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1 results

  • Quantifiers on languages and codensity monads

  • Mai Gehrke, Daniela Petrişan, Luca Reggio
  • Journal:
    Mathematical Structures in Computer Science / Volume 30 / Issue 10 / November 2020
    Published online by Cambridge University Press:
    23 June 2021, pp. 1054-1088

  • 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.