Quantifiers on languages and codensity monads [article]

Mai Gehrke, Daniela Petrisan, Luca Reggio
2019 arXiv   pre-print
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
more » ... 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.
arXiv:1702.08841v3 fatcat:35gre5ddqfhgbbcadv67yi45am