论文标题
关于没有布尔操作的语言品种
On Language Varieties Without Boolean Operations
论文作者
论文摘要
艾伦伯格（Eilenberg）的多样性定理标志着常规语言代数理论的一个里程碑，通过在普通语言的属性与识别有限的单体属性之间建立正式对应关系。由量子有限自动机所接受的语言类别的动机，我们介绍了普通语言的基本品种，这是Eilenberg的原始概念的弱化，该概念在任何布尔操作下都不需要关闭，并为其证明了一种多样性的定理。为此，我们研究了晶格双模型对语言的代数认可，概括了Klima和Polak的晶格代数，我们利用了代数完全分布的晶格和Posets之间的双重性。
Eilenberg's variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by classes of languages accepted by quantum finite automata, we introduce basic varieties of regular languages, a weakening of Eilenberg's original concept that does not require closure under any boolean operations, and prove a variety theorem for them. To do so, we investigate the algebraic recognition of languages by lattice bimodules, generalizing Klima and Polak's lattice algebras, and we utilize the duality between algebraic completely distributive lattices and posets.
