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Lax916827.SSTIffRegular

Streaming string transducers compute exactly the regular functions

concepts/Lax916827/SSTIffRegular.lean · lax-916827

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    In the paper

    Theorem

    A string-to-string function is computed by a streaming string transducer if and only if it is regular (Theorem C.3.2 of Transducers). The two implications are the separate statements SSTOfRegularSSTOfRegular and RegularOfSSTRegularOfSST; this statement is their conjunction.

    Lean source view on GitHub

    1import Lax916827.RegularFunctions
    2import Lax916827.StreamingStringTransducers
    3
    4/-!
    5---
    6title: Streaming string transducers compute exactly the regular functions
    7type: theorem
    8---
    9A string-to-string function is computed by a streaming string transducer if and
    10only if it is regular (Theorem C.3.2 of *Transducers*). The two implications
    11are the separate statements `SSTOfRegular` and `RegularOfSST`; this statement
    12is their conjunction.
    13
    14# Formalization notes
    15
    16Both alphabets are assumed finite.
    17-/
    18
    19namespace Lax916827.SSTIffRegular
    20
    21open Lax916827.RegularFunctions Lax916827.StreamingStringTransducers
    22
    23/-- A function is computed by a streaming string transducer if and only if it is
    24regular. -/
    25axiom isSST_iff_isRegularFun {A B : Type} [Finite A] [Finite B] (f : List A → List B) :
    26 IsSST f ↔ IsRegularFun f
    27
    28end Lax916827.SSTIffRegular
    29
    Show Proof

    Formalization notes

    Both alphabets are assumed finite.

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