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Feb 24, 2023 333 likes •532 views

rt sts s r t s r s r

SLIDE 1

❖♣❡r❛t✐♥❣ ❙②st❡♠s✿ ❉❡❛❞❧♦❝❦s

❙❤❛♥❦❛r ▼❛② ✼✱ ✷✵✶✺

SLIDE 2

❖✉t❧✐♥❡

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇ ❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ✫ ❘❡❝♦✈❡r② ❍❛♥❞❧✐♥❣ ❉❡❛❞❧♦❝❦s ✐♥ ❘❡❛❧✐t②

SLIDE 3

❲❤❛t ❛r❡ ❉❡❛❞❧♦❝❦s

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇

❉❡❛❞❧♦❝❦✿ ❙❡t ♦❢ ♣r♦❝❡ss❡s P✶✱ · · · ✱ PN ❞❡❛❞❧♦❝❦❡❞ ✐✛ ❡✈❡r② Pi ✐s ❜❧♦❝❦❡❞✱ ❛♥❞ ❡✈❡r② Pi ✐s ✇❛✐t✐♥❣ ❢♦r ❛♥ ❡✈❡♥t ❞♦❛❜❧❡ ♦♥❧② ❜② s♦♠❡ Pj ✴✴ ❡✈❡♥t✿ r❡❧❡❛s❡✱ s✐❣♥❛❧✱ ❱✱ ✐♥t❡rr✉♣t ❡♥❛❜❧❡✱ ✳✳✳ ❉❡❛❞❧♦❝❦ ❢r❡❡❞♦♠✿ ❞❡s✐r❡❞ ♣r♦♣❡rt② ♦❢ ♠✉❧t✐✲t❤r❡❛❞❡❞ ♣r♦❣r❛♠s ❡♥s✉r✐♥❣ t❤✐s ✐s ❤❛r❞ ❢♦r ❛ ❣❡♥❡r❛❧ ♠✉❧t✐✲t❤r❡❛❞❡❞ ♣r♦❣r❛♠ ❜✉t ❡❛s✐❡r ❢♦r ❛ r❡s♦✉r❝❡✲♠❛♥❛❣❡r s②st❡♠ ❡①❛♠✐♥❡❞ ♥❡①t ❆s✐❞❡✿ ▲✐✈❡❧♦❝❦ ✐s ❞❡❛❞❧♦❝❦ ✇✐t❤♦✉t ❜❧♦❝❦✐♥❣ ♣r♦❝❡ss❡s ❛r❡ ✐♥ ❢r✉✐t❧❡ss ❧♦♦♣s ❤❛r❞❡r t♦ ❞❡t❡❝t ✭✉♥❧❡ss ❧♦♦♣s ❛r❡ ✈❡r② ❧♦❝❛❧✐③❡❞✮ ❞❡❛❞❧♦❝❦ ❝❛♥ ❜❡ ❧✐✈❡❧♦❝❦ ❛t ❛ ❧♦✇❡r ✭s♣✐♥✲❧♦❝❦✮ ❧❡✈❡❧

SLIDE 4

❘❡s♦✉r❝❡ ▼❛♥❛❣❡r ❙②st❡♠

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇

❙②st❡♠ ❂ r❡s♦✉r❝❡ ♠❛♥❛❣❡r ✰ ✉s❡r ♣r♦❝❡ss❡s ♣r♦❝❡ss❡s✿ r❡q✉❡st r❡s♦✉r❝❡s✱ ❣❡t t❤❡♠✱ r❡❧❡❛s❡ t❤❡♠ RES✿ s❡t ♦❢ ❛❧❧ r❡s♦✉r❝❡s✱ ✐♥✐t✐❛❧❧② ❤❡❧❞ ❜② ♠❛♥❛❣❡r alloc(p)✿ r❡s♦✉r❝❡s ❝✉rr❡♥t❧② ❤❡❧❞ ❜② p avail✿ r❡s♦✉r❝❡s ❝✉rr❡♥t❧② ❤❡❧❞ ❜② ♠❛♥❛❣❡r ❋✉♥❝t✐♦♥ req(p, res)✿ r❡q✉❡st ❜② p ❢♦r r❡s♦✉r❝❡s res ❝❛❧❧❛❜❧❡ ✐✛ res ✰ alloc(p) ⊆ RES ❜❧♦❝❦✐♥❣ ❝❛❧❧ p ❣❡ts res ❛t r❡t✉r♥❀ ❤❛♣♣❡♥s ♦♥❧② ✐❢ res ⊆ avail ❋✉♥❝t✐♦♥ rel(p, res)✿ r❡❧❡❛s❡ ❜② p ♦❢ res ❝❛❧❧❛❜❧❡ ✐✛ res ⊆ alloc(p) ♥♦♥❜❧♦❝❦✐♥❣ ❙②st❡♠ ❝❛♥ ❞❡❛❞❧♦❝❦ ✇✐t❤♦✉t ❢✉rt❤❡r ❝♦♥str❛✐♥ts ✸ ❛♣♣r♦❛❝❤❡s✿ ♣r❡✈❡♥t✐♦♥✱ ❛✈♦✐❞❛♥❝❡✱ ❞❡t❡❝t✐♦♥✴r❡❝♦✈❡r②

SLIDE 5

❖✉t❧✐♥❡

Pr❡✈❡♥t✐♦♥

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇ ❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ✫ ❘❡❝♦✈❡r② ❍❛♥❞❧✐♥❣ ❉❡❛❞❧♦❝❦s ✐♥ ❘❡❛❧✐t②

SLIDE 6

❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❆♣♣r♦❛❝❤

Pr❡✈❡♥t✐♦♥

■♠♣♦s❡ ❢✉rt❤❡r ❝♦♥str❛✐♥ts ♦♥ req ❝❛❧❧s t♦ ♣r❡❝❧✉❞❡ ❞❡❛❞❧♦❝❦ ♥♦ ❢✉rt❤❡r ❝♦♥str❛✐♥ts ♦♥ req r❡t✉r♥s ❙t❡♣ ✶✿ ✐❞❡♥t✐❢② ❛ ♥❡❝❡ss❛r② ❝♦♥❞✐t✐♦♥ ❢♦r ❞❡❛❞❧♦❝❦✱ ❡❣✿ r❡s♦✉r❝❡ t❤❛t ✐s ♥♦♥✲s❤❛r❡❛❜❧❡ ❛♥❞ ♥♦♥✲♣r❡❡♠♣t❛❜❧❡ ♣r♦❝❡ss ❤♦❧❞s ❛ r❡s♦✉r❝❡ ❛♥❞ r❡q✉❡sts ♠♦r❡ r❡s♦✉r❝❡s ❝②❝❧❡ ♦❢ ♣r♦❝❡ss❡s✿ ❡❛❝❤ r❡q✉❡st✐♥❣ ❛ r❡s♦✉r❝❡ ❤❡❧❞ ❜② t❤❡ ♥❡①t ❙t❡♣ ✷✿ ❝♦♥str❛✐♥ req ❝❛❧❧s t♦ ♣r❡❝❧✉❞❡ ❛ ♥❡❝❡ss❛r② ❝♦♥❞✐t✐♦♥ ❍❡♥❝❡❢♦rt❤ ❛ss✉♠❡ ♥♦♥✲s❤❛r❡❛❜❧❡✴♥♦♥✲♣r❡❡♠♣t❛❜❧❡ r❡s♦✉r❝❡s ❊①❛♠♣❧❡s ♦❢ ❞❡❛❞❧♦❝❦ ♣r❡✈❡♥t✐♦♥ r✉❧❡s req(p, res) ❝❛♥ ❜❡ ❝❛❧❧❡❞ ♦♥❧② ✇❤❡♥ alloc(p) ✐s ❡♠♣t② ■♠♣♦s❡ ❛ t♦t❛❧ ♦r❞❡r✐♥❣ ♦♥ ❛❧❧ r❡s♦✉r❝❡s ✐♥ RES req(p, res) ❝❛♥ ❜❡ ❝❛❧❧❡❞ ♦♥❧② ✇❤❡♥ res > max(alloc(p))

SLIDE 7

❖✉t❧✐♥❡

❆✈♦✐❞❛♥❝❡

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇ ❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ✫ ❘❡❝♦✈❡r② ❍❛♥❞❧✐♥❣ ❉❡❛❞❧♦❝❦s ✐♥ ❘❡❛❧✐t②

SLIDE 8

❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❆♣♣r♦❛❝❤

❆✈♦✐❞❛♥❝❡

❉❡❛❞❧♦❝❦ ❛✈♦✐❞❛♥❝❡✿ ✐♠♣♦s❡ ❢✉rt❤❡r ❝♦♥str❛✐♥ts ♦♥ req r❡t✉r♥s t♦ ♣r❡❝❧✉❞❡ ❞❡❛❞❧♦❝❦ s♦ req(p, res) r❡t✉r♥ ♠❛② ✇❛✐t ❡✈❡♥ ✐❢ res ⊆ avail ♠❛② ❛❧s♦ ✐♥✈♦❧✈❡ ✇❡❛❦ ❝♦♥str❛✐♥ts ♦♥ req ❝❛❧❧s ❡❣✱ ❧✐♠✐t ♦♥ t♦t❛❧ r❡s♦✉r❝❡s t❤❛t ❛ ♣r♦❝❡ss ❝❛♥ ❤♦❧❞ ❝❛♥ ❛❧❧♦✇ ♠♦r❡ ♣❛r❛❧❧❡❧✐s♠ t❤❛♥ ❞❡❛❞❧♦❝❦ ♣r❡✈❡♥t✐♦♥ ❜✉r❞❡♥ ✐s ♦♥ ♠❛♥❛❣❡r ✭✉♥❧✐❦❡ ❞❡❛❞❧♦❝❦ ♣r❡✈❡♥t✐♦♥✮ ❈❧❛ss✐❝❛❧ ❞❡❛❞❧♦❝❦ ❛✈♦✐❞❛♥❝❡ s♦❧✉t✐♦♥ ✉s❡s t❤❡ ✏❇❛♥❦❡r✬s ❛❧❣♦r✐t❤♠✑

SLIDE 9

❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❙♦❧✉t✐♦♥ ✕ ✶

❆✈♦✐❞❛♥❝❡

❘❡s♦✉r❝❡s✿ ♦r❣❛♥✐③❡❞ ✐♥t♦ t②♣❡s ✶, · · · , M Tot = [Tot✶, · · · , TotM] ✴✴ t♦t❛❧ ★ ♦❢ ❡❛❝❤ r❡s♦✉r❝❡ t②♣❡ Pr♦❝❡ss❡s✿ ✶, · · · , N Maxi✿ [Maxi,✶, · · · Maxi,M] ✴✴ ♠❛① t♦t❛❧ ♥❡❡❞ ♦❢ ♣r♦❝❡ss i ❱❛r✐❛❜❧❡s alloci✿ [alloci,✶, · · · , alloci,M] ✴✴ r❡s♦✉r❝❡s ❤❡❧❞ ❜② ♣r♦❝❡ss i avail✿ [avail✶, · · · , availM] ✴✴ r❡s♦✉r❝❡s ❤❡❧❞ ❜② ♠❛♥❛❣❡r reqi✿ [reqi,✶, · · · , reqi,M] ✴✴ ♣r♦❝❡ss i✬s ♦♥❣♦✐♥❣ r❡q✉❡st needi✿ Maxi − alloci ✴✴ ♣r♦❝❡ss i✬s ♠❛① ♣♦ss✐❜❧❡ r❡q✉❡st

SLIDE 10

❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❙♦❧✉t✐♦♥ ✕ ✷

❆✈♦✐❞❛♥❝❡

❆ss✉♠♣t✐♦♥✿ ■❢ ❛ ♣r♦❝❡ss i ❛❧✇❛②s ❣❡ts t❤❡ r❡s♦✉r❝❡s ✐t ❛s❦s ❢♦r✱ ✐t ❡✈❡♥t✉❛❧❧② r❡❧❡❛s❡s ❛❧❧ ✐ts r❡s♦✉r❝❡s ❙♦ ✐❢ needi ≤ avail ❛♥❞ t❤❡ ♠❛♥❛❣❡r ❣r❛♥ts ♦♥❧② r❡q✉❡sts ♦❢ i✱ t❤❡♥ ✐t ❡✈❡♥t✉❛❧❧② ❣❡ts alloci ❜❛❝❦ ❆ st❛t❡ ✐s s❛❢❡ ✐✛ ✐t ❤❛s ❛ s❛❢❡ s❡q✉❡♥❝❡ ❆ s❛❢❡ s❡q✉❡♥❝❡ ✐s ❛ ♣❡r♠✉t❛t✐♦♥ i✶, · · · , iN ♦❢ ♣r♦❝❡ss ✐❞s s✳t✳ needi✶ ≤ avail needi✷ ≤ avail + alloci✶ ✳✳✳ neediN ≤ avail + alloci✶ + · · · + allociN−✶ ❆ s❛❢❡ st❛t❡ ✐s ♥♦t ❞❡❛❞❧♦❝❦❡❞ ❛♥❞ ❝❛♥♥♦t ❧❡❛❞ t♦ ❛ ❞❡❛❞❧♦❝❦

SLIDE 11

❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❙♦❧✉t✐♦♥ ✕ ✷

❆✈♦✐❞❛♥❝❡

❇❛♥❦❡r✬s ❆❧❣♦r✐t❤♠✿ ❞❡t❡r♠✐♥❡s ✇❤❡t❤❡r ♦r ♥♦t ❛ st❛t❡ ✐s s❛❢❡ ❱❛r✐❛❜❧❡s xavail ← avail ✴✴ t❡♠♣♦r❛r② avail done[i] ← ❢❛❧s❡✱ ❢♦r i = ✶, · · · , N ✴✴ tr✉❡ ✐✛ i ❛❝❝♦✉♥t❡❞ ❢♦r ❲❤✐❧❡ ✭t❤❡r❡ ✐s ❛♥ i s✳t✳ done[i] = ❢❛❧s❡ ❛♥❞ needi ≤ xavail✮ xavail ← xavail + alloci done[i] ← true ❙❛❢❡ ✐✛ done[i] = true ❢♦r ❡✈❡r② i ❘❡t✉r♥ req(p, res) ♦♥❧② ✐❢ t❤❡ r❡s✉❧t✐♥❣ st❛t❡ ✇♦✉❧❞ ❜❡ s❛❢❡✱ ✐❡✱ ❛♣♣❧② ❇❛♥❦❡r✬s ❛❧❣♦r✐t❤♠ t♦ t❤❡ ❝✉rr❡♥t st❛t❡ ✇✐t❤ avail ❞❡❝r❡❛s❡❞ ❜② res alloci ✐♥❝r❡❛s❡❞ ❜② res

SLIDE 12

❇❛♥❦❡r✬s ❆❧❣♦r✐t❤♠ ❊①❛♠♣❧❡

❆✈♦✐❞❛♥❝❡

✺ ♣r♦❝❡ss❡s✱ ✸ r❡s♦✉r❝❡ t②♣❡s Tot✿ ❬✶✵ ✺ ✼❪ ❙t❛t❡ ▼❛① P✶ ✼ ✺ ✸ P✷ ✸ ✷ ✷ P✸ ✾ ✵ ✷ P✹ ✷ ✷ ✷ P✺ ✹ ✸ ✸ ❛❧❧♦❝ ✵ ✶ ✵ ✷ ✵ ✵ ✸ ✵ ✷ ✷ ✶ ✶ ✵ ✵ ✷ ❙❛❢❡❄

SLIDE 13

❇❛♥❦❡r✬s ❆❧❣♦r✐t❤♠ ❊①❛♠♣❧❡

❆✈♦✐❞❛♥❝❡

✺ ♣r♦❝❡ss❡s✱ ✸ r❡s♦✉r❝❡ t②♣❡s Tot✿ ❬✶✵ ✺ ✼❪ ❙t❛t❡ ▼❛① P✶ ✼ ✺ ✸ P✷ ✸ ✷ ✷ P✸ ✾ ✵ ✷ P✹ ✷ ✷ ✷ P✺ ✹ ✸ ✸ ❛❧❧♦❝ ✵ ✶ ✵ ✷ ✵ ✵ ✸ ✵ ✷ ✷ ✶ ✶ ✵ ✵ ✷ ♥❡❡❞ ✼ ✹ ✸ ✶ ✷ ✷ ✻ ✵ ✵ ✵ ✶ ✶ ✹ ✸ ✶ ❙❛❢❡❄

SLIDE 14

❇❛♥❦❡r✬s ❆❧❣♦r✐t❤♠ ❊①❛♠♣❧❡

❆✈♦✐❞❛♥❝❡

✺ ♣r♦❝❡ss❡s✱ ✸ r❡s♦✉r❝❡ t②♣❡s Tot✿ ❬✶✵ ✺ ✼❪ ❙t❛t❡ ▼❛① P✶ ✼ ✺ ✸ P✷ ✸ ✷ ✷ P✸ ✾ ✵ ✷ P✹ ✷ ✷ ✷ P✺ ✹ ✸ ✸ ❛❧❧♦❝ ✵ ✶ ✵ ✷ ✵ ✵ ✸ ✵ ✷ ✷ ✶ ✶ ✵ ✵ ✷ ♥❡❡❞ ✼ ✹ ✸ ✶ ✷ ✷ ✻ ✵ ✵ ✵ ✶ ✶ ✹ ✸ ✶ ❛✈❛✐❧ ✸ ✸ ✷ ❙❛❢❡❄

SLIDE 15

❇❛♥❦❡r✬s ❆❧❣♦r✐t❤♠ ❊①❛♠♣❧❡

❆✈♦✐❞❛♥❝❡

✺ ♣r♦❝❡ss❡s✱ ✸ r❡s♦✉r❝❡ t②♣❡s Tot✿ ❬✶✵ ✺ ✼❪ ❙t❛t❡ ▼❛① P✶ ✼ ✺ ✸ P✷ ✸ ✷ ✷ P✸ ✾ ✵ ✷ P✹ ✷ ✷ ✷ P✺ ✹ ✸ ✸ ❛❧❧♦❝ ✵ ✶ ✵ ✷ ✵ ✵ ✸ ✵ ✷ ✷ ✶ ✶ ✵ ✵ ✷ ♥❡❡❞ ✼ ✹ ✸ ✶ ✷ ✷ ✻ ✵ ✵ ✵ ✶ ✶ ✹ ✸ ✶ ❞♦♥❡ ❛✈❛✐❧ ✸ ✸ ✷ P✷ ✺ ✸ ✷ P✹ ✼ ✹ ✸ P✺ ✼ ✹ ✺ P✶ ✼ ✺ ✺ P✸ ✶✵ ✺ ✼ ❙❛❢❡❄ ❨❡s✳ ❙❛❢❡ s❡q✉❡♥❝❡✿ P✷✱ P✹✱ P✶✱ P✸

SLIDE 16

❖✉t❧✐♥❡

❉❡t❡❝t✐♦♥✲❘❡❝♦✈❡r②

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇ ❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ✫ ❘❡❝♦✈❡r② ❍❛♥❞❧✐♥❣ ❉❡❛❞❧♦❝❦s ✐♥ ❘❡❛❧✐t②

SLIDE 17

❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ❛♥❞ ❘❡❝♦✈❡r②

❉❡t❡❝t✐♦♥✲❘❡❝♦✈❡r②

❉♦ ♥♦t ❝♦♥str❛✐♥ req ❝❛❧❧s ♦r r❡t✉r♥s ■♥st❡❛❞ ♣❡r✐♦❞✐❝❛❧❧② ❝❤❡❝❦ ❢♦r ❞❡❛❞❧♦❝❦✳ ■❢ ②❡s✱ ❝❤♦♦s❡ ❛ ♣r♦❝❡ss i ❛♥❞ ❢♦r❝❡❛❜❧② r❡❧❡❛s❡ alloci ❉❡❛❞❧♦❝❦ ❞❡t❡❝t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r M r❡s♦✉r❝❡ t②♣❡s ✴✴ ✈❛r✐❛t✐♦♥ ♦❢ ❇❛❦❡r✬s ❛❧❣♦r✐t❤♠ ❱❛r✐❛❜❧❡s xavail ← avail ✴✴ t❡♠♣♦r❛r② avail done[i] ← ❢❛❧s❡✱ ❢♦r i = ✶, · · · , N ✴✴ tr✉❡ ✐✛ i ❛❝❝♦✉♥t❡❞ ❢♦r ❲❤✐❧❡ ✭t❤❡r❡ ✐s ❛♥ i s✳t✳ done[i] = ❢❛❧s❡ ❛♥❞ reqi ≤ xavail✮ xavail ← xavail + alloci done[i] ← true ❉❡❛❞❧♦❝❦ ✐✛ done[i] = ❢❛❧s❡ ❢♦r ❡✈❡r② i

SLIDE 18

❖✉t❧✐♥❡

❘❡❛❧✐t②

❉❡❛❞❧♦❝❦s ❖✈❡r✈✐❡✇ ❉❡❛❞❧♦❝❦ Pr❡✈❡♥t✐♦♥ ❉❡❛❞❧♦❝❦ ❆✈♦✐❞❛♥❝❡ ❉❡❛❞❧♦❝❦ ❉❡t❡❝t✐♦♥ ✫ ❘❡❝♦✈❡r② ❍❛♥❞❧✐♥❣ ❉❡❛❞❧♦❝❦s ✐♥ ❘❡❛❧✐t②

SLIDE 19

❲❤❛t ❤❛♣♣❡♥s ✐♥ r❡❛❧✲❧✐❢❡

❘❡❛❧✐t②

❘❡s♦✉r❝❡s ❛r❡ ✐♥❝r❡❛s✐♥❣❧② s❤❛r❡❛❜❧❡ ❞✐s❦s ✭✈s t❛♣❡s✮ ❞❡♠❛♥❞✲♣❛❣✐♥❣ ✭✈s ❡♥t✐r❡ ♣r♦❝❡ss s♣❛❝❡ ✐♥ ♣❤②s✐❝❛❧ ♠❡♠♦r②✮ ✈✐rt✉❛❧✐③❛t✐♦♥ ♦❢ ❡✈❡r②t❤✐♥❣ ❍❡♥❝❡ ❧✐✈❡❧♦❝❦ ✭♦r t❤r❛s❤✐♥❣✮ ✐s ♠♦r❡ ❝♦♠♠♦♥ t❤❛♥ ❞❡❛❞❧♦❝❦ ❍❡♥❝❡ ❞❡❛❞❧♦❝❦ ♣r❡✈❡♥t✐♦♥✴❛✈♦✐❞❛♥❝❡✴❞❡t❡❝t✐♦♥ ✐s r❛r❡❧② ✉s❡❞ ■♥st❡❛❞✱ ✐❢ s②st❡♠ ✏❛♣♣❡❛rs✑ t♦ ❜❡ ✐♥ ❞❡❛❞❧♦❝❦ ✭♦r ❧✐✈❡❧♦❝❦✮✱ ❦✐❧❧ ❛♥❞✴♦r r❡st❛rt ♣r♦❝❡ss❡s ♦r ❡♥t✐r❡ s②st❡♠