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MSO-definable word languages are NFA-recognizable

Lax52.MSOToNFA · concepts/Lax52/MSOToNFA.lean · lax-52

proven

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    Natural Language Statement

    Theorem

    Every monadic second-order sentence over finite words on a finite alphabet is recognized by a nondeterministic finite automaton.

    Concept map
    5 concepts; 1 descendant hidden
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    1import Lax52.NFARecognizable
    2import Lax52.WordStructure
    3
    4/-!
    5---
    6title: MSO-definable word languages are NFA-recognizable
    7type: theorem
    8---
    9
    10Every monadic second-order sentence over finite words on a finite alphabet is
    11recognized by a nondeterministic finite automaton.
    12-/
    13
    14namespace Lax52.MSOToNFA
    15
    16open Lax52.MSOSyntax
    17open Lax52.WordStructure
    18open Lax52.NFARecognizable
    19
    20universe u
    21
    22axiom mso_definable_is_nfaRecognizable {Sigma : Type u} [Fintype Sigma]
    23 (phi : MSOSyntax.Sentence (wordLanguage Sigma)) :
    24 NFARecognizable (sentenceLanguage phi)
    25
    26end Lax52.MSOToNFA
    27
    Show Proof
    Builds on
    Used by
    From Mathlib

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