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arXiv · 1702.08841

Quantifiers on languages and codensity monads

Mai Gehrke·Daniela Petrisan·Luca Reggio
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Abstract

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.

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Mai Gehrke, Daniela Petrisan, Luca Reggio. 2017-02-28. Quantifiers on languages and codensity monads. https://doi.org/10.1017/s0960129521000074

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