Lax Lean Archive

MSO-definable word languages are NFA-recognizable

Lax146103.MSOToNFA · concepts/Lax146103/MSOToNFA.lean · lax-146103

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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.

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

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    1import Lax146103.NFARecognizable
    2import Lax146103.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 Lax146103.MSOToNFA
    15
    16open Lax146103.MSOSyntax
    17open Lax146103.WordStructure
    18open Lax146103.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 Lax146103.MSOToNFA
    27
    Show Proof
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    From Mathlib

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