Lax Lean Archive

Rational functions are exactly the MSO relabellings

Lax314295.RationalIffRelabelling · concepts/Lax314295/RationalIffRelabelling.lean · lax-314295

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    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.

    Concept map
    6 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    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.

    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…