次正则表达式及其表达能力
Subregular Expressions and Their Expressive Power
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中文总结 AI 辅助
本文综述了基于受限算子集的次正则表达式系统，整理其表达能力等结果，比较不同字母表下的语言类，旨在为相关语言家族提供统一视角并指出研究方向。
中文摘要 AI 辅助
本文对通过修改由并、连接和Kleene星组成的经典算子集得到的几类次正则表达式进行了综述。更具体地说，我们考虑基于从并、交、补、连接和Kleene星中选取的两个或三个操作集构建的表达式系统。由此产生的语言家族范围从有限语言到全部正则语言类。我们收集并整理了这些家族在表达能力和结构性质方面的已知结果，比较了在一元字母表和任意字母表上得到的语言类，并总结了已知的包含、相等和不可比结果。本次综述旨在为受限算子集诱导的语言家族提供统一视角，并突出未解决的关系和进一步研究的可能方向。
英文摘要
We provide a survey of several families of subregular expressions obtained by modifying the classical operator set consisting of union, concatenation, and Kleene star. More specifically, we consider expression systems based on sets of two or three operations chosen from union, intersection, complementation, concatenation, and Kleene star. The resulting language families range from finite languages to the full class of regular languages. We collect and organize known results on the expressive power and structural properties of these families. We compare the resulting language classes over unary and arbitrary alphabets and summarize known inclusion, equality, and incomparability results. The aim of this survey is to provide a unified view of the language families induced by restricted operator sets and to highlight open relations and possible directions for further research.
