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Lax916827.DuplicationContinuous

String duplication is continuous

concepts/Lax916827/DuplicationContinuous.lean · lax-916827

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    In the paper

    Theorem

    String duplication w↦www \mapsto ww is continuous (Lemma C.1.2 of Transducers, second half): the inverse image of a regular language LL is the union, over the states qq of an automaton for LL, of the strings that lead from an initial state to qq and from qq to an accepting state.

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    1import Lax765601.Continuity
    2
    3/-!
    4---
    5title: String duplication is continuous
    6type: theorem
    7---
    8String duplication w↦www \mapsto ww is continuous (Lemma C.1.2 of *Transducers*,
    9second half): the inverse image of a regular language LL is the union, over
    10the states qq of an automaton for LL, of the strings that lead from an initial
    11state to qq and from qq to an accepting state.
    12
    13# Formalization notes
    14
    15The alphabet is assumed finite, as in the book.
    16-/
    17
    18namespace Lax916827.DuplicationContinuous
    19
    20open Lax765601.Continuity
    21
    22/-- String duplication is continuous. -/
    23axiom continuous_duplicate {A : Type} [Finite A] : Continuous (fun w : List A => w ++ w)
    24
    25end Lax916827.DuplicationContinuous
    26
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    Formalization notes

    The alphabet is assumed finite, as in the book.

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