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Feb 03, 2023 260 likes •607 views

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SLIDE 1

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦

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SLIDE 2

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❙✉♠♠❛r②

▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s ❇❛❝❦❥✉♠♣✐♥❣
  • r❛♣❤ ❇❛s❡❞ ❇❛❝❦❥✉♠♣✐♥❣

◆♦✲●♦♦❞ ❘❡❝♦r❞✐♥❣

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SLIDE 3

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

▲♦♦❦❜❛❝❦

❇❛s✐❝ ■❞❡❛s ❧♦♦❦❛❤❡❛❞ s❝❤❡♠❡s

❢♦r❡s❡❡ ❛♥❞ ❛✈♦✐❞ ❞❡❛❞✲❡♥❞s ✐♥ t❤❡ ❢✉t✉r❡ ♦♣❡r❛t❡s ❞✉r✐♥❣ t❤❡ ❢♦r✇❛r❞ ♣❤❛s❡

❧♦♦❦❜❛❝❦ s❝❤❡♠❡s✿ ❛✈♦✐❞ r❡♣❡❛t✐♥❣ t❤❡ s❛♠❡ ❡rr♦r ✐♥ t❤❡ s❡❛r❝❤

❛✈♦✐❞ r❡♣❡❛t✐♥❣ s❛♠❡ ❡rr♦rs ✇❤❡♥ ❛ ❞❡❛✲❞❡♥❞ ✐s ❢♦✉♥❞ ♦♣❡r❛t❡s ❞✉r✐♥❣ t❤❡ ❜❛❝❦✇❛r❞ s❡❛r❝❤

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SLIDE 4

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

▲♦♦❦❜❛❝❦ ❙❝❤❡♠❡s

▼❛✐♥ ❆♣♣r♦❛❝❤❡s ❇❛❝❦❥✉♠♣✐♥❣

✐♠♣r♦✈❡s ♦♥ ❜❛❝❦tr❛❝❦✐♥❣ ♦♥❡ st❡♣ ❜❛❝❦✇❛r❞s ❛♥❛❧②s✐♥❣ t❤❡ r❡❛s♦♥ ❢♦r t❤❡ ❞❡❛✲❞❡♥❞ ✇❡ ❝❛♥ ❛✈♦✐❞ ✐rr❡❧❡✈❛♥t ❜❛❝❦tr❛❝❦ ♣♦✐♥ts ❥✉♠♣ t♦ t❤❡ s♦✉r❝❡ ♦❢ ❢❛✐❧✉r❡ ✭❝✉❧♣r✐t✮

❈♦♥str❛✐♥t ❘❡❝♦r❞✐♥❣ ✭♥♦✲❣♦♦❞ ❧❡❛r♥✐♥❣✮

r❡❝♦r❞ t❤❡ r❡❛s♦♥ ❢♦r ❞❡❛❞✲❡♥❞ ❛s ❛ ♥❡✇ ❝♦♥str❛✐♥t ❛✈♦✐❞ ✜♥❞✐♥❣ t❤❡ s❛♠❡ ✐♥❝♦♥s✐st❡♥❝✐❡s ❛❣❛✐♥

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SLIDE 5

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❊①❛♠♣❧❡

❊①❛♠♣❧❡ ✭●r❛♣❤ ❈♦❧♦r✐♥❣✮ ❱❛r✐❛❜❧❡s✿ ①✶, ①✷, ①✸, ①✹, ①✺, ①✻, ①✼✱ ❉♦♠❛✐♥s✿ ❉①✶ = {❇, ❘, ●}, ❉①✷ = ❉①✺ = {❇, ●}, ❉①✸ = ❉①✹ = ❉①✼ = {❘, ❇}, ❉①✻ = {❘, ●, ❨ } ❈♦♥str❛✐♥ts✿ ①✶! = ①✷, ①✶! = ①✸, ①✶! = ①✹, ①✶! = ①✼, ①✷! = ①✻, ①✸! = ①✼, ①✹! = ①✺, ①✹! = ①✼, ①✺! = ①✻, ①✺! = ①✼ ❇❛❝❦tr❛❝❦✐♥❣ ✇✐t❤ ❞ = {①✶, ①✷, ①✸, ①✹, ①✺, ①✻, ①✼} ❈♦♥s✐❞❡r ❛ss✐❣♥♠❡♥t {❘, ❇, ❇, ❇, ●, ❘} ❉❡❛❞✲❡♥❞ ❛t ①✼ ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ ①✻

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SLIDE 6

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❊①❛♠♣❧❡

❊①❛♠♣❧❡ ✭●r❛♣❤ ❈♦❧♦r✐♥❣✮ (❘, ❇, ❇, ❇, ●, ❘) ❛ ❝♦♥✢✐❝t s❡t ❢♦r ①✼ (❘, −, ❇, ❇, ●, −) ❛♥♦t❤❡r ❝♦♥✢✐❝t s❡t ❢♦r ①✼ (❘, −, ❇, −, −, −) ♠✐♥✐♠❛❧ ❝♦♥✢✐❝t s❡t ❢♦r ①✼ (❘, ❇, ❇, ❇, ●, ❘) ❧❡❛❢ ❞❡❛❞ ❡♥❞ ❡✈❡r② ❝♦♥✢✐❝t s❡t ✐s ❛ ♥♦✲❣♦♦❞

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SLIDE 7

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❉❡❛❞ ❡♥❞

❉❡✜♥✐t✐♦♥ ✭❉❡❛❞ ❊♥❞ ❙t❛t❡ ❛t ▲❡✈❡❧ ✐✮ ❛ss✐❣♥♠❡♥t ¯ ❛✐ = {❛✶, · · · , ❛✐} ∀❛✐+✶ ∈ ❉①✐+✶ {❛✶, · · · , ❛✐, ❛✐+✶} ✐s ✐♥❝♦♥s✐st❡♥t ①✐+✶ ❞❡❛❞ ❡♥❞ ✈❛r✐❛❜❧❡ ❙♦❧✈✐♥❣ ❉❡❛❞ ❊♥❞s t❤❡r❡ ♠✐❣❤t ❜❡ s✉❜✲t✉♣❧❡s ♦❢ ¯ ❛✐ t❤❛t ❝♦♥✢✐❝t ✇✐t❤ ①✐ t❤❡r❡❢♦r❡ ❜❛❝❦tr❛❝❦✐♥❣ t♦ ①✐ ♠✐❣❤t ❜❡ ✉s❡❧❡ss ✇❡ s❤♦✉❧❞ ❥✉♠♣ t♦ ①❜ s✉❝❤ t❤❛t ¯ ❛❜−✶ ❝♦♥t❛✐♥s ♥♦ ❝♦♥✢✐❝t s❡ts ❢♦r ①✐+✶

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SLIDE 8

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❈♦♥✢✐❝t ❙❡t

❉❡✜♥✐t✐♦♥ ✭❈♦♥✢✐❝t ❙❡t✮ ¯ ❛ = {❛✐✶, · · · , ❛✐❦} ❝♦♥s✐st❡♥t ✐♥st❛♥t✐❛t✐♦♥ ♦❢ ❛r❜✐tr❛r② s✉❜s❡t ① ♥♦t ✐♥st❛♥t✐❛t❡❞ ✈❛r✐❛❜❧❡ ✐❢ ∃❜ ∈ ❉①| < ¯ ❛, ① = ❜ > ✐s ❝♦♥s✐st❡♥t ¯ ❛ ✐s ❛ ❝♦♥✢✐❝t s❡t ❢♦r ① ✐❢ ¯ ❛ ❞♦❡s ♥♦t ❝♦♥t❛✐♥ ❛ s✉❜t✉♣❧❡ t❤❛t ❝♦♥✢✐❝ts ✇✐t❤ ①✱ ¯ ❛ ✐s ❛ ♠✐♥✐♠❛❧ ❝♦♥✢✐❝t s❡t ♦❢ ① ❉❡✜♥✐t✐♦♥ ✭▲❡❛❢ ❉❡❛❞✲❊♥❞✮ ♣❛rt✐❛❧ s♦❧✉t✐♦♥ ¯ ❛✐ t❤❛t ❝♦♥✢✐❝ts ✇✐t❤ ①✐+✶ ①✐+✶ ✐s t❤❡ ❧❡❛❢ ❞❡❛❞✲❡♥❞ ✈❛r✐❛❜❧❡

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SLIDE 9

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

◆♦✲●♦♦❞

❉❡✜♥✐t✐♦♥ ✭◆♦ ❣♦♦❞✮

  • ✐✈❡♥ ❛ ♥❡t✇♦r❦ R = {❳, ❉, ❈}

❛♥② ♣❛rt✐❛❧ ✐♥st❛♥t✐❛t✐♦♥ ¯ ❛ t❤❛t ❞♦❡s ♥♦t ❛♣♣❡❛r ✐♥ ❛♥② s♦❧✉t✐♦♥ ♦❢ ❘ ✐s ❛ ♥♦✲❣♦♦❞ ◆♦ ❣♦♦❞ ❛♥② ❝♦♥✢✐❝t s❡t ❢♦r ❛♥② ✈❛r✐❛❜❧❡ ✐s ❛ ♥♦✲❣♦♦❞ t❤❡r❡ ❛r❡ ♥♦✲❣♦♦❞ t❤❛t ❛r❡ ♥♦t ❝♦♥✢✐❝t s❡ts ❢♦r ❛♥② s✐♥❣❧❡ ✈❛r✐❛❜❧❡ ❋♦r ♣r❡✈✐♦✉s ●❈ ❡①❛♠♣❧❡ ①✶ = ❘, ①✷ = ● ✐s ❛ ♥♦✲❣♦♦❞ ❜✉t ✐s ♥♦t ❛ ❝♦♥✢✐❝t s❡t ❢♦r ❛♥② ✈❛r✐❛❜❧❡

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SLIDE 10

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❏✉♠♣✐♥❣ ❜❛❝❦

▼❛✐♥ ✐❞❡❛ ♦❢ ❜❛❝❦❥✉♠♣✐♥❣ ❲❤❡♥ ❞❡❛❞✲❡♥❞✱ ❥✉♠♣ ❜❛❝❦ ❛s ❢❛r ❛s ♣♦ss✐❜❧❡ ✇✐t❤♦✉t ❧♦♦s✐♥❣ ♣♦ss✐❜❧❡ s♦❧✉t✐♦♥s ♠❛①✐♠❛❧ ❥✉♠♣✿ ❥✉♠♣ ❛s ❜❛❝❦ ❛s ♣♦ss✐❜❧❡ s❛❢❡ ❥✉♠♣✿ ❞♦ ♥♦t s❦✐♣ ❛♥② s♦❧✉t✐♦♥s

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SLIDE 11

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❙❛❢❡ ❏✉♠♣

❉❡✜♥✐t✐♦♥ ✭❙❛❢❡ ❏✉♠♣✮ ¯ ❛✐ = {❛✶, · · · , ❛✐} ❧❡❛❢ ❞❡❛❞ ❡♥❞ st❛t❡ ①❥ ❥ ≤ ✐ ✐s s❛❢❡ ✭r❡❧❛t✐✈❡ t♦ ¯ ❛✐✮ ✐❢ ¯ ❛❥ ✐s ❛ ♥♦✲❣♦♦❞ ◆♦t❡ s❛❢❡t② ♦❢ ❥✉♠♣ ✐s ❛❧❣♦r✐t❤♠ ✐♥❞❡♣❡♥❞❡♥t ♠❛①✐♠❛❧✐t② ✐s ❛❧❣♦r✐t❤♠ ❞❡♣❡♥❞❡♥t

slide-12
SLIDE 12

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❇❛❝❦❏✉♠♣✐♥❣ ❙t②❧❡s

❙t②❧❡s ❇❛❝❦tr❛❝❦✐♥❣ t❤❛t ❜❛❝❦s ✉♣ s❡✈❡r❛❧ ❧❛②❡rs ✇❤❡♥ ❛ ♥♦t ❡①t❡♥s✐❜❧❡ ❛ss✐❣♥♠❡♥t ✐s ❢♦✉♥❞

  • ❛s❝❤♥✐❣✬s
  • r❛♣❤ ❜❛s❡❞

❈♦♥✢✐❝ts✲❞✐r❡❝t❡❞

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SLIDE 13

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • ❛s❝❤♥✐❣✬s ❇❛❝❦❥✉♠♣✐♥❣

❲❤❡♥ ❛♥❞ ✇❤❡r❡ t♦ ❥✉♠♣ ❲❤❡♥✿ ❇❛❝❦tr❛❝❦ ✇❤❡♥ ❧❡❛❢ ❞❡❛❞ ❡♥❞s ❛r❡ ❢♦✉♥❞ ❲❤❡r❡✿ ❇❛❝❦tr❛❝❦ t♦ t❤❡ ❝✉❧♣r✐t ✈❛r✐❛❜❧❡

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SLIDE 14

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❈✉❧♣r✐t ❱❛r✐❛❜❧❡

❉❡✜♥✐t✐♦♥ ✭❝✉❧♣r✐t ✈❛r✐❛❜❧❡✮ ¯ ❛✐ = ❛✶, · · · , ❛✐ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ❝✉❧♣r✐t ✐♥❞❡① → ❝✉❧♣(❛) = ♠✐♥✶≤❥≤✐{❛✶, · · · , ❛❥} ❝♦♥✢✐❝ts ✇✐t❤ ①✐+✶

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SLIDE 15

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • ❛s❝❤♥✐❣✬s ❇❛❝❦❥✉♠♣✐♥❣✿ ❊①❛♠♣❧❡

❊①❛♠♣❧❡ ✭●❈ ❊①❛♠♣❧❡✮ ❈♦♥s✐❞❡r ♣r❡✈✐♦✉s ●❈ ❡①❛♠♣❧❡ ✇✐t❤ s❛♠❡ ♦r❞❡r ❈♦♥s✐❞❡r t❤❡ ❢♦❧❧♦✇✐♥❣ tr❛❝❡ ❢♦r ❜❛❝❦tr❛❝❦✿ ❘, ❇, ❇, ❇, ●, ❘ ❚❤✐s ✐s ❛ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ❛♥❞ ●❛s❝❤♥✐❣ ❇❛❝❦❥✉♠♣ ✇✐❧❧ ❜❛❝❦tr❛❝❦ t♦ ①✸ ■t s❛✈❡s s❡❛r❝❤✐♥❣ t❤❡ ❜r❛♥❝❤ ✇❤❡r❡ ①✻ = ❨

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SLIDE 16

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • ❛s❝❤♥✐❣✬s ❇❛❝❦❥✉♠♣✐♥❣✿ Pr♦♣❡rt✐❡s

Pr♦♣❡rt✐❡s ❍✐st♦r✐❝❛❧❧② ✜rst ❜❛❝❦ ❥✉♠♣ ❛❧❣♦r✐t❤♠ P❡r❢♦r♠s ♦♥❧② s❛❢❡ ❥✉♠♣ ■t ♣❡r❢♦r♠s ♠❛①✐♠❛❧ ❥✉♠♣s

❥✉♠♣✐♥❣ ❢✉rt❤❡r ❜❛❝❦ ✇❡ ❝♦✉❧❞ ❧♦♦s❡ s♦❧✉t✐♦♥s

❈❛♥ ❜❡ ✐♠♣❧❡♠❡♥t❡❞ ❡✣❝✐❡♥t❧②

❈✉❧♣r✐t ✈❛r✐❛❜❧❡s ❝♦✉❧❞ ❜❡ ♠❛r❦❡❞ ✐♥ t❤❡ ❢♦r✇❛r❞ ♣❤❛s❡

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SLIDE 17

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • ❛s❝❤♥✐❣✬s ❇❛❝❦❥✉♠♣✐♥❣✿ ▲✐♠✐t❛t✐♦♥s

▲✐♠✐t❛t✐♦♥s ◆♦t ✈❡r② ♣♦✇❡r❢✉❧

❉♦ ♥♦t ❝✉t s✐❣♥✐✜❝❛♥t ♣❛rts ♦❢ t❤❡ s❡❛r❝❤ s♣❛❝❡ ❊①♣❛♥❞s str✐❝t❧② ♠♦r❡ s♣❛❝❡ t❤❛♥ ❢♦r✇❛r❞ ❝❤❡❝❦✐♥❣

■t ❜❛❝❦tr❛❝❦ ♦♥❧② ❛t ❧❡❛❢ ❞❡❛❞ ❡♥❞s

t♦♦ ❧❛t❡✱ ♠♦st ♦❢ t❤❡ ✇♦r❦ ❛❧r❡❛❞② ❞♦♥❡✳

  • r❛♣❤✲❇❛s❡❞ ❇❛❝❦❥✉♠♣✐♥❣ ✐♠♣r♦✈❡s ♦♥ t❤✐s
slide-18
SLIDE 18

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • r❛♣❤✲❇❛s❡❞ ❇❛❝❦❥✉♠♣✐♥❣

▼❛✐♥ ■❞❡❛s ❥✉♠♣s ❜❛❝❦ ❛t ❧❡❛❢ ❞❡❛❞ ❡♥❞s ❛♥❞ ❛t ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s ✉s❡s ♦♥❧② ✐♥❢♦r♠❛t✐♦♥ ❞❡r✐✈❡❞ ❢r♦♠ t❤❡ ❣r❛♣❤ str✉❝t✉r❡ t♦ ❥✉♠♣

❞♦ ♥♦t ✉s❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥ ✈❛r✐❛❜❧❡s✬ ❞♦♠❛✐♥ ♦r ♦♥ ♥❛t✉r❡ ♦❢ ❝♦♥str❛✐♥ts

❉❡✜♥✐t✐♦♥ ✭✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s✮ ❆ ♥♦✲❣♦♦❞ t❤❛t ✐s ❞❡✜♥❡❞ ♦♥ t❤❡ ✜rst ✐ ✈❛r✐❛❜❧❡s ❛♥❞ ✐s ♥♦t ❛ ❧❡❛❢ ❞❡❛❞ ❡♥❞✳

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SLIDE 19

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❏✉♠♣s ❛♥❞ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s

❊①❛♠♣❧❡ ✭■♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s✮ ❈♦♥s✐❞❡r t❤❡ ●❈ ❡①❛♠♣❧❡ ①✸ ✐s ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s ■♥ ❣❡♥❡r❛❧✱ ①✐ ✐s ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞ ✐❢ ❛ ❜❛❝❦❥✉♠♣✐♥❣ ❛❧❣♦r✐t❤♠ ❥✉♠♣s t❤❡r❡ ❢r♦♠ ❛ ❧❡❛❢ ❞❡❛❞ ❡♥❞✱ ❛♥❞ t❤❡r❡ ❛r❡ ♥♦ ♠♦r❡ ❝❛♥❞✐✲ ❞❛t❡ ✈❛❧✉❡s t♦ ✐♥st❛♥t✐❛t❡✳

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SLIDE 20

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • r❛♣❤✲❇❛s❡❞ ❇❛❝❦❥✉♠♣✐♥❣✿ ❲❤❡r❡ t♦ ❏✉♠♣

❯s✐♥❣ ●r❛♣❤✲❜❛s❡❞ ✐♥❢♦ ✉s❡ ♣r❡❝❡❞✐♥❣ ❛❞❥❛❝❡♥t ✈❛r✐❛❜❧❡s ❛s ❛♥ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ ❛ ♠✐♥✐♠❛❧ ❝♦♥✢✐❝t s❡t

❛❞❥❛❝❡♥t✿ ❝♦♥♥❡❝t❡❞ ♦♥ t❤❡ ♣r✐♠❛❧ ❣r❛♣❤

❛ss✉♠❡ ❛❧❧ ♣♦ss✐❜❧❡ ❝♦♥✢✐❝ts ❞♦ ❛♣♣❡❛r

t❤✐s r❡❛❧❧② ❞❡♣❡♥❞s ♦♥ t❤❡ ♣❛rt✐❝✉❧❛r ❛ss✐❣♥♠❡♥t

▲❛t❡st ♣r❡❝❡❞✐♥❣ ❛❞❥❛❝❡♥t ✈❛r✐❛❜❧❡ ✐s t❤❡ ❝✉❧♣r✐t ✈❛r✐❛❜❧❡

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SLIDE 21

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❯s❡❢✉❧ ❞❡✜♥✐t✐♦♥s

❉❡✜♥✐t✐♦♥ ✭❆♥❝❡st♦r✱ ♣❛r❡♥t✮

  • ✐✈❡♥ ❝♦♥str❛✐♥t ❣r❛♣❤✱ ♥♦❞❡ ♦r❞❡r✐♥❣ ❛♥❞ ❛ ✈❛r✐❛❜❧❡ ①

❚❤❡ ❛♥❝❡st♦r s❡t ♦❢ ① ❛♥❝(①) s❡t ♦❢ ✈❛r✐❛❜❧❡ t❤❛t ♣r❡❝❡❞❡ ❛♥❞ ❛r❡ ❝♦♥♥❡❝t❡❞ t♦ ① ❚❤❡ ♣❛r❡♥t ♦❢ ① ♣(①) ✐s t❤❡ ♠❛①✐♠❛❧ ✭♦r ❧❛t❡st✮ ✈❛r✐❛❜❧❡ ✐♥ ❛♥❝(①)

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SLIDE 22

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❙❛❢❡ ❏✉♠♣ ❢♦r ●❇✲❇❛❝❦❥✉♠♣✐♥❣

❚❤❡♦r❡♠ ✭s❛❢❡ ❥✉♠♣✮

  • ✐✈❡♥ ¯

❛✐ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ❛♥❞ ①✐+✶ t❤❡ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ✈❛r✐❛❜❧❡ ❚❤❡♥ ♣(①✐+✶) ✐s ❛ s❛❢❡ ❥✉♠♣ Pr♦♦❢✳ ¯ ❛✐ ❝♦♥s✐st❡♥t ❜✉t ❛♥② ❡①t❡♥s✐♦♥ t♦ ①✐+✶ ✐♥❝♦♥s✐st❡♥t t❤❡♥ ¯ ❛✐ ✐s ❛ ❝♦♥✢✐❝t s❡t ❢♦r ①✐+✶ t❤❡♥ ❛❧s♦ ¯ ❛♣(①✐+✶) ✐s ❛ ❝♦♥✢✐❝t s❡t ❢♦r ①✐+✶ ❜❡❝❛✉s❡ t❤❡r❡ ❛r❡ ♥♦ ✈❛r✐❛❜❧❡s ①❥ ✇✐t❤ ♣(①✐+✶) < ❥ < ✐ + ✶ t❤❛t ❛r❡ ❛❞❥❛❝❡♥t t♦ ①✐+✶ s✐♥❝❡ ❛♥② ❝♦♥✢✐❝t s❡t ✐s ❛ ♥♦✲❣♦♦❞ t❤❡♥ t❤❡ ❥✉♠♣ ✐s s❛❢❡

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SLIDE 23

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❈♦♠♣❛r✐♥❣ t♦ ●❛s❝❤♥✐❣

❝♦♠♣❛r✐s♦♥ ❏✉♠♣✐♥❣ ❜❛❝❦ t♦ t❤❡ ♣❛r❡♥t ❝❛♥ ♥♦t ❜❡ ❜❡tt❡r t❤❛♥ ❥✉♠♣✐♥❣ ❜❛❝❦ t♦ ❝✉❧♣r✐t ✈❛r✐❛❜❧❡✱ ✐♥ ❣❡♥❡r❛❧ ✐t ❝❛♥ ❜❡ ✇♦rs❡ ❇✉t ✇❡ ❝❛♥ ❥✉♠♣ ❢r♦♠ ✐♥t❡r♥❛❧ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ❛s ✇❡❧❧ s✐♠♣❧❡ ✐❞❡❛✿ ❥✉♠♣ ❜❛❝❦ t♦ t❤❡ ♣❛r❡♥t ♦❢ t❤❡ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞ ✈❛r✐❛❜❧❡ t❤✐s ✐s ✇r♦♥❣✿ ✇❡ ❝♦✉❧❞ ❧♦♦s❡ s♦❧✉t✐♦♥s

slide-24
SLIDE 24

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❯♥s❛❢❡ ❏✉♠♣s

❊①❛♠♣❧❡ ✭❯♥s❛❢❡ ❏✉♠♣✮ ❈♦♥s✐❞❡r t❤❡ ●❈ ❡①❛♠♣❧❡ ❙✉♣♣♦s❡ ①✺ ✐s ❧❡❛❢ ❞❡❛❞ ❡♥❞✱ ✐❢ ①✹ = ♣(①✺) ✐s ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞ ✐t ✐s s❛❢❡ t♦ ❥✉♠♣ ❜❛❝❦ t♦ ①✶ = ♣(①✹) ❙✉♣♣♦s❡ ①✼ ✐s ❧❡❛❢ ❞❡❛❞ ❡♥❞✱ ✇❡ ❥✉♠♣ t♦ ①✺ = ♣(①✼)✱ ✐❢ ①✺ ✐s ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞ ✐t ✐s s❛❢❡ t♦ ❥✉♠♣ t♦ ①✹ = ♣(①✺)✱ ❤♦✇❡✈❡r ✐t ✐s ♥♦t s❛❢❡ t♦ ❥✉♠♣ t♦ ①✶ = ♣(①✹) ①✶ < ①✸ ❛♥❞ ①✸ ∈ ❛♥❝(①✼) ▲❡ss♦♥✿ t♦ ❞❡❝✐❞❡ ✇❤❡r❡ t♦ ❥✉♠♣ ❢r♦♠ ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞✲❡♥❞ ✐t ❞♦❡s ♠❛tt❡r ✇❤✐❝❤ ✈❛r✐❛❜❧❡s ✐♥✐t✐❛t❡❞ t❤❡ ❜❛❝❦tr❛❝❦

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SLIDE 25

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❚❤❡ ❝♦♥❝❡♣t ♦❢ s❡ss✐♦♥

❉❡✜♥✐t✐♦♥ ✭■♥✈✐s✐t✮ ❚❤❡ ❜❛❝❦tr❛❝❦ ❛❧❣♦r✐t❤♠ ✐♥✈✐s✐ts ①✐ ✇❤❡♥ ✐t ❛tt❡♠♣ts t♦ ❡①t❡♥❞ t❤❡ ❛ss✐❣♥♠❡♥t ¯ ❛✐−✶ t♦ ①✐ ❉❡✜♥✐t✐♦♥ ✭❙❡ss✐♦♥✮ ❆ s❡ss✐♦♥ ❢♦r ①✐ st❛rts ✇❤❡♥ ①✐ ✐s ✐♥✈✐s✐t❡❞ ❜② t❤❡ ❜❛❝❦tr❛❝❦ ❛❧❣♦r✐t❤♠ ❛♥❞ ❡♥❞s ✇❤❡♥ t❤❡ ❛❧❣♦r✐t❤♠ ❜❛❝❦tr❛❝❦s ❢r♦♠ ①✐ ✭✐✳❡✳ ❛❧❧ ♣♦ss✐❜❧❡ ✈❛❧✉❡s ♦❢ ①✐ ❤❛✈❡ ❜❡❡♥ tr✐❡❞✮✳ ■t ❝♦♥t❛✐♥s ①✐ ❛♥❞ ❛❧❧ t❤❡ ❧❛t❡r ✈❛r✐❛❜❧❡s ✈✐s✐t❡❞ ❞✉r✐♥❣ t❤❡ s❡ss✐♦♥✳

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SLIDE 26

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❘❡❧❡✈❛♥t ❞❡❛❞ ❡♥❞s

❉❡✜♥✐t✐♦♥ ✭❘❡❧❡✈❛♥t ❞❡❛❞ ❡♥❞s✮ r(①✐) = {①✐} ✇❤❡♥ ①✐ ✐s ✐♥✈✐s✐t❡❞ r(①✐) = r(①✐) ∪ r(①❥) ✇✐t❤ ❥ > ✐ ✇❤❡♥ t❤❡ ❛❧❣♦r✐t❤♠ ❜❛❝❦tr❛❝❦ t♦ ①✐ ❢r♦♠ ①❥ ✭❞❡❛❞✲❡♥❞✮

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SLIDE 27

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • ❇✲❇❛❝❦❥✉♠♣ ❆❧❣♦r✐t❤♠

❆❧❣♦r✐t❤♠ ❲❤❡♥ ❛t ❛ ✭❧❡❛❢ ♦r ✐♥t❡r♥❛❧✮ ❞❡❛❞ ❡♥❞ ¯ ❛✐ ❏✉♠♣ ❜❛❝❦ t♦ t❤❡ ❧❛t❡st ❛♥❝❡st♦r ♦❢ ❛♥② ✈❛r✐❛❜❧❡ ✐♥ r(①✐) t❤❛t ✐s ❜❡❢♦r❡ ①✐ ✭❝✉❧♣r✐t ❢♦r ●❇ ❜❛❝❦❥✉♠♣✐♥❣✮ ❚❤❡♦r❡♠ ✭s♦✉♥❞♥❡ss✮

  • r❛♣❤ ❜❛s❡❞ ❜❛❝❦❥✉♠♣ ♦♥❧② ♣❡r❢♦r♠s s❛❢❡✱ ♠❛①✐♠❛❧ ❥✉♠♣s
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SLIDE 28

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❈♦♥✢✐❝t ❉✐r❡❝t❡❞ ❇❛❝❦❥✉♠♣✐♥❣

❈♦♠❜✐♥✐♥❣ t❤❡ ❛♣♣r♦❛❝❤❡s

  • ❛s❝❤♥✐❣✿ ❡①♣❧♦✐ts ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t ♠✐♥✐♠❛❧ ♣r❡✜①

❝♦♥✢✐❝ts t♦ ❥✉♠♣ ❢✉rt❤❡r ❢r♦♠ ❧❡❛❢ ❞❡❛❞ ❡♥❞s

  • r❛♣❤✲❇❛s❡❞✿ ❡①♣❧♦✐ts ❝♦♥♥❡❝t✐✈✐t② ✐♥❢♦r♠❛t✐♦♥ t♦ ❥✉♠♣

❛❧s♦ ❛t ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞s ■❞❡❛s ❝❛♥ ❜❡ ❝♦♠❜✐♥❡❞✿ ❈♦♥✢✐❝t ❉✐r❡❝t❡❞ ❇❛❝❦❥✉♠♣✐♥❣ ❇❡tt❡r✿ ❛✈♦✐❞s ♠♦r❡ st❛t❡ t❤❛♥ ❡✐t❤❡r ♦❢ t❤❡ t✇♦ ♣r❡✈✐♦✉s ❛♣♣r♦❛❝❤❡s

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SLIDE 29

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❆✈♦✐❞✐♥❣ t❤r❛s❤✐♥❣ ❇❛❝❦❥✉♠♣✐♥❣ ❝❛♥ ❛✈♦✐❞ ♠❛♥② ✐rr❡❧❡✈❛♥t ❝❤♦✐❝❡s t❤✉s r❡❞✉❝✐♥❣ t❤❡ s❡❛r❝❤ s♣❛❝❡ ❚❤r❛s❤✐♥❣ ❝❛♥ st✐❧❧ ❤❛♣♣❡♥✿ s❛♠❡ ♥♦✲❣♦♦❞ r❡❞✐s❝♦✈❡r❡❞ ♦✈❡r ❛♥❞ ♦✈❡r ❛❣❛✐♥ ◆♦✲❣♦♦❞ ❧❡❛r♥✐♥❣ ♦r ❝♦♥str❛✐♥t r❡❝♦r❞✐♥❣ ❝❛♥ ❛✈♦✐❞ t❤✐s

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SLIDE 30

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

❆❞❞✐♥❣ ◆♦✲●♦♦❞s

❇❛s✐❝ ■❞❡❛ ❱❡r② s✐♠♣❧❡ ❝♦♥❝❡♣t ❲❤❡♥ ❜❛❝❦tr❛❝❦ ✭♦r ❥✉♠♣ ❜❛❝❦✮ ❉❡t❡r♠✐♥❡ ❛ ❝♦♥✢✐❝t s❡t ❆❞❞ ❛ ❝♦♥str❛✐♥t t♦ t❤❡ ♥❡t✇♦r❦ t❤❛t ❛✈♦✐❞s t❤❛t ❝♦♥✢✐❝t s❡t

slide-31
SLIDE 31

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

▼❛♥② ♣♦ss✐❜✐❧✐t✐❡s

◆♦✲●♦♦❞ ❧❡❛r♥✐♥❣ ✈❛r✐❛t✐♦♥s ❙❤❛❧❧♦✇ ▲❡❛r♥✐♥❣✿ ❞❡t❡r♠✐♥❡ ❛ ♥♦✲❣♦♦❞ t❤❛t ✐s ❡❛s② t♦ ❣❡♥❡r❛t❡ ❜✉t ♥♦t ♠✐♥✐♠❛❧ ❉❡❡♣ ▲❡❛r♥✐♥❣✿ ❉❡t❡r♠✐♥❡ ❛ ♥♦✲❣♦♦❞ ✇❤✐❝❤ ✐s ♠✐♥✐♠❛❧ ❛♥❞ ❡✈❡♥ ❞❡r✐✈❡ ❛❧❧ ♠✐♥✐♠❛❧ ♦♥❡s ❢r♦♠ t❤✐s ♥♦✲❣♦♦❞ ❇♦✉♥❞❡❞ ▲❡❛r♥✐♥❣✿ ❙t♦r❡ ♦♥❧② ❝♦♥str❛✐♥t ✇✐t❤ ❛ ❜♦✉♥❞❡❞ ❛r✐t② ✭s♠❛❧❧❡r t❤❛♥ ❛ ♣r❡❞❡t❡r♠✐♥❡❞ ♣❛r❛♠❡t❡r✮ ❘❡❧❡✈❛♥❝❡ ❜♦✉♥❞❡❞ ❧❡❛r♥✐♥❣✿ ❞♦ ♥♦t r❡❝♦r❞ t❤❡ ♥♦✲❣♦♦❞ ✐❢ t❤❡ ❝✉rr❡♥t st❛t❡ ❞✐✛❡rs ❢r♦♠ t❤❡ ♥♦✲❣♦♦❞ ✐♥ ♠♦r❡ t❤❛♥ ❝ ✈❛r✐❛❜❧❡s

slide-32
SLIDE 32

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣✿ tr❛❞❡✲♦✛s

❋✐♥❞✐♥❣ ❛ ❜❛❧❛♥❝❡ Pr✉♥✐♥❣ ♣♦✇❡r✿ ♠♦r❡ ♥♦✲❣♦♦❞ → ❧❡ss ✈✐s✐t❡❞ st❛t❡s ❈♦♠♣✉t❛t✐♦♥✿ ♠♦r❡ ♥♦✲❣♦♦❞ → ♠♦r❡ ❡✛♦rt ✐♥ ❝❤❡❝❦✐♥❣ ❝♦♥s✐st❡♥❝② ❈♦♠♣✉t❛t✐♦♥ ❖✈❡r❤❡❛❞✿ ♣r♦❝❡ss✐♥❣ ♥♦✲❣♦♦❞s t♦ ✜♥❞ ♠✐♥✐♠❛❧ ❝♦♥✢✐❝ts s❡ts ❤❛s ❛ ❝♦st ❙♣❛❝❡ ❖✈❡r❤❡❛❞✿ st♦r✐♥❣ ♥♦✲❣♦♦❞

slide-33
SLIDE 33

❙❡❛r❝❤ ❙tr❛t❡❣✐❡s✿ ▲♦♦❦❜❛❝❦ ▲♦♦❦❜❛❝❦ s❝❤❡♠❡s

  • ❛s❝❤♥✐❣✬s

❇❛❝❦❥✉♠♣✐♥❣

  • r❛♣❤ ❇❛s❡❞

❇❛❝❦❥✉♠♣✐♥❣ ◆♦✲●♦♦❞ ▲❡❛r♥✐♥❣

  • r❛♣❤ ❜❛s❡❞ ❧❡❛r♥✐♥❣
  • ❇ ▲❡❛r♥✐♥❣

■♥ s♦♠❡ ❝❛s❡s ✜♥❞✐♥❣ r❡❧❡✈❛♥t ♥♦✲❣♦♦❞ ✐s ❡❛s②

❲❤❡♥ ❥✉♠♣✐♥❣ ❜❛❝❦ ❢r♦♠ ❛ ❧❡❛❢ ❞❡❛❞ ❡♥❞ ¯ ❛✐ ✇✐t❤ ❞❡❛❞ ❡♥❞ ✈❛r✐❛❜❧❡ ①✐✱ ❘❡❧(①✐) = ❛♥❝(①✐) ❲❤❡♥ ❥✉♠♣✐♥❣ ❜❛❝❦ ❢r♦♠ ❛♥ ✐♥t❡r♥❛❧ ❞❡❛❞ ❡♥❞ ①✐✱ ❘❡❧(①✐) t❤❡ s❡t ♦❢ ❛♥❝❡st♦rs ♦❢ ❛❧❧ ✈❛r✐❛❜❧❡s ✐♥ r(①✐) t❤❛t ♣r❡❝❡❞❡ ①✐ ❆❞❞ t❤❡ ♥♦✲❣♦♦❞ {< ①, ✈ > |① ∈ ❘❡❧(①✐) ∧ ✈ = ¯ ❛✐(①)}