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Lax314295.RationalIffRelabelling

Rational functions are exactly the MSO relabellings

concepts/Lax314295/RationalIffRelabelling.lean · lax-314295

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    In the paper

    Theorem

    A string-to-string function is rational if and only if it is definable by an mso relabelling (Theorem C.4.4 of Transducers, Bloem and Engelfriet). The two implications are the separate statements RelabellingOfRationalRelabellingOfRational and RationalOfRelabellingRationalOfRelabelling; this statement is their conjunction.

    Lean source view on GitHub

    1import Lax132576.RationalFunctions
    2import Lax314295.MSORelabellings
    3
    4/-!
    5---
    6title: Rational functions are exactly the MSO relabellings
    7type: theorem
    8---
    9A string-to-string function is rational if and only if it is definable by an
    10mso relabelling (Theorem C.4.4 of *Transducers*, Bloem and Engelfriet). The two
    11implications are the separate statements `RelabellingOfRational` and
    12`RationalOfRelabelling`; this statement is their conjunction.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite.
    17-/
    18
    19namespace Lax314295.RationalIffRelabelling
    20
    21open Lax132576.RationalFunctions Lax314295.MSORelabellings
    22
    23/-- A function is rational if and only if it is an mso relabelling. -/
    24axiom isRationalFun_iff_isMSORelabelling {A B : Type} [Finite A] [Finite B]
    25 (f : List A → List B) : IsRationalFun f ↔ IsMSORelabelling f
    26
    27end Lax314295.RationalIffRelabelling
    28
    Show Proof

    Formalization notes

    Both alphabets are assumed finite.

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