■❈❊❈❈❙ ✷✵✶✸ ✶✽t❤ ❏✉❧② ✷✵✶✸ ❙✐♥❣❛♣♦r❡ ❖❜s❡r✈❡r P❛tt❡r♥s ❢♦r ❘❡❛❧✲❚✐♠❡ ❙②st❡♠s ➱t✐❡♥♥❡ ❆♥❞ré ▲❛❜♦r❛t♦✐r❡ ❞✬■♥❢♦r♠❛t✐q✉❡ ❞❡ P❛r✐s ◆♦r❞ ❯♥✐✈❡rs✐té P❛r✐s ✶✸✱ ❙♦r❜♦♥♥❡ P❛r✐s ❈✐té✱ ❋r❛♥❝❡ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✶ ✴ ✷✻
■♥tr♦❞✉❝t✐♦♥ ❈♦♥t❡①t✿ ❱❡r✐❢②✐♥❣ ❈♦♠♣❧❡① ❚✐♠❡❞ ❙②st❡♠s ✭✶✴✷✮ ◆❡❡❞ ❢♦r ❡❛r❧② ❜✉❣ ❞❡t❡❝t✐♦♥ ❇✉❣s ❞✐s❝♦✈❡r❡❞ ✇❤❡♥ ✜♥❛❧ t❡st✐♥❣✿ ❡①♣❡♥s✐✈❡ � ◆❡❡❞ ❢♦r ❛ t❤♦r♦✉❣❤ ♠♦❞❡❧✐♥❣ ❛♥❞ ✈❡r✐✜❝❛t✐♦♥ ♣❤❛s❡ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✷ ✴ ✷✻
◗✉❡st✐♦♥✿ ❞♦❡s t❤❡ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ s❛t✐s❢② t❤❡ ♣r♦♣❡rt②❄ ❨❡s ◆♦ ❈♦✉♥t❡r❡①❛♠♣❧❡ ■♥tr♦❞✉❝t✐♦♥ ❈♦♥t❡①t✿ ❱❡r✐❢②✐♥❣ ❈♦♠♣❧❡① ❚✐♠❡❞ ❙②st❡♠s ✭✷✴✷✮ ❯s❡ ❢♦r♠❛❧ ♠❡t❤♦❞s ✐s ✉♥r❡❛❝❤❛❜❧❡ ❆ ♣r♦♣❡rt② t♦ ❜❡ s❛t✐s✜❡❞ ❆ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✸ ✴ ✷✻
❨❡s ◆♦ ❈♦✉♥t❡r❡①❛♠♣❧❡ ■♥tr♦❞✉❝t✐♦♥ ❈♦♥t❡①t✿ ❱❡r✐❢②✐♥❣ ❈♦♠♣❧❡① ❚✐♠❡❞ ❙②st❡♠s ✭✷✴✷✮ ❯s❡ ❢♦r♠❛❧ ♠❡t❤♦❞s ? | ✐s ✉♥r❡❛❝❤❛❜❧❡ = ❆ ♣r♦♣❡rt② t♦ ❜❡ s❛t✐s✜❡❞ ❆ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ ◗✉❡st✐♦♥✿ ❞♦❡s t❤❡ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ s❛t✐s❢② t❤❡ ♣r♦♣❡rt②❄ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✸ ✴ ✷✻
■♥tr♦❞✉❝t✐♦♥ ❈♦♥t❡①t✿ ❱❡r✐❢②✐♥❣ ❈♦♠♣❧❡① ❚✐♠❡❞ ❙②st❡♠s ✭✷✴✷✮ ❯s❡ ❢♦r♠❛❧ ♠❡t❤♦❞s ? | ✐s ✉♥r❡❛❝❤❛❜❧❡ = ❆ ♣r♦♣❡rt② t♦ ❜❡ s❛t✐s✜❡❞ ❆ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ ◗✉❡st✐♦♥✿ ❞♦❡s t❤❡ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ s❛t✐s❢② t❤❡ ♣r♦♣❡rt②❄ ❨❡s ◆♦ ❈♦✉♥t❡r❡①❛♠♣❧❡ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✸ ✴ ✷✻
■♥tr♦❞✉❝t✐♦♥ ❈♦♥t❡①t✿ ❱❡r✐❢②✐♥❣ ❈♦♠♣❧❡① ❚✐♠❡❞ ❙②st❡♠s ✭✷✴✷✮ ❯s❡ ❢♦r♠❛❧ ♠❡t❤♦❞s ? | ✐s ✉♥r❡❛❝❤❛❜❧❡ = ❆ ♣r♦♣❡rt② t♦ ❜❡ s❛t✐s✜❡❞ ❆ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ ◗✉❡st✐♦♥✿ ❞♦❡s t❤❡ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ s❛t✐s❢② t❤❡ ♣r♦♣❡rt②❄ ❨❡s ◆♦ ❈♦✉♥t❡r❡①❛♠♣❧❡ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✸ ✴ ✷✻
■♥tr♦❞✉❝t✐♦♥ ❙♣❡❝✐❢②✐♥❣ Pr♦♣❡rt✐❡s ❢♦r ❘❡❛❧✲❚✐♠❡ ❙②st❡♠s ✭❚✐♠❡❞✮ t❡♠♣♦r❛❧ ❧♦❣✐❝s ❬P♥✉❡❧✐✱ ✶✾✼✼✱ ❇❛✐❡r ❛♥❞ ❑❛t♦❡♥✱ ✷✵✵✽❪ � ❱❡r② ❡①♣r❡ss✐✈❡ � ◆♦t ❡❛s② t♦ ❤❛♥❞❧❡ ❜② ♥♦♥✲❡①♣❡rts EF (( EX.P ) U ( AG.Q )) � ❊①♣r❡ss✐✈❡♥❡ss ♥♦t ♦❢t❡♥ s✉♣♣♦rt❡❞ ✐♥ ❢✉❧❧ ❜② t♦♦❧s � ❘❡q✉✐r❡s ❝♦♠♣❧❡① ♠♦❞❡❧ ❝❤❡❝❦✐♥❣ ❛❧❣♦r✐t❤♠s � ❚♦♦ ❡①♣r❡ss✐✈❡❄ ❖❜s❡r✈❡r✲❜❛s❡❞ ♣r♦♣❡rt✐❡s ❬❆❝❡t♦ ❡t ❛❧✳✱ ✶✾✾✽❜✱ ❆❝❡t♦ ❡t ❛❧✳✱ ✶✾✾✽❛❪ � ◗✉✐t❡ ❡①♣r❡ss✐✈❡ � ❉♦ ♥♦t r❡q✉✐r❡ ❝♦♠♣❧❡① ❛❧❣♦r✐t❤♠s � ◆♦t ❡❛s② t♦ ❤❛♥❞❧❡ ❜② ♥♦♥✲❡①♣❡rts � ❚♦♦ ❡①♣r❡ss✐✈❡❄ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✹ ✴ ✷✻
❖✉t❧✐♥❡ ❖✉t❧✐♥❡ ❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ ✶ ❈♦♠♠♦♥ P❛tt❡r♥s ✷ ❈♦♥❝❧✉s✐♦♥ ❛♥❞ P❡rs♣❡❝t✐✈❡s ✸ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✺ ✴ ✷✻
❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ ❖✉t❧✐♥❡ ❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ ✶ ❈♦♠♠♦♥ P❛tt❡r♥s ✷ ❈♦♥❝❧✉s✐♦♥ ❛♥❞ P❡rs♣❡❝t✐✈❡s ✸ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✻ ✴ ✷✻
❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ P❛tt❡r♥s ●♦❛❧ ■❞❡♥t✐❢② ❛♥❞ ❡①♣r❡ss ❝♦♠♠♦♥ ♣r♦♣❡rt✐❡s ♠❡t ✐♥ t❤❡ ❞❡s✐❣♥ ❛♥❞ ✈❡r✐✜❝❛t✐♦♥ ♦❢ ❝♦♠♣❧❡① r❡❛❧✲t✐♠❡ s②st❡♠s ❉❡✜♥❡ ❛♥ ❛ss♦❝✐❛t❡❞ ❢♦r♠❛❧ s❡♠❛♥t✐❝s ❙❤❛❧❧ ❜❡ ♥♦♥✲❝♦♠♣♦s✐t✐♦♥❛❧ � ❆✈♦✐❞s ♠✐st❛❦❡s ♦r ✐❧❧✲❢♦r♠❡❞ ♣r♦♣❡rt✐❡s � ❉✐s❝❛r❞s ♣r♦♣❡rt✐❡s ♥❡✈❡r ♦r r❛r❡❧② ♠❡t ✐♥ ♣r❛❝t✐❝❡ � ◆♦♥✲❝♦♠♣❧❡t❡ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✼ ✴ ✷✻
❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ P❛tt❡r♥s P❛tt❡r♥s✿ ❘❡❧❛t❡❞ ❲♦r❦s ❉❡s✐❣♥ ♣❛tt❡r♥s ❢♦r s♦❢t✇❛r❡ ❡♥❣✐♥❡❡r✐♥❣ ❬●❛♠♠❛ ❡t ❛❧✳✱ ✶✾✾✺❪ = ◆♦♥✲♦r✐❣✐♥❛❧✱ ♥♦♥✲❝♦♠♣♦s✐t✐♦♥❛❧✱ ♥♦♥✲❝♦♠♣❧❡t❡ � = ❈❛♥ ❜❡ ✐♥s❡rt❡❞ ✐♥t♦ ❢r❡❡❧② ✇r✐tt❡♥ ❝♦❞❡ ❚✐♠❡❞ ❛✉t♦♠❛t❛ ♣❛tt❡r♥s ❬❉♦♥❣ ❡t ❛❧✳✱ ✷✵✵✽❪ = ❙♣❡❝✐✜❝❛t✐♦♥ ❢♦r r❡❛❧✲t✐♠❡ ❝♦♥❝✉rr❡♥t s②st❡♠s � = ❙♣❡❝✐❢② t❤❡ ♠♦❞❡❧ ❛♥❞ ♥♦t t❤❡ ♣r♦♣❡rt② � = ❆✐♠ ❛t ❝♦♠♣❧❡t❡♥❡ss ❖t❤❡r ♣❛tt❡r♥s ❢♦r r❡❛❧✲t✐♠❡ s②st❡♠s ❉❡❞✐❝❛t✐♦♥ t♦ s❝❤❡❞✉❧✐♥❣ ♣r♦❜❧❡♠s ❬❑❤❛t✐❜ ❡t ❛❧✳✱ ✷✵✵✶❪ ❙♣❡❝✐✜❝❛t✐♦♥ ✉s✐♥❣ ❯▼▲ ❬▼❡❦❦✐ ❡t ❛❧✳✱ ✷✵✵✾❪ ❚✐♠❡❞ ❛✉t♦♠❛t❛ ♣❛tt❡r♥s ❣❡♥❡r❛t❡❞ ❢r♦♠ ❘❚❊❙▼s ❬❍❛♥ ❡t ❛❧✳✱ ✷✵✶✸❪ ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✽ ✴ ✷✻
❲❤② ❖❜s❡r✈❡r P❛tt❡r♥s❄ ❖❜s❡r✈❡rs ❖❜s❡r✈❡rs✿ ❆❧❧ ✐s ❘❡❛❝❤❛❜✐❧✐t② ❖❜s❡r✈❡r✿ ❛❞❞✐t✐♦♥❛❧ s✉❜s②st❡♠ ♠♦♥✐t♦r✐♥❣ t❤❡ s②st❡♠ ❜❡❤❛✈✐♦r ❙②♥❝❤r♦♥✐③❛t✐♦♥ ✇✐t❤ t❤❡ s②st❡♠ ❡✈❡♥ts ❉❡✜♥✐t✐♦♥ ♦❢ ❜❛❞ ✴ ❣♦♦❞ st❛t❡s ❘❡❞✉❝t✐♦♥ t♦ ♣✉r❡ r❡❛❝❤❛❜✐❧✐t② ♣r♦♣❡rt✐❡s ❍❡r❡✱ ✇❡ ❝♦♥s✐❞❡r ✷ ♠❛✐♥ ❦✐♥❞s ♦❢ ♣r♦♣❡rt✐❡s✿ ✶ ◆❡✈❡r r❡❛❝❤ t❤❡ ❜❛❞ st❛t❡ ✷ ❆❧✇❛②s ❡♥❞ ✐♥ ❛ ❣♦♦❞ st❛t❡ ❆❞✈❛♥t❛❣❡s ❆♥② t♦♦❧ ✐♠♣❧❡♠❡♥t✐♥❣ ✭♥♦♥✲✮r❡❛❝❤❛❜✐❧✐t② ❝❛♥ ✐♠♣❧❡♠❡♥t s✉❝❤ ♣❛tt❡r♥s ➱t✐❡♥♥❡ ❆♥❞ré ✭P❛r✐s ✶✸✮ ❖❜s❡r✈❡r P❛tt❡r♥s ✶✽t❤ ❏✉❧② ✷✵✶✸ ✾ ✴ ✷✻
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