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Lax194892.PebbleIffFor

Pebble transducers and for-transducers compute the same functions

concepts/Lax194892/PebbleIffFor.lean · lax-194892

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    In the paper

    Theorem

    Pebble transducers and for-transducers compute the same string-to-string functions (Theorem D.2.4 of Transducers). The two implications are the separate statements ForOfPebbleForOfPebble and PebbleOfForPebbleOfFor; this statement is their conjunction.

    Lean source view on GitHub

    1import Lax194892.PebbleTransducers
    2import Lax194892.ForTransducers
    3
    4/-!
    5---
    6title: Pebble transducers and for-transducers compute the same functions
    7type: theorem
    8---
    9Pebble transducers and for-transducers compute the same string-to-string
    10functions (Theorem D.2.4 of *Transducers*). The two implications are the
    11separate statements `ForOfPebble` and `PebbleOfFor`; this statement is their
    12conjunction.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite.
    17-/
    18
    19namespace Lax194892.PebbleIffFor
    20
    21open Lax194892.PebbleTransducers Lax194892.ForTransducers
    22
    23/-- A function is computed by a pebble transducer if and only if it is computed by
    24a for-transducer. -/
    25axiom isPebbleTransducer_iff_isForTransducer {A B : Type} [Finite A] [Finite B]
    26 (f : List A → List B) : IsPebbleTransducer f ↔ IsForTransducer f
    27
    28end Lax194892.PebbleIffFor
    29
    Show Proof

    Formalization notes

    Both alphabets are assumed finite.

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