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Lax314295.MSOTransductionIffRegular

MSO transductions define exactly the regular functions

concepts/Lax314295/MSOTransductionIffRegular.lean · lax-314295

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    In the paper

    Theorem

    String-to-string mso transductions define exactly the regular functions (Theorem C.4.8 of Transducers, Engelfriet and Hoogeboom). The two implications are the separate statements RegularOfMSOTransductionRegularOfMSOTransduction and MSOTransductionOfRegularMSOTransductionOfRegular; this statement is their conjunction.

    Lean source view on GitHub

    1import Lax916827.RegularFunctions
    2import Lax314295.MSOTransductions
    3
    4/-!
    5---
    6title: MSO transductions define exactly the regular functions
    7type: theorem
    8---
    9String-to-string mso transductions define exactly the regular functions
    10(Theorem C.4.8 of *Transducers*, Engelfriet and Hoogeboom). The two
    11implications are the separate statements `RegularOfMSOTransduction` and
    12`MSOTransductionOfRegular`; this statement is their conjunction.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite.
    17-/
    18
    19namespace Lax314295.MSOTransductionIffRegular
    20
    21open Lax916827.RegularFunctions Lax314295.MSOTransductions
    22
    23/-- A function is defined by an mso transduction if and only if it is regular. -/
    24axiom isMSOTransduction_iff_isRegularFun {A B : Type} [Finite A] [Finite B]
    25 (f : List A → List B) : IsMSOTransduction f ↔ IsRegularFun f
    26
    27end Lax314295.MSOTransductionIffRegular
    28
    Show Proof

    Formalization notes

    Both alphabets are assumed finite.

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