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  1. ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ✐♥ ♦♥❡ ❤♦✉r ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ❚❤♦♠❛s P❡②r✐♥ ■◆❘■❆ ❘♦❝q✉❡♥❝♦✉rt✱ ❚❡❛♠ ❙❊❈❘❊❚ ❖r❛♥❣❡ ▲❛❜s ✲ ❆■❙❚ ❋❙❊ ❋❡❜r✉❛r② ✶✵✲✶✸✱ ✷✵✵✽ ▲❛✉s❛♥♥❡ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶ ✴ ✷✻

  2. ❖✉t❧✐♥❡ ■♥tr♦❞✉❝t✐♦♥ ✶ Pr❡✈✐♦✉s ❈♦❧❧✐s✐♦♥ ❆tt❛❝❦s ♦♥ ❙❍❆✲✵ ✷ ◆❡✇ ❘❡s✉❧ts ♦♥ ❙❍❆✲✵ ✸ ❈♦♥❝❧✉s✐♦♥ ✹ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✷ ✴ ✷✻

  3. ❖✉t❧✐♥❡ ■♥tr♦❞✉❝t✐♦♥ ✶ Pr❡✈✐♦✉s ❈♦❧❧✐s✐♦♥ ❆tt❛❝❦s ♦♥ ❙❍❆✲✵ ✷ ◆❡✇ ❘❡s✉❧ts ♦♥ ❙❍❆✲✵ ✸ ❈♦♥❝❧✉s✐♦♥ ✹ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✸ ✴ ✷✻

  4. ❈r②♣t♦❣r❛♣❤✐❝ ❤❛s❤ ❢✉♥❝t✐♦♥ ❆♥ ❛❧❣♦r✐t❤♠ t❤❛t ♠❛♣s ✐♥♣✉t str✐♥❣s ♦❢ ❛r❜✐tr❛r② ❧❡♥❣t❤ t♦ ✧s❤♦rt✧ ✜①❡❞ ❧❡♥❣t❤ ♦✉t♣✉t str✐♥❣s✳ ❊①♣❡❝t❡❞ s❡❝✉r✐t② ♣r♦♣❡rt✐❡s✿ ◮ Pr❡✐♠❛❣❡ r❡s✐st❛♥❝❡✿ ❣✐✈❡♥ ❛♥② s♣❡❝✐✜❡❞ ♦✉t♣✉t✱ ✐t ✐s ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥❢❡❛s✐❜❧❡ t♦ ✜♥❞ ❛♥② ✐♥♣✉t ✇❤✐❝❤ ❤❛s❤❡s t♦ t❤✐s ♦✉t♣✉t✳ ◮ ❙❡❝♦♥❞ ♣r❡✐♠❛❣❡ r❡s✐st❛♥❝❡✿ ❣✐✈❡♥ ❛♥② s♣❡❝✐✜❡❞ ✐♥♣✉t✱ ✐t ✐s ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥❢❡❛s✐❜❧❡ t♦ ✜♥❞ ❛♥♦t❤❡r ✐♥♣✉t ✇❤✐❝❤ ❤❛s❤❡s t♦ t❤❡ s❛♠❡ ♦✉t♣✉t✳ ◮ ❈♦❧❧✐s✐♦♥ r❡s✐st❛♥❝❡✿ ✐t ✐s ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥❢❡❛s✐❜❧❡ t♦ ✜♥❞ t✇♦ ❞✐st✐♥❝t ✐♥♣✉t ✇❤✐❝❤ ❤❛s❤❡s t♦ t❤❡ s❛♠❡ ♦✉t♣✉t✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✹ ✴ ✷✻

  5. ❉♦♠❛✐♥ ❡①t❡♥❞❡r ◦ ❚❤❡ ▼❡r❦❧❡✲❉❛♠❣ ❛r❞ ❛❧❣♦r✐t❤♠✿ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✺ ✴ ✷✻

  6. ❈♦♠♣r❡ss✐♦♥ ❢✉♥❝t✐♦♥ ❚❤❡ ❉❛✈✐❡s✲▼❡②❡r ❝♦♥str✉❝t✐♦♥✿ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✻ ✴ ✷✻

  7. ❚❤❡ ❙❍❆✲✵ ❤❛s❤ ❢✉♥❝t✐♦♥ ❇✉✐❧t ✐♥ ✶✾✾✸✱ ✶✻✵ ❜✐ts ♦✉t♣✉t✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✼ ✴ ✷✻

  8. ❚❤❡ ❙❍❆✲✵ ❤❛s❤ ❢✉♥❝t✐♦♥ ▼❡ss❛❣❡ ❡①♣❛♥s✐♦♥✿ � ▼ ❦ , ❢♦r ✵ ≤ ❦ ≤ ✶✺ ❲ ❦ = ❲ ❦ − ✶✻ ⊕ ❲ ❦ − ✶✹ ⊕ ❲ ❦ − ✽ ⊕ ❲ ❦ − ✸ , ❢♦r ✶✻ ≤ ❦ ≤ ✼✾ ❇♦♦❧❡❛♥ ❢✉♥❝t✐♦♥s✿ st❡♣ ❦ ❢ ❦ ( ❇ , ❈ , ❉ ) ✶ ≤ ❦ ≤ ✷✵ ❢ ■❋ = ( ❇ ∧ ❈ ) ⊕ ( ❇ ∧ ❉ ) ✷✶ ≤ ❦ ≤ ✹✵ ❢ ❳❖❘ = ❇ ⊕ ❈ ⊕ ❉ ✹✶ ≤ ❦ ≤ ✻✵ ❢ ▼❆❏ = ( ❇ ∧ ❈ ) ⊕ ( ❇ ∧ ❉ ) ⊕ ( ❈ ∧ ❉ ) ✻✶ ≤ ❦ ≤ ✽✵ ❢ ❳❖❘ = ❇ ⊕ ❈ ⊕ ❉ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✽ ✴ ✷✻

  9. ❖✉t❧✐♥❡ ■♥tr♦❞✉❝t✐♦♥ ✶ Pr❡✈✐♦✉s ❈♦❧❧✐s✐♦♥ ❆tt❛❝❦s ♦♥ ❙❍❆✲✵ ✷ ◆❡✇ ❘❡s✉❧ts ♦♥ ❙❍❆✲✵ ✸ ❈♦♥❝❧✉s✐♦♥ ✹ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✾ ✴ ✷✻

  10. ❈❤❛❜❛✉❞ ❛♥❞ ❏♦✉① ❬❈❘❨P❚❖ ✾✽❪ ▲♦❝❛❧ ❝♦❧❧✐s✐♦♥s✿ ✐♥s❡rt ❛ ♣❡rt✉r❜❛t✐♦♥ ❛♥❞ ❝♦rr❡❝t ✐t ✐♥ t❤❡ ♥❡①t ✺ st❡♣s✳ ❋✐♥❞ ❧✐♥❡❛r ❞✐✛❡r❡♥t✐❛❧ ♣❛t❤ ♦❢ ✐♥t❡r❧❡❛✈❡❞ ❧♦❝❛❧ ❝♦❧❧✐s✐♦♥s ✇✐t❤ ✸ ❝♦♥str❛✐♥ts ♦♥ t❤❡ ♣❡rt✉r❜❛t✐♦♥ ✈❡❝t♦r✿ ◮ ♥♦ tr✉♥❝❛t❡❞ ❧♦❝❛❧ ❝♦❧❧✐s✐♦♥s✱ ◮ ♥♦ ❝♦♥s❡❝✉t✐✈❡ ♣❡rt✉r❜❛t✐♦♥s ✐♥ t❤❡ ✜rst ✶✻ st❡♣s✱ ◮ ♥♦ ♣❡rt✉r❜❛t✐♦♥ st❛rt✐♥❣ ❛❢t❡r st❡♣ ✼✹✳ ❈♦♠♣❧❡①✐t② ✐s ❡✈❛❧✉❛t❡❞ ✐♥ t❡r♠s ♦❢ ♣r♦❜❛❜✐❧✐t② ❢♦r ❧♦❝❛❧ ❝♦❧❧✐s✐♦♥s t♦ ❤♦❧❞✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶✵ ✴ ✷✻

  11. ❇✐❤❛♠ ❡t ❛❧✳ ❇✐❤❛♠ ❛♥❞ ❈❤❡♥ ❬❈❘❨P❚❖ ✵✹❪ ◮ ❙♣❡❡❞✉♣ t❡❝❤♥✐q✉❡ ❞✉r✐♥❣ ❝♦❧❧✐s✐♦♥ s❡❛r❝❤✿ ✉s✐♥❣ ♥❡✉tr❛❧ ❜✐ts✱ t❤❡ ❝♦♥❢♦r♠❛♥❝❡ t♦ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ♣❛t❤ ✐s ❛ss✉r❡❞ ✉♣ t♦ st❡♣ ✷✸✳ ❇✐❤❛♠ ❡t ❛❧✳ ❬❊❯❘❖❈❘❨P❚ ✷✵✵✺❪ ◮ ▼✉❧t✐✲❜❧♦❝❦ t❡❝❤♥✐q✉❡✿ ✉s❡ s❡✈❡r❛❧ ❜❧♦❝❦s t♦ ✜♥❞ ❛ ❝♦❧❧✐s✐♦♥✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶✶ ✴ ✷✻

  12. ❲❛♥❣ ❡t ❛❧✳ ❬❈❘❨P❚❖ ✵✺❪ ❘❡❧❛① t❤❡ ✜rst t✇♦ ❝♦♥str❛✐♥ts ♦♥ t❤❡ ♣❡rt✉r❜❛t✐♦♥ ✈❡❝t♦r t♦ ✜♥❞ ❛ ❜❡tt❡r ♦♥❡✳ ▼♦❞✐❢② ✭❜② ❤❛♥❞s✮ t❤❡ ✜rst st❡♣s ♦❢ t❤❡ ❞✐✛❡r❡♥t✐❛❧ ♣❛t❤ t♦ ❝♦♠♣❡♥s❛t❡ tr✉♥❝❛t❡❞ ❛♥❞ ❝♦♥s❡❝✉t✐✈❡ ❧♦❝❛❧ ❝♦❧❧✐s✐♦♥s✱ ✉s✐♥❣ ❞✐✛❡r❡♥t t♦♦❧s✿ ◮ ♠♦❞✉❧❛r s✉❜tr❛❝t✐♦♥✱ ◮ ❝❛rr② ❡✛❡❝t✱ ◮ ♥♦♥✲❧✐♥❡❛r✐t② ♦❢ t❤❡ ❜♦♦❧❡❛♥ ❢✉♥❝t✐♦♥ ❢ ■❋ ✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶✷ ✴ ✷✻

  13. ❲❛♥❣ ❡t ❛❧✳ ❬❈❘❨P❚❖ ✵✺❪ ❇✉✐❧❞ ❢r♦♠ ❛ r❛♥❞♦♠ ✜rst ❜❧♦❝❦ ♦❢ ♠❡ss❛❣❡ ❛ ❝❤❛✐♥✐♥❣ ✈❛r✐❛❜❧❡ ✈❡r✐❢②✐♥❣ s♣❡❝✐✜❝ ❝♦♥❞✐t✐♦♥s✳ ▼❡ss❛❣❡ ♠♦❞✐✜❝❛t✐♦♥s✿ ❛♥♦t❤❡r s♣❡❡❞✉♣ t❡❝❤♥✐q✉❡✳ ◮ ❈♦♠♣❧❡①✐t② ✐s ❣✐✈❡♥ ✐♥ t❡r♠s ♦❢ ♥✉♠❜❡r ♦❢ ❝♦♥❞✐t✐♦♥s t♦ ❢✉❧✜❧❧ ✭st❛rts ❢r♦♠ st❡♣ ✷✵✮✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶✸ ✴ ✷✻

  14. ◆❛✐t♦ ❡t ❛❧✳ ❬❆❙■❆❈❘❨P❚ ✵✻❪ ❇❛s❡❞ ♦♥ t❤❡ ❧✐♥❡❛r ❛♥❞ ♥♦♥✲❧✐♥❡❛r ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❲❛♥❣ ❡t ❛❧✳ ❙✉❜♠❛r✐♥❡ ♠♦❞✐✜❝❛t✐♦♥s✿ ❝♦♥❞✐t✐♦♥ ❝♦✉♥t✐♥❣ st❛rts ❢r♦♠ st❡♣ ✷✹✳ ❈♦♠♣❧❡①✐t②✿ ◮ ✷ ✸✻ ❢✉♥❝t✐♦♥ ❝❛❧❧s t❤❡♦r❡t✐❝❛❧❧② ✳✳✳ ◮ ✳✳✳ ❜✉t r❡q✉✐r❡s ✶✵✵ ❤♦✉rs ♦♥ ❛✈❡r❛❣❡ ✇✐t❤ ❛ ❣♦♦❞ P❈✳ ◮ ❖✉r ❡st✐♠❛t✐♦♥✿ ✷ ✹✵ , ✺ ❢✉♥❝t✐♦♥ ❝❛❧❧s ♣r❛❝t✐❝❛❧❧②✳ ❈♦♠♣❧❡①✐t② s❤♦✉❧❞ ❜❡ ❣✐✈❡♥ ✐♥ t❡r♠s ♦❢ ❢✉♥❝t✐♦♥ ❝❛❧❧s ✇✐t❤ ❛♥ ❡✣❝✐❡♥t ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦♥ t❤❡ s❛♠❡ ❝♦♠♣✉t❡r ✭ ✐✳❡✳ ❖♣❡♥❙❙▲✮ ❛❝❝♦r❞✐♥❣ t♦ ❉❡ ❈❛♥♥✐èr❡ ❡t ❛❧✳ ♣r♦♣♦s❛❧ ❬❍❛s❤ ❲♦r❦s❤♦♣ ✷✵✵✼❪✳ ❙té♣❤❛♥❡ ▼❛♥✉❡❧ ✭■◆❘■❆✮ ❈♦❧❧✐s✐♦♥s ♦♥ ❙❍❆✲✵ ❋❙❊ ✷✵✵✽ ✶✹ ✴ ✷✻

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