The category of MSO transductions

05/29/2023

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by   Mikołaj Bojańczyk, et al.

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MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such as recognizability or tree decompositions, can be defined in an abstract way that only refers to MSO transductions and their compositions.