Problem
Research questions and friction points this paper is trying to address.
subregular expressions
expressive power
language families
operator sets
structural properties
Subregular Expressions and Their Expressive Power
🤖 AI Summary
该文通过修改经典运算符集，研究了不同子正则表达式的表达能力及其所生成的语言家族，并对比了这些语言类在不同字母表上的关系。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
subregular expressions
expressive power
operator set
language families
unary vs. arbitrary alphabets
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