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X ➄➍➉➣➫➣➁✬➄➍➎✘❽➏➁✫➁❨➡❨❻✂➁✏➄➆❻✂➁✫➇✪➎➒➇✝➊❢➎➣➄ A ê✪✫✝➸❁❼❾➐✂➁✫➊➌➄➍❿➥➤➒0➭➌➄➍1❻❢➁➱➉✺➊✂❽➏n−1 ➡✍➁✫➇✪➐✂➁✏→❜➁✏➊✂➐✂❽✉➎➒➊➢➨❜➎➣➄➆❻ x ∈ L(A) ➉➣➊✂➐ ✏ ➙ ✒➱➎✺➄➍❼➂➃✏➁➜➄➆❻❪➉✺➄ ❼➥➟✩➉➣➊✂➐✧➎➒➊✂❿❾➤➢❼➥➟✼➄➆❻✂➁✫➇➏➁➀➉➣➇➏➁ ❽➏➅✂➃t❻✿➄➍❻❪➉Ô➄ A ➺ à★⑥ ✑➌➼ x x ∈ L(A) x x x qi , i < n + 1 xn−1 i0 = q0 →0 q1 →1 q2 →2 q2 . . xj i0 −→ qj+1 ❼➥➬ qj+1 ∈ Hj+1 å➜➁✫➊✂➃✏➁➣➭ ❼❾➬ ➙✉ý❪➎➒➇✉➄➍❻✂➁✏➊✡➄➆❻✂➁✫➇➏➁✘➁➧➻➑❼➂❽↕➄➍❽❨➉➣➊✡➉✺➃✫➃✫➁✏→❢➄➍❼❾➊✂↔➢❽➏➄➍➉✺➄➍➁➀❼❾➊ x ∈ L(A) Hn ∩ F = ∅ ➙➀å➱➁✏➇➆➁❝➁✫➉➣➃t❻➋❽➏➄➆➁✫→☞➄➍➉➣➫➣➁✏❽➝➄➍❼❾➔✧➁❊➵✴➅❪➉➣➐✂➇➆➉✺➄➍❼❾➃➈❼❾➊➓➄➍❻✂➁➈➊✴➅✂➔❝➨✸➁✫➇➀➎➣➟❂❽➏➄t➉Ô➄➍➁✫❽✏ç➜➟❫➎➣➇➱↔➒❼➥➸➒➁✏➊ Hn ➭✂➡●➁➞➃✏➎➒➔✧→❢➅❢➄➍➁ ➨➌➤✖➐✂➎➣❼➂➊✂↔ ➔✧➉➣➊➌➤✿❿❾➎➑➎➣➫❁➅❢→✂❽⑦➟❫➎➒➇✬➁✏➸➣➁✫➇↕➤ ➙✪å➜➎❄➡✍➁✏➸➣➁✫➇✏➭ Hj Hj+1 Q q ∈ Hj ➄➆❻✂❼➂❽➈➊❁➅❢➔❝➨❜➁✏➇❯❼➂❽➈➨❪➉➣❽➆❼❾➃✤➉➣❿❾❿❾➤➩➨✸➎➒➅✂➊✂➐✂➁✏➐❅➟❫➎➒➇✛↔➒❼➥➸➒➁✏➊ ➙ ✰ ➎☞➄➆❻✂➁❩➄➍❼❾➔✧➁✧➇➆➁✏➵❁➅❢❼➂➇➆➁✏➔✧➁✏➊➌➄❯❼➂❽ A ➐✂➎✷➡❨➊✣➄➍➎➩➉➩➃✏➎➒➊✂❽↕➄t➉➣➊➌➄✧➐✂➁✫→✸➁✫➊✂➐❢❼➂➊✂↔➩➎➒➊ ➄➍❼❾➔✧➁✏❽❝➄➍❻✂➁✡❿➂➁✏➊✂↔➣➄➆❻Û➎➣➟ ➙✢❺✬❻✂❼➂❽☎❼➂❽❯➔✛➅✂➃t❻ A ➨✸➁✏➄➏➄➍➁✫➇✏➙✡å➱➎✷➡✍➁✏➸➒➁✏➇✫➭✝❼❾➊➳→✂➇➆➉➣➃✏➄➆❼➂➃✫➉➣❿✝➄➍➁✫➇➏➔✧❽➞ ➄➍❻❢❼➂❽❊❼➂❽➞❽➏➄➆❼➂❿➂❿✝➊❢➎➣➄✛↔➣➎➑➎❁➐➳➁✏x➊✂➎➒➅✂↔➣❻♥✬ ➙ ❞●➁✫➃✫➉➣➅✂❽➏➁ ➄➆❻✂➁❯➃✫➎➒➊❢❽➏➄t➉✺➊✴➄➞❼➥➄➝➄➍➉➣➫➣➁✏❽➞➄➆➎✖➃✫➎➒➔☎→✂➅❢➄➆➁❯➉✿❽➆❼❾➊✂↔➒❿❾➁✛❽➏➄➆➁✫→➩❼➂❽➝➄➆➎➑➎❩❿➮➉➣➇➏↔➒➁➣➙➞❺✬❻✂❼❾❽➀❼➂❽➀➨✸➁✫➃✫➉➣➅✂❽➏➁ ➄➍➎ ➙è➯➶➟➞➄➍❻✂➁➋❽↕➄➍➇➆❼❾➊✂↔➦❼❾❽❩➸➒➁✏➇➏➤❵❿❾➎➒➊✂↔✂➭⑦➄➆❻✂❼➂❽ ➡✍➁➋➇➆➁✏➃✫➎➒➔☎→✂➅❢➄➆➁➓➄➍❻✂➁☞➄➆➇➍➉➣➊❢❽➆❼❾➄➆❼➂➎➒➊ Hj Hj+1 ➔☎➁✤➉➣➊❢❽❨➄➆❻❪➉✺➄❨➡✍➁➈➇➏➁✫➃✫➎➣➔✧→✂➅➑➄➍➁➞➄➍❻✂➁➞❽➍➉✺➔✧➁➞→✂➇➏➎➒➨✂❿➂➁✏➔❶➎✷➸➒➁✏➇➀➉➣➊✂➐✦➎✷➸➒➁✏➇✫➙⑦➯➲➊✂❽↕➄➍➁✫➉➣➐♥➭❪➡●➁❊➃✤➉✺➊ →✂➇➏➁✫➃✏➎➒➔✧→❢➅❢➄➍➁❨➉➣❿❾❿➑➄➆❻✂➁⑦➄➍➇➆➉➣➊✂❽➆❼➥➄➍❼❾➎➒➊✂❽✫➙❑➯➶➄✝➄➍➅✂➇➏➊✂❽✝➎➒➅❢➄✝➄➆❻❪➉✺➄✝➡✍➁❨➃✤➉➣➊➢➐✂s➁ ✮❪➊✂➁➜➉➣➊☎➉➣➅❢➄➆➎➒➔❩➉Ô➄➍➎➒➊ ❼❾➊✡➄➆❻✂❼➂❽⑦➡●➉✤➤✖➄➍❻❪➉Ô➄✬➡●➁➞➃✤➉✺➊➠➅✂❽➏➁➈❼❾➊✿➄➍❻✂➁➞→✂❿➂➉➣➃✫➁➞➎➣➟ ➙ A ❀②❋➁❼➂s➃ A = A, Q, i , F, δ ➣✶⑤❩⑨✽➥➆➟➠➂s➃ Q : U ∩ F = ∅} ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ➺ à★⑥ ✳➒➼ ➄ 0 δ ℘ = { H, a, J : ➋ ➊❙➝✈⑦✘➟❾➟ q∈H ↔✻➉❶➂s⑨ ④③ ➂✇⑦✘⑨í⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨✽➣ ➈➢❱➃ ➃❾➉❶➂s➝➸➂ F ℘ := {U ⊆ ➅ a ➦ q ∈J q→q} ⑥ ➺ à★⑥ ❚➌➼ A℘ = A, ℘(Q), {i0 }, F ℘ , δ ℘ ➅✲➤➑⑦✘➟❾➟➠➂➑➥➆➃✢➉❶➂✼→ ❛➔❤↕❝➯✟→✁➯✓➒✞➏✞➍ ÿ↕ ➙ ➣ A ➦ ❆❈ ❀⑧⑨⑤ ✡⑦ ☎⑩ ❷❶ ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ❩⑨②⑦✘➢❱➃➻➊❙➞➆⑦✘➃➻➊❙⑨ ➅ ✻→✁➒➸→✁➳ ❨➏➻➯Ò➏➻➎✘➒❢➏➑➐ ➋❐➋ ➊❙➝➆⑦✘➟❾➟ ⑦✘⑨✽➥ ➦ ➦ q ∈Q a∈A ➃❾➉❶➂s➝➸➂ ➅✈⑦✘➃➈➞❑➊★➅s➃✿➊❙⑨❜➂ ➅s➢➹➤➡➉✪➃❾➉♥⑦✘➃ ➣ a ➦ q ∈Q q→q à➒à ➙ ➾ ➎➒➔☎→✂❿➂➁þ➻❢❼➥➄➲➤✖➉➣➊❢➐➓➚✦❼➂➊✂❼❾➔❩➉➣❿❜➛➝➅❢➄➆➎➒➔✧➉✺➄t➉ ✜ ⑥ ➯➶➄✛❼➂❽❊➃✫❿➂➁✫➉➣➇➈➄➆❻❪➉✺➄❊➟❫➎➒➇❝➉✦➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃☎➉➣➊❢➐ ➄➍➎➣➄➍➉➣❿✍➉➣➅❢➄➍➎➣➔❩➉✺➄➆➎➒➊♥➭❑➉➣❿➂❿✝➡✍➁✿❻❪➉✤➸➒➁✧➄➍➎☞➐✂➎ ❼❾❽➝➄➍➎✿❿❾➎➑➎➣➫✦➅❢→✙➄➆❻✂➁❯➊✂➁þ➻➑➄➞❽↕➄t➉✺➄➆➁❝❼➂➊✣➺ ★à ⑥ ✑➌➼t➭✼➡❨❻✂❼❾➃t❻✙➁➧➻➑❼➂❽↕➄➍❽➞➉➣➊✂➐➋❼❾❽➀➅✂➊✂❼❾➵✴➅✂➁➣➙➈ý❪➎➒➇➱➄➆❻✂➁✫❽➏➁ ➉➣➅➑➄➍➎➒➔✧➉✺➄t➉➑➭❢➇➆➁✏➃✫➎➒↔➣➊✂➠❼ ô✏❼➂➊✂↔❝➄➆❻✂➁➞❿➮➉➣➊✂↔➣➅❪➉➣↔➒➁➀❼❾❽✬❿➂❼❾➊✂➁✤➉➣➇●❼➂➊✖➄➍❻✂➁➞❽↕➄➍➇➆❼❾➊✂↔✂➙ € ▲☛ ❹❸❺♠ ❝❻ ❯❋ ✑✏ ã ❸✡❿➹Ï❫❸ ❼ ➀ ❼➊❙➝✇➂s➜✘➂s➝€⑩❂⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨ ➇☞➃❾➉❶➂✬➂ ❃➩❶➊❙⑨❜➂s⑨❶➃ ⑦✘➟ ℘ ➅➫➃❢➊❙➃ó⑦✘➟ ⑦✘⑨✽➥Û➥✛➂ A ➦ A ➦ ➣ ➃➻➂s➝€➞ ⑨ ➅s➃ ➤➛➣ ➧➊❙➝➸➂➡➊❙➜✘➂s➝➸➇ ℘ L(A ) = L(A) ➦ ➦ ➦ ✜✣ ✰ ➎❢➭♥➄➍❻✂➁❯➇➏➁✫➃✫❼❾→❜➁❝➄➆➎✡➉✺➄➆➄➍➉➣➃t➫➓➄➆❻✂➁❯→✂➇➆➎➣➨✂❿➂➁✏➔ ê ❼➂❽➱➄➍❻✂❼❾❽✫ç❩✮❪➇➏❽➏➄➞➃✏➎➒➔✧→❢➅❢➄➍➁ ℘ x ∈ L(A) ➉➣➊❢➐✛➄➍❻✂➁✏➊❝➃t❻✂➁✏➃t➫ ➙ ✰ ❼➂➊✂➃✏➁✉➄➆❻✂➁●❿➂➉✺➄➆➄➆➁✫➇❏❼➂❽❏➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃✺➭Ô➄➆❻✂➁✍➄➆❼➂➔☎➁✪➊✂➁✫➁✏➐✂A➁✫➐ ❼❾❽➈➉✺➃✏➄➍➅✂➉➣❿➂❿➥➤☞❿➂❼❾➊✂➁✤➉✺x➇✘❼➂∈➊✙L(A)?

X ➄➍➉➣➫➣➁✬➄➍➎✘❽➏➁✫➁❨➡❨❻✂➁✏➄➆❻✂➁✫➇✪➎➒➇✝➊❢➎➣➄ A ê✪✫✝➸❁❼❾➐✂➁✫➊➌➄➍❿➥➤➒0➭➌➄➍1❻❢➁➱➉✺➊✂❽➏n−1 ➡✍➁✫➇✪➐✂➁✏→❜➁✏➊✂➐✂❽✉➎➒➊➢➨❜➎➣➄➆❻ x ∈ L(A) ➉➣➊✂➐ ✏ ➙ ✒➱➎✺➄➍❼➂➃✏➁➜➄➆❻❪➉✺➄ ❼➥➟✩➉➣➊✂➐✧➎➒➊✂❿❾➤➢❼➥➟✼➄➆❻✂➁✫➇➏➁➀➉➣➇➏➁ ❽➏➅✂➃t❻✿➄➍❻❪➉Ô➄ A ➺ à★⑥ ✑➌➼ x x ∈ L(A) x x x qi , i < n + 1 xn−1 i0 = q0 →0 q1 →1 q2 →2 q2 . . xj i0 −→ qj+1 ❼➥➬ qj+1 ∈ Hj+1 å➜➁✫➊✂➃✏➁➣➭ ❼❾➬ ➙✉ý❪➎➒➇✉➄➍❻✂➁✏➊✡➄➆❻✂➁✫➇➏➁✘➁➧➻➑❼➂❽↕➄➍❽❨➉➣➊✡➉✺➃✫➃✫➁✏→❢➄➍❼❾➊✂↔➢❽➏➄➍➉✺➄➍➁➀❼❾➊ x ∈ L(A) Hn ∩ F = ∅ ➙➀å➱➁✏➇➆➁❝➁✫➉➣➃t❻➋❽➏➄➆➁✫→☞➄➍➉➣➫➣➁✏❽➝➄➍❼❾➔✧➁❊➵✴➅❪➉➣➐✂➇➆➉✺➄➍❼❾➃➈❼❾➊➓➄➍❻✂➁➈➊✴➅✂➔❝➨✸➁✫➇➀➎➣➟❂❽➏➄t➉Ô➄➍➁✫❽✏ç➜➟❫➎➣➇➱↔➒❼➥➸➒➁✏➊ Hn ➭✂➡●➁➞➃✏➎➒➔✧→❢➅❢➄➍➁ ➨➌➤✖➐✂➎➣❼➂➊✂↔ ➔✧➉➣➊➌➤✿❿❾➎➑➎➣➫❁➅❢→✂❽⑦➟❫➎➒➇✬➁✏➸➣➁✫➇↕➤ ➙✪å➜➎❄➡✍➁✏➸➣➁✫➇✏➭ Hj Hj+1 Q q ∈ Hj ➄➆❻✂❼➂❽➈➊❁➅❢➔❝➨❜➁✏➇❯❼➂❽➈➨❪➉➣❽➆❼❾➃✤➉➣❿❾❿❾➤➩➨✸➎➒➅✂➊✂➐✂➁✏➐❅➟❫➎➒➇✛↔➒❼➥➸➒➁✏➊ ➙ ✰ ➎☞➄➆❻✂➁❩➄➍❼❾➔✧➁✧➇➆➁✏➵❁➅❢❼➂➇➆➁✏➔✧➁✏➊➌➄❯❼➂❽ A ➐✂➎✷➡❨➊✣➄➍➎➩➉➩➃✏➎➒➊✂❽↕➄t➉➣➊➌➄✧➐✂➁✫→✸➁✫➊✂➐❢❼➂➊✂↔➩➎➒➊ ➄➍❼❾➔✧➁✏❽❝➄➍❻✂➁✡❿➂➁✏➊✂↔➣➄➆❻Û➎➣➟ ➙✢❺✬❻✂❼➂❽☎❼➂❽❯➔✛➅✂➃t❻ A ➨✸➁✏➄➏➄➍➁✫➇✏➙✡å➱➎✷➡✍➁✏➸➒➁✏➇✫➭✝❼❾➊➳→✂➇➆➉➣➃✏➄➆❼➂➃✫➉➣❿✝➄➍➁✫➇➏➔✧❽➞ ➄➍❻❢❼➂❽❊❼➂❽➞❽➏➄➆❼➂❿➂❿✝➊❢➎➣➄✛↔➣➎➑➎❁➐➳➁✏x➊✂➎➒➅✂↔➣❻♥✬ ➙ ❞●➁✫➃✫➉➣➅✂❽➏➁ ➄➆❻✂➁❯➃✫➎➒➊❢❽➏➄t➉✺➊✴➄➞❼➥➄➝➄➍➉➣➫➣➁✏❽➞➄➆➎✖➃✫➎➒➔☎→✂➅❢➄➆➁❯➉✿❽➆❼❾➊✂↔➒❿❾➁✛❽➏➄➆➁✫→➩❼➂❽➝➄➆➎➑➎❩❿➮➉➣➇➏↔➒➁➣➙➞❺✬❻✂❼❾❽➀❼➂❽➀➨✸➁✫➃✫➉➣➅✂❽➏➁ ➄➍➎ ➙è➯➶➟➞➄➍❻✂➁➋❽↕➄➍➇➆❼❾➊✂↔➦❼❾❽❩➸➒➁✏➇➏➤❵❿❾➎➒➊✂↔✂➭⑦➄➆❻✂❼➂❽ ➡✍➁➋➇➆➁✏➃✫➎➒➔☎→✂➅❢➄➆➁➓➄➍❻✂➁☞➄➆➇➍➉➣➊❢❽➆❼❾➄➆❼➂➎➒➊ Hj Hj+1 ➔☎➁✤➉➣➊❢❽❨➄➆❻❪➉✺➄❨➡✍➁➈➇➏➁✫➃✫➎➣➔✧→✂➅➑➄➍➁➞➄➍❻✂➁➞❽➍➉✺➔✧➁➞→✂➇➏➎➒➨✂❿➂➁✏➔❶➎✷➸➒➁✏➇➀➉➣➊✂➐✦➎✷➸➒➁✏➇✫➙⑦➯➲➊✂❽↕➄➍➁✫➉➣➐♥➭❪➡●➁❊➃✤➉✺➊ →✂➇➏➁✫➃✏➎➒➔✧→❢➅❢➄➍➁❨➉➣❿❾❿➑➄➆❻✂➁⑦➄➍➇➆➉➣➊✂❽➆❼➥➄➍❼❾➎➒➊✂❽✫➙❑➯➶➄✝➄➍➅✂➇➏➊✂❽✝➎➒➅❢➄✝➄➆❻❪➉✺➄✝➡✍➁❨➃✤➉➣➊➢➐✂s➁ ✮❪➊✂➁➜➉➣➊☎➉➣➅❢➄➆➎➒➔❩➉Ô➄➍➎➒➊ ❼❾➊✡➄➆❻✂❼➂❽⑦➡●➉✤➤✖➄➍❻❪➉Ô➄✬➡●➁➞➃✤➉✺➊➠➅✂❽➏➁➈❼❾➊✿➄➍❻✂➁➞→✂❿➂➉➣➃✫➁➞➎➣➟ ➙ A ❀②❋➁❼➂s➃ A = A, Q, i , F, δ ➣✶⑤❩⑨✽➥➆➟➠➂s➃ Q : U ∩ F = ∅} ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ➺ à★⑥ ✳➒➼ ➄ 0 δ ℘ = { H, a, J : ➋ ➊❙➝✈⑦✘➟❾➟ q∈H ↔✻➉❶➂s⑨ ④③ ➂✇⑦✘⑨í⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨✽➣ ➈➢❱➃ ➃❾➉❶➂s➝➸➂ F ℘ := {U ⊆ ➅ a ➦ q ∈J q→q} ⑥ ➺ à★⑥ ❚➌➼ A℘ = A, ℘(Q), {i0 }, F ℘ , δ ℘ ➅✲➤➑⑦✘➟❾➟➠➂➑➥➆➃✢➉❶➂✼→ ❛➔❤↕❝➯✟→✁➯✓➒✞➏✞➍ ÿ↕ ➙ ➣ A ➦ ❆❈ ❀⑧⑨⑤ ✡⑦ ☎⑩ ❷❶ ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ❩⑨②⑦✘➢❱➃➻➊❙➞➆⑦✘➃➻➊❙⑨ ➅ ✻→✁➒➸→✁➳ ❨➏➻➯Ò➏➻➎✘➒❢➏➑➐ ➋❐➋ ➊❙➝➆⑦✘➟❾➟ ⑦✘⑨✽➥ ➦ ➦ q ∈Q a∈A ➃❾➉❶➂s➝➸➂ ➅✈⑦✘➃➈➞❑➊★➅s➃✿➊❙⑨❜➂ ➅s➢➹➤➡➉✪➃❾➉♥⑦✘➃ ➣ a ➦ q ∈Q q→q à➒à ➙ ➾ ➎➒➔☎→✂❿➂➁þ➻❢❼➥➄➲➤✖➉➣➊❢➐➓➚✦❼➂➊✂❼❾➔❩➉➣❿❜➛➝➅❢➄➆➎➒➔✧➉✺➄t➉ ✜ ⑥ ➯➶➄✛❼➂❽❊➃✫❿➂➁✫➉➣➇➈➄➆❻❪➉✺➄❊➟❫➎➒➇❝➉✦➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃☎➉➣➊❢➐ ➄➍➎➣➄➍➉➣❿✍➉➣➅❢➄➍➎➣➔❩➉✺➄➆➎➒➊♥➭❑➉➣❿➂❿✝➡✍➁✿❻❪➉✤➸➒➁✧➄➍➎☞➐✂➎ ❼❾❽➝➄➍➎✿❿❾➎➑➎➣➫✦➅❢→✙➄➆❻✂➁❯➊✂➁þ➻➑➄➞❽↕➄t➉✺➄➆➁❝❼➂➊✣➺ ★à ⑥ ✑➌➼t➭✼➡❨❻✂❼❾➃t❻✙➁➧➻➑❼➂❽↕➄➍❽➞➉➣➊✂➐➋❼❾❽➀➅✂➊✂❼❾➵✴➅✂➁➣➙➈ý❪➎➒➇➱➄➆❻✂➁✫❽➏➁ ➉➣➅➑➄➍➎➒➔✧➉✺➄t➉➑➭❢➇➆➁✏➃✫➎➒↔➣➊✂➠❼ ô✏❼➂➊✂↔❝➄➆❻✂➁➞❿➮➉➣➊✂↔➣➅❪➉➣↔➒➁➀❼❾❽✬❿➂❼❾➊✂➁✤➉➣➇●❼➂➊✖➄➍❻✂➁➞❽↕➄➍➇➆❼❾➊✂↔✂➙ € ▲☛ ❹❸❺♠ ❝❻ ❯❋ ✑✏ ã ❸✡❿➹Ï❫❸ ❼ ➀ ❼➊❙➝✇➂s➜✘➂s➝€⑩❂⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨ ➇☞➃❾➉❶➂✬➂ ❃➩❶➊❙⑨❜➂s⑨❶➃ ⑦✘➟ ℘ ➅➫➃❢➊❙➃ó⑦✘➟ ⑦✘⑨✽➥Û➥✛➂ A ➦ A ➦ ➣ ➃➻➂s➝€➞ ⑨ ➅s➃ ➤➛➣ ➧➊❙➝➸➂➡➊❙➜✘➂s➝➸➇ ℘ L(A ) = L(A) ➦ ➦ ➦ ✜✣ ✰ ➎❢➭♥➄➍❻✂➁❯➇➏➁✫➃✫❼❾→❜➁❝➄➆➎✡➉✺➄➆➄➍➉➣➃t➫➓➄➆❻✂➁❯→✂➇➆➎➣➨✂❿➂➁✏➔ ê ❼➂❽➱➄➍❻✂❼❾❽✫ç❩✮❪➇➏❽➏➄➞➃✏➎➒➔✧→❢➅❢➄➍➁ ℘ x ∈ L(A) ➉➣➊❢➐✛➄➍❻✂➁✏➊❝➃t❻✂➁✏➃t➫ ➙ ✰ ❼➂➊✂➃✏➁✉➄➆❻✂➁●❿➂➉✺➄➆➄➆➁✫➇❏❼➂❽❏➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃✺➭Ô➄➆❻✂➁✍➄➆❼➂➔☎➁✪➊✂➁✫➁✏➐✂A➁✫➐ ❼❾❽➈➉✺➃✏➄➍➅✂➉➣❿➂❿➥➤☞❿➂❼❾➊✂➁✤➉✺x➇✘❼➂∈➊✙L(A)?

Xj i0 −→ qj+1 ❼➥➬ qj+1 ∈ Hj+1 å➜➁✫➊✂➃✏➁➣➭ ❼❾➬ ➙✉ý❪➎➒➇✉➄➍❻✂➁✏➊✡➄➆❻✂➁✫➇➏➁✘➁➧➻➑❼➂❽↕➄➍❽❨➉➣➊✡➉✺➃✫➃✫➁✏→❢➄➍❼❾➊✂↔➢❽➏➄➍➉✺➄➍➁➀❼❾➊ x ∈ L(A) Hn ∩ F = ∅ ➙➀å➱➁✏➇➆➁❝➁✫➉➣➃t❻➋❽➏➄➆➁✫→☞➄➍➉➣➫➣➁✏❽➝➄➍❼❾➔✧➁❊➵✴➅❪➉➣➐✂➇➆➉✺➄➍❼❾➃➈❼❾➊➓➄➍❻✂➁➈➊✴➅✂➔❝➨✸➁✫➇➀➎➣➟❂❽➏➄t➉Ô➄➍➁✫❽✏ç➜➟❫➎➣➇➱↔➒❼➥➸➒➁✏➊ Hn ➭✂➡●➁➞➃✏➎➒➔✧→❢➅❢➄➍➁ ➨➌➤✖➐✂➎➣❼➂➊✂↔ ➔✧➉➣➊➌➤✿❿❾➎➑➎➣➫❁➅❢→✂❽⑦➟❫➎➒➇✬➁✏➸➣➁✫➇↕➤ ➙✪å➜➎❄➡✍➁✏➸➣➁✫➇✏➭ Hj Hj+1 Q q ∈ Hj ➄➆❻✂❼➂❽➈➊❁➅❢➔❝➨❜➁✏➇❯❼➂❽➈➨❪➉➣❽➆❼❾➃✤➉➣❿❾❿❾➤➩➨✸➎➒➅✂➊✂➐✂➁✏➐❅➟❫➎➒➇✛↔➒❼➥➸➒➁✏➊ ➙ ✰ ➎☞➄➆❻✂➁❩➄➍❼❾➔✧➁✧➇➆➁✏➵❁➅❢❼➂➇➆➁✏➔✧➁✏➊➌➄❯❼➂❽ A ➐✂➎✷➡❨➊✣➄➍➎➩➉➩➃✏➎➒➊✂❽↕➄t➉➣➊➌➄✧➐✂➁✫→✸➁✫➊✂➐❢❼➂➊✂↔➩➎➒➊ ➄➍❼❾➔✧➁✏❽❝➄➍❻✂➁✡❿➂➁✏➊✂↔➣➄➆❻Û➎➣➟ ➙✢❺✬❻✂❼➂❽☎❼➂❽❯➔✛➅✂➃t❻ A ➨✸➁✏➄➏➄➍➁✫➇✏➙✡å➱➎✷➡✍➁✏➸➒➁✏➇✫➭✝❼❾➊➳→✂➇➆➉➣➃✏➄➆❼➂➃✫➉➣❿✝➄➍➁✫➇➏➔✧❽➞ ➄➍❻❢❼➂❽❊❼➂❽➞❽➏➄➆❼➂❿➂❿✝➊❢➎➣➄✛↔➣➎➑➎❁➐➳➁✏x➊✂➎➒➅✂↔➣❻♥✬ ➙ ❞●➁✫➃✫➉➣➅✂❽➏➁ ➄➆❻✂➁❯➃✫➎➒➊❢❽➏➄t➉✺➊✴➄➞❼➥➄➝➄➍➉➣➫➣➁✏❽➞➄➆➎✖➃✫➎➒➔☎→✂➅❢➄➆➁❯➉✿❽➆❼❾➊✂↔➒❿❾➁✛❽➏➄➆➁✫→➩❼➂❽➝➄➆➎➑➎❩❿➮➉➣➇➏↔➒➁➣➙➞❺✬❻✂❼❾❽➀❼➂❽➀➨✸➁✫➃✫➉➣➅✂❽➏➁ ➄➍➎ ➙è➯➶➟➞➄➍❻✂➁➋❽↕➄➍➇➆❼❾➊✂↔➦❼❾❽❩➸➒➁✏➇➏➤❵❿❾➎➒➊✂↔✂➭⑦➄➆❻✂❼➂❽ ➡✍➁➋➇➆➁✏➃✫➎➒➔☎→✂➅❢➄➆➁➓➄➍❻✂➁☞➄➆➇➍➉➣➊❢❽➆❼❾➄➆❼➂➎➒➊ Hj Hj+1 ➔☎➁✤➉➣➊❢❽❨➄➆❻❪➉✺➄❨➡✍➁➈➇➏➁✫➃✫➎➣➔✧→✂➅➑➄➍➁➞➄➍❻✂➁➞❽➍➉✺➔✧➁➞→✂➇➏➎➒➨✂❿➂➁✏➔❶➎✷➸➒➁✏➇➀➉➣➊✂➐✦➎✷➸➒➁✏➇✫➙⑦➯➲➊✂❽↕➄➍➁✫➉➣➐♥➭❪➡●➁❊➃✤➉✺➊ →✂➇➏➁✫➃✏➎➒➔✧→❢➅❢➄➍➁❨➉➣❿❾❿➑➄➆❻✂➁⑦➄➍➇➆➉➣➊✂❽➆❼➥➄➍❼❾➎➒➊✂❽✫➙❑➯➶➄✝➄➍➅✂➇➏➊✂❽✝➎➒➅❢➄✝➄➆❻❪➉✺➄✝➡✍➁❨➃✤➉➣➊➢➐✂s➁ ✮❪➊✂➁➜➉➣➊☎➉➣➅❢➄➆➎➒➔❩➉Ô➄➍➎➒➊ ❼❾➊✡➄➆❻✂❼➂❽⑦➡●➉✤➤✖➄➍❻❪➉Ô➄✬➡●➁➞➃✤➉✺➊➠➅✂❽➏➁➈❼❾➊✿➄➍❻✂➁➞→✂❿➂➉➣➃✫➁➞➎➣➟ ➙ A ❀②❋➁❼➂s➃ A = A, Q, i , F, δ ➣✶⑤❩⑨✽➥➆➟➠➂s➃ Q : U ∩ F = ∅} ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ➺ à★⑥ ✳➒➼ ➄ 0 δ ℘ = { H, a, J : ➋ ➊❙➝✈⑦✘➟❾➟ q∈H ↔✻➉❶➂s⑨ ④③ ➂✇⑦✘⑨í⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨✽➣ ➈➢❱➃ ➃❾➉❶➂s➝➸➂ F ℘ := {U ⊆ ➅ a ➦ q ∈J q→q} ⑥ ➺ à★⑥ ❚➌➼ A℘ = A, ℘(Q), {i0 }, F ℘ , δ ℘ ➅✲➤➑⑦✘➟❾➟➠➂➑➥➆➃✢➉❶➂✼→ ❛➔❤↕❝➯✟→✁➯✓➒✞➏✞➍ ÿ↕ ➙ ➣ A ➦ ❆❈ ❀⑧⑨⑤ ✡⑦ ☎⑩ ❷❶ ❷✇❸❛❹✚❺❼❻❾❽❫❻✕❿✽❺ ❩⑨②⑦✘➢❱➃➻➊❙➞➆⑦✘➃➻➊❙⑨ ➅ ✻→✁➒➸→✁➳ ❨➏➻➯Ò➏➻➎✘➒❢➏➑➐ ➋❐➋ ➊❙➝➆⑦✘➟❾➟ ⑦✘⑨✽➥ ➦ ➦ q ∈Q a∈A ➃❾➉❶➂s➝➸➂ ➅✈⑦✘➃➈➞❑➊★➅s➃✿➊❙⑨❜➂ ➅s➢➹➤➡➉✪➃❾➉♥⑦✘➃ ➣ a ➦ q ∈Q q→q à➒à ➙ ➾ ➎➒➔☎→✂❿➂➁þ➻❢❼➥➄➲➤✖➉➣➊❢➐➓➚✦❼➂➊✂❼❾➔❩➉➣❿❜➛➝➅❢➄➆➎➒➔✧➉✺➄t➉ ✜ ⑥ ➯➶➄✛❼➂❽❊➃✫❿➂➁✫➉➣➇➈➄➆❻❪➉✺➄❊➟❫➎➒➇❝➉✦➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃☎➉➣➊❢➐ ➄➍➎➣➄➍➉➣❿✍➉➣➅❢➄➍➎➣➔❩➉✺➄➆➎➒➊♥➭❑➉➣❿➂❿✝➡✍➁✿❻❪➉✤➸➒➁✧➄➍➎☞➐✂➎ ❼❾❽➝➄➍➎✿❿❾➎➑➎➣➫✦➅❢→✙➄➆❻✂➁❯➊✂➁þ➻➑➄➞❽↕➄t➉✺➄➆➁❝❼➂➊✣➺ ★à ⑥ ✑➌➼t➭✼➡❨❻✂❼❾➃t❻✙➁➧➻➑❼➂❽↕➄➍❽➞➉➣➊✂➐➋❼❾❽➀➅✂➊✂❼❾➵✴➅✂➁➣➙➈ý❪➎➒➇➱➄➆❻✂➁✫❽➏➁ ➉➣➅➑➄➍➎➒➔✧➉✺➄t➉➑➭❢➇➆➁✏➃✫➎➒↔➣➊✂➠❼ ô✏❼➂➊✂↔❝➄➆❻✂➁➞❿➮➉➣➊✂↔➣➅❪➉➣↔➒➁➀❼❾❽✬❿➂❼❾➊✂➁✤➉➣➇●❼➂➊✖➄➍❻✂➁➞❽↕➄➍➇➆❼❾➊✂↔✂➙ € ▲☛ ❹❸❺♠ ❝❻ ❯❋ ✑✏ ã ❸✡❿➹Ï❫❸ ❼ ➀ ❼➊❙➝✇➂s➜✘➂s➝€⑩❂⑦✘➢❱➃➻➊❙➞➆⑦✘➃❢➊❙⑨ ➇☞➃❾➉❶➂✬➂ ❃➩❶➊❙⑨❜➂s⑨❶➃ ⑦✘➟ ℘ ➅➫➃❢➊❙➃ó⑦✘➟ ⑦✘⑨✽➥Û➥✛➂ A ➦ A ➦ ➣ ➃➻➂s➝€➞ ⑨ ➅s➃ ➤➛➣ ➧➊❙➝➸➂➡➊❙➜✘➂s➝➸➇ ℘ L(A ) = L(A) ➦ ➦ ➦ ✜✣ ✰ ➎❢➭♥➄➍❻✂➁❯➇➏➁✫➃✫❼❾→❜➁❝➄➆➎✡➉✺➄➆➄➍➉➣➃t➫➓➄➆❻✂➁❯→✂➇➆➎➣➨✂❿➂➁✏➔ ê ❼➂❽➱➄➍❻✂❼❾❽✫ç❩✮❪➇➏❽➏➄➞➃✏➎➒➔✧→❢➅❢➄➍➁ ℘ x ∈ L(A) ➉➣➊❢➐✛➄➍❻✂➁✏➊❝➃t❻✂➁✏➃t➫ ➙ ✰ ❼➂➊✂➃✏➁✉➄➆❻✂➁●❿➂➉✺➄➆➄➆➁✫➇❏❼➂❽❏➐✂➁✏➄➆➁✫➇➏➔✧❼❾➊✂❼➂❽↕➄➍❼➂➃✺➭Ô➄➆❻✂➁✍➄➆❼➂➔☎➁✪➊✂➁✫➁✏➐✂A➁✫➐ ❼❾❽➈➉✺➃✏➄➍➅✂➉➣❿➂❿➥➤☞❿➂❼❾➊✂➁✤➉✺x➇✘❼➂∈➊✙L(A)?

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