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Quantifiers on languages and codensity monads
Mathematical Structures in Computer Science ( IF 0.5 ) Pub Date : 2021-06-23 , DOI: 10.1017/s0960129521000074
Mai Gehrke , Daniela Petrişan , Luca Reggio

This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem. Our main tools are codensity monads and duality theory. Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the Vietoris monad on Boolean spaces is the codensity monad of the finite powerset functor.

中文翻译:

语言和共密度单子的量词

本文有助于超越常规设置的语言的拓扑代数识别技术,因为它们与单词的逻辑有关。特别是,我们提供了一个对应于添加一层各种量词的识别器的一般构造,并证明了相应的罗伊特纳型定理。我们的主要工具是共密度单子和对偶理论。我们的构造取决于自由的有限单子的测度理论表征小号-semimodule monad 用于有限和交换半环小号,这概括了我们之前的见解,即布尔空间上的 Vietoris 单子是有限幂集函子的共密度单子。
更新日期:2021-06-23
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