发表机构
American University of Armenia（亚美尼亚美国大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对模糊模式匹配问题，提出泛化KMP算法前缀函数概念的轨迹，构建统一框架，分别解决序列与偏序结构中的模糊模式匹配问题。
AI 中文摘要
模式匹配问题，即在字符串中查找给定模式的所有出现位置，是计算机科学的基础问题之一，在诸多领域均有应用。本文研究模糊模式，其被定义为基于基本字母表的模糊属性序列。我们首先针对基本字母表元素序列研究模糊模式匹配，随后将该问题扩展至由基本字母表元素标记的节点偏序集。对于序列，我们寻找与模式匹配的片段；对于偏序结构，我们寻找与模式匹配的饱和节点链。解决这些问题的核心概念是轨迹，它是对Knuth–Morris–Pratt（KMP）算法中前缀函数概念的泛化。轨迹与对应的数据结构共同处理，使得所提出的算法可表示为转换系统，其状态对于序列为轨迹，对于偏序结构为与节点关联的轨迹。基于轨迹的方法为各类数据结构中的模糊模式匹配提供了统一框架。
英文摘要
The problem of pattern matching, that is, finding all occurrences of a given pattern in a string, is one of the fundamental problems in computer science that has applications in many areas. In this paper, we consider fuzzy patterns, defined as sequences of fuzzy properties over the basic alphabet. We first consider fuzzy pattern matching for sequences of elements of the basic alphabet and then extend the problem to partially ordered sets of nodes labeled by elements of the basic alphabet. For sequences, we seek segments that match the pattern, whereas for partially ordered structures, we seek saturated chains of nodes that match the pattern. The key concept underlying the solutions to these problems is the notion of a trajectory, which generalizes the concept of the prefix function used in the Knuth--Morris--Pratt (KMP) algorithm. A trajectory is processed together with the corresponding data structure, allowing the proposed algorithms to be represented as transition systems whose states are trajectories for sequences and trajectories associated with nodes for partially ordered structures. The trajectory-based approach provides a unified framework for fuzzy pattern matching in various data structures.
