systems is undecidable too. 5'->3' String Assembly Systems belong to String Assembly Systems type formal language generating models. The 5'->3' denotes that, in these variants, the derivations of the generated words start from the two extremes. The notation and the new model are bio-motivated as any double stranded DNA has two opposite oriented 5'->3' strands.
