次正则形式语言的张量积表示
Tensor Product Representations of Subregular Formal Languages
摘要：
本文给出了正则语言子类的几何刻画。我们使用有限模型理论将字符串和树等对象描述为关系结构。满足这些模型上的某些标准的逻辑语句定义了语言的子正则类。这些语句的语义可以编译成张量结构，使用多线性映射作为函数应用程序进行评估。这种方法适用于考虑两个适当的亚正则语言在不同的字符串模型。
英文摘要：
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over these models define subregular classes of languages. The semantics of such statements can be compiled into tensor structures, using multilinear maps as function application for evaluation. This method is applied to consider two properly subregular languages over different string models.
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