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Jan 24, 2024 282 likes •768 views

t tts rrt Prrs rrt tr s P

SLIDE 1

❱❛❧✐❞❛t✐♥❣ ❖♣t✐♠✐③❛t✐♦♥s ♦❢ ❈♦♥❝✉rr❡♥t ❈✴❈✰✰ Pr♦❣r❛♠s ❙♦❤❛♠ ❈❤❛❦r❛❜♦rt② ❱✐❦t♦r ❱❛❢❡✐❛❞✐s

▼P■✲❙❲❙

❈●❖ ✷✵✶✻

SLIDE 2

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❳ = ✶; ✐❢ (❳) r = ❨;

❘❛❝❡ ♦♥ ❳ ✉♥❞❡✜♥❡❞ s❡♠❛♥t✐❝s

✶ ✹ ✐s ♣♦ss✐❜❧❡ ✭✐✳❡✳✱ t❤❡ ♣r♦❣r❛♠ ✐s ✇r♦♥❣✮

✷

SLIDE 3

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❳ = ✶; ✐❢ (❳) r = ❨;

❘❛❝❡ ♦♥ ❳ ❀ ✉♥❞❡✜♥❡❞ s❡♠❛♥t✐❝s

X == ✶ ∧ r = ✹ ✐s ♣♦ss✐❜❧❡ ✭✐✳❡✳✱ t❤❡ ♣r♦❣r❛♠ ✐s ✇r♦♥❣✮

✷

SLIDE 4

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 5

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 6

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 7

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 8

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 9

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 10

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ✵ ✹

r❡❧

✶ ✐❢

❛❝q

✸

SLIDE 11

❈♦♥❝✉rr❡♥t Pr♦❣r❛♠♠✐♥❣ ✐♥ ❈✶✶ ❛t♦♠✐❝❴✐♥t ❳ = ✵; ✐♥t ❨ = ✵; ❨ = ✹; ❛t♦♠✐❝❴st♦r❡(&❳, ✶, ♠♦❴r❡❧❡❛s❡); ✐❢ (❛t♦♠✐❝❴❧♦❛❞(&❳, ♠♦❴❛❝q✉✐r❡)) r = ❨; ⇓ X = Y = ✵; Y = ✹; Xr❡❧ = ✶; ✐❢(X❛❝q) r = Y ;

✸

SLIDE 12

❆♥ ❯♥s❛❢❡ ❘❡♦r❞❡r✐♥❣ X = Y = ✵; Y = ✹; Xr❡❧ = ✶; r = ✹; ✐❢(X❛❝q) r = Y ; ❆❧✇❛②s r❡t✉r♥s r == ✹ ❀ X = Y = ✵; Xr❡❧ = ✶; Y = ✹; r = ✹; ✐❢(X❛❝q) r = Y ; ▼❛② r❡t✉r♥ r == ✵ ❖♣t✐♠✐③❛t✐♦♥s ❢♦r s❡q✉❡♥t✐❛❧ ♣r♦❣r❛♠s ❛r❡ ◆❖❚ ❛❧✇❛②s s❛❢❡ ❢♦r ❝♦♥❝✉rr❡♥t ♣r♦❣r❛♠s✳

✹

SLIDE 13

❆♥ ❯♥s❛❢❡ ❘❡♦r❞❡r✐♥❣ X = Y = ✵; Y = ✹; Xr❡❧ = ✶; r = ✹; ✐❢(X❛❝q) r = Y ; ❆❧✇❛②s r❡t✉r♥s r == ✹ ❀ X = Y = ✵; Xr❡❧ = ✶; Y = ✹; r = ✹; ✐❢(X❛❝q) r = Y ; ▼❛② r❡t✉r♥ r == ✵ ❖♣t✐♠✐③❛t✐♦♥s ❢♦r s❡q✉❡♥t✐❛❧ ♣r♦❣r❛♠s ❛r❡ ◆❖❚ ❛❧✇❛②s s❛❢❡ ❢♦r ❝♦♥❝✉rr❡♥t ♣r♦❣r❛♠s✳

✹

SLIDE 14

❆♥♦t❤❡r ❊①❛♠♣❧❡

X = Y = ✵; Y = ✹; Xr❡❧ = ✶; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

❖✉t♣✉t✿ ✹ ❛❧✇❛②s

✺

SLIDE 15

❆♥♦t❤❡r ❊①❛♠♣❧❡

X = Y = ✵; Y = ✹; Xr❡❧ = ✶; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

❖✉t♣✉t✿ b == ✹ ❛❧✇❛②s

✺

SLIDE 16

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ★✷✷✺✶✹ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

−O✸

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; b = t ? s : ✹; ❈♦♥t❡①t✿    Y = ✹; Xr❡❧ = ✶;   

❖✉t♣✉t b == ✵ ♣♦ss✐❜❧❡ ✐♥ t❛r❣❡t✳

✻

SLIDE 17

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 18

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 19

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 20

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 21

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 22

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❇✉❣ ✐♥ ▼♦r❡ ❉❡t❛✐❧ X = Y = ✵; f = false; · · · a = f ? Y : ✵; b = X❛❝q ? Y : ✹;

(✶)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q; r = Y ; b = t ? r : ✹;

(✷)

❀ X = Y = ✵; f = false; · · · s = Y ; a = f ? s : ✵; t = X❛❝q;

✘✘✘✘ ✘

r = Y ; b = t ? s : ✹; ❈✶✶✿ ✭✶✮ ❊rr♦r ✭✷✮ ❈♦rr❡❝t ▲▲❱▼✿ ✭✶✮ ❈♦rr❡❝t ✭✷✮ ❊rr♦r

✼

SLIDE 23

❚❤✐s ❲♦r❦✿ ▲▲❱▼ ❱❛❧✐❞❛t✐♦♥ Psrc

▲▲❱▼

= = = ⇒ Ptgt ? ❈♦rr❡❝t : P♦t❡♥t✐❛❧ ❊rr♦r ⇓ Psrc

(R∪E)∗

= = = = ⇒ Ptgt ? ❈♦rr❡❝t : P♦t❡♥t✐❛❧ ❊rr♦r ❉❡✜♥❡ ❛ s❡t ♦❢ s❛❢❡ r❡♦r❞❡r✐♥❣s ✫ ❡❧✐♠✐♥❛t✐♦♥s✿ ❋♦r t❤❡ ▲▲❱▼ ♠♦❞❡❧ ❋♦r t❤❡ ❈✶✶ ♠♦❞❡❧ ❬P❖P▲✬✶✺❪

✽

SLIDE 24

❈♦♠♣✐❧❡r✲■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ❈❛♥ ❜❡ ✉s❡❞ ✐♥ ✈❛❧✐❞❛t✐♥❣ ♦t❤❡r ❝♦♠♣✐❧❡rs✳ ❙t❡♣s✿ ■❞❡♥t✐❢② ❝♦rr❡s♣♦♥❞✐♥❣ ♣r♦❣r❛♠ ♣❛t❤s ❈♦♠♣✉t❡ ❞❡❧❡t❛❜✐❧✐t② ♦❢ ❛❝❝❡ss❡s ▼❛t❝❤ ❛❝❝❡ss s❡q✉❡♥❝❡s ❛♥❞ ❛♥❛❧②③❡

✾

SLIDE 25

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ s✶ = X s✷ = X V = ✶ s✹ = Z❛❝q Y = ✶ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 26

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X s✷ = X V = ✶ s✹ = Z❛❝q Y = ✶ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 27

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X V = ✶ s✹ = Z❛❝q Y = ✶ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 28

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X V = ✶ ✓ s✹ = Z❛❝q Y = ✶ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 29

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X V = ✶ ✓ s✹ = Z❛❝q Y = ✶ ✓ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 30

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 31

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷

✶ ✷ ❛❝q

✷ ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 32

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 33

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 34

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 35

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 36

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 37

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 38

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 39

❈♦♠♣✐❧❡r ■♥❞❡♣❡♥❞❡♥t ▼❛t❝❤✐♥❣ ✓ s✶ = X ✗ s✷ = X ✓ V = ✶ ✓ s✹ = Z❛❝q ✗ Y = ✶ ✓ Y = ✷ t✶ = X t✷ = Z❛❝q Y = ✷ V = ✶

❈♦rr❡❝t

❈❤❡❝❦ t❤❛t ✉♥♠❛t❝❤❡❞ ❛❝❝❡ss❡s ❛r❡ ❞❡❧❡t❛❜❧❡ ❈❤❡❝❦ t❤❛t r❡♦r❞❡r✐♥❣s ❛r❡ ❛❧❧♦✇❡❞

✶✵

SLIDE 40

❈♦♥tr♦❧ ❋❧♦✇ ▼❛t❝❤✐♥❣ f✶ f✷ f✶ ❆ ❇ ❈ ❉ ❊ ❋ ❆

❈ ❋ ❯s❡ ❜r❛♥❝❤✐♥❣ ❝♦♥❞✐t✐♦♥s t♦ ♠❛t❝❤ t❤❡ ♣❛t❤s ❯♥r♦❧❧ ❧♦♦♣s ❛ ✜①❡❞ ♥✉♠❜❡r ♦❢ t✐♠❡s

✶✶

SLIDE 41

❊①♣❡r✐♠❡♥t❛❧ ❊✈❛❧✉❛t✐♦♥ ❱❛❧✐❞❛t❡❞ ❛❝❝♦r❞✐♥❣ t♦ ▲▲❱▼ ♠❡♠♦r② ♠♦❞❡❧ ❚❡st ❝❧❛ss ★ ❘❡♣♦rt❡❞ ❡rr♦rs ✭✶✵✵ ♣r♦❣✳✴❝❧❛ss✮ ▲▲❱▼ ✸✳✻ ▲▲❱▼ ✸✳✼r❝✷ ❙tr❛✐❣❤t❧✐♥❡ ✾✺ ✵ ❲✐t❤ ❜r❛♥❝❤❡s ✻✹ ✵ ❲✐t❤ ❞❡❛❞ ♣❛t❤s ✺✽ ✵ ❲✐t❤ ❧♦♦♣s ✹✾ ✵ ❙♠❛❧❧❡r t❡sts ✸✷ ✵ ❊①❛♠♣❧❡s ❢r❡q✉❡♥t❧② ❡①♣♦s❡ ❡rr♦rs ✐♥ ▲▲❱▼ ✸✳✻ ◆♦ ❢❛❧s❡ ♣♦s✐t✐✈❡s✦

✶✷

SLIDE 42

❊①♣❡r✐♠❡♥t❛❧ ❊✈❛❧✉❛t✐♦♥ ❱❛❧✐❞❛t❡❞ ❛❝❝♦r❞✐♥❣ t♦ ❈✶✶ ♠❡♠♦r② ♠♦❞❡❧ ❚❡st ❝❧❛ss ★ ❘❡♣♦rt❡❞ ❡rr♦rs ✭✶✵✵ ♣r♦❣✳✴❝❧❛ss✮ ▲▲❱▼ ✸✳✻ ▲▲❱▼ ✸✳✼r❝✷ ❙tr❛✐❣❤t❧✐♥❡ ✵ ✵ ❲✐t❤ ❜r❛♥❝❤❡s ✶✸ ✶ ❲✐t❤ ❞❡❛❞ ♣❛t❤s ✻ ✵ ❲✐t❤ ❧♦♦♣s ✻ ✵ ❙♠❛❧❧❡r t❡sts ✼ ✺ ❊rr♦rs ♦❢t❡♥ ♠❛s❦❡❞ ❜② ❛❞❥❛❝❡♥t ❛❝❝❡ss❡s

✶✸

SLIDE 43

▼❛s❦✐♥❣ ♦❢ ❊rr♦rs ❜② ❆❞❥❛❝❡♥t ❆❝❝❡ss❡s

✶

s✷ = Z❛❝q s✸ = X

✶ ✶

t✷ = X t✸ = Z❛❝q

✹

✶✹

SLIDE 44

▼❛s❦✐♥❣ ♦❢ ❊rr♦rs ❜② ❆❞❥❛❝❡♥t ❆❝❝❡ss❡s s✶ = X s✷ = Z❛❝q s✸ = X s✶ = X t✶ = X t✷ = X t✸ = Z❛❝q t✹ = X

✶✹

SLIDE 45

▼❛s❦✐♥❣ ♦❢ ❊rr♦rs ❜② ❆❞❥❛❝❡♥t ❆❝❝❡ss❡s s✶ = X s✷ = Z❛❝q s✸ = X s✶ = X t✶ = X t✷ = X t✸ = Z❛❝q t✹ = X

✶✹

SLIDE 46

▼❡t❛❞❛t❛✲❇❛s❡❞ ▼❛t❝❤✐♥❣ s✶ = X ✦❆ s✷ = Z❛❝q ✦❇ s✸ = X ✦❈ s✹ = X ✦❉ t✶ = X ✦❆ t✷ = X ✦❈ t✸ = Z❛❝q ✦❇ t✹ = X ✦❉

✶✺

SLIDE 47

❈♦♥❝❧✉s✐♦♥ ❙✉♠♠❛r② ❈✶✶ ❛♥❞ ▲▲❱▼ s❡♠❛♥t✐❝s ❛r❡ ❞✐✛❡r❡♥t ❘❡♣♦rt❡❞ t❤r❡❡ ▲▲❱▼ ❝♦♥❝✉rr❡♥❝② ❝♦♠♣✐❧❛t✐♦♥ ❜✉❣s❀ ❛❧❧ ✇❡r❡ ✜①❡❞✳ ❱❛❧✐❞❛t♦r✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴✈❛❧✐❞❝✴ ❋✉t✉r❡ ❲♦r❦ ❍❛♥❞❧❡ ❛rr❛②s✱ ♣♦✐♥t❡rs✱ s❡q✉❡♥t✐❛❧ ♦♣t✐♠✐s❛t✐♦♥s ■♥t❡❣r❛t❡ ✇✐t❤ s❡q✉❡♥t✐❛❧ ✈❛❧✐❞❛t♦r ❋♦r♠❛❧✐③❡ t❤❡ ▲▲❱▼ ❝♦♥❝✉rr❡♥❝② ♠♦❞❡❧

✶✻