若干生物启发操作的算法层面
Algorithmical Aspects of Some Bio Inspired Operations
AI总结：
本文研究前后缀复制、有界前后缀复制和前后缀平方补全三类生物启发字操作，分析其语言与无限字生成性质，并扩展有间隙重复及回文检测问题。
摘要：
本论文研究三种受生物启发的操作：前后缀复制、有界前后缀复制以及前后缀平方补全。复制是一种常见的基因突变，涉及DNA序列的重复，本文将其建模为作用于字上的形式操作。前后缀复制即使从简单的初始字出发，也会生成非上下文无关语言。为更好地反映生物过程，我们提出一种限制复制长度的有界变体，解决了若干悬而未决的问题，并与生化现实保持一致。我们还引入了前后缀平方补全操作，该操作在序列末端生成平方。这一操作能够生成Fibonacci、Period-doubling和Thue-Morse等无限字，这些无限字包含平方但避免更高指数的重复，突显了独特的结构性质。相比之下，前后缀复制无法生成某些无限字，例如Thue-Morse，但能够生成无立方字。此外，我们处理了有间隙重复和回文结构的检测问题，这些结构在DNA和RNA分析中十分重要。它们涉及位于中央间隙两侧的重复因子或逆序因子。以往研究对间隙长度或臂与间隙之间的关系施加了限制；我们通过在三种新设定下求解该问题对此进行了扩展。本工作推进了关于生物启发操作及其在遗传建模中计算应用的理论认识。
英文摘要：
This thesis investigates three biologically inspired operations: prefix-suffix duplication, bounded prefix-suffix duplication, and prefix-suffix-square completion. Duplication, a common genetic mutation, involves repeating DNA sequences and is modeled here as formal operations on words. The prefix-suffix duplication generates non-context-free languages, even from simple initial words. To better reflect biological processes, we propose a bounded variant that limits duplication length, resolving unsolved problems and aligning with biochemical realities. We also introduce the prefix-suffix-square completion operation, which generates squares at sequence ends. This operation enables the generation of infinite words such as Fibonacci, Period-doubling, and Thue-Morse, which contain squares but avoid higher exponent repetitions, highlighting unique structural properties. In contrast, prefix-suffix duplication cannot generate certain infinite words, such as Thue-Morse, but can produce cube-free words. Additionally, we address the detection of gapped repeats and palindromes-structures important in DNA and RNA analysis. These involve repeating or reversed factors flanking a central gap. Previous studies imposed constraints on gap length or arm-gap relationships; we extend this by solving the problem in three novel settings. This work advances theoretical insights into biologically inspired operations and their computational applications in genetic modeling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
