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Determinization of tree automata

Lax53.Determinization · concepts/Lax53/Determinization.lean · lax-53

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    Natural Language Statement

    Theorem

    Every bottom-up tree automaton with finitely many states has an equivalent deterministic tree automaton with finitely many states over the same ranked alphabet.

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    3 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax53.RankedTree
    2import Lax53.TreeAutomaton
    3
    4/-!
    5---
    6title: Determinization of tree automata
    7type: theorem
    8---
    9
    10Every bottom-up tree automaton with finitely many states has an equivalent
    11deterministic tree automaton with finitely many states over the same ranked
    12alphabet.
    13-/
    14
    15namespace Lax53.Determinization
    16
    17open Lax53.RankedTree
    18open Lax53.TreeAutomaton
    19
    20universe u v
    21
    22axiom exists_deterministic_equivalent {A : RankedAlphabet.{u}} {Q : Type v}
    23 [Fintype Q] (M : Automaton A Q) :
    24 ∃ Q' : Type v, ∃ _ : Fintype Q', ∃ D : Automaton A Q',
    25 D.Deterministic ∧ D.language = M.language
    26
    27end Lax53.Determinization
    28
    Show Proof
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