Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax52.MSOToNFA

MSO-definable word languages are NFA-recognizable

concepts/Lax52/MSOToNFA.lean · lax-52

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    Theorem

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

    Lean source view on GitHub

    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

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…