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tt ss strt r t t - - PowerPoint PPT Presentation

Nov 18, 2022 421 likes •686 views

tt ss strt r t t trst Ptr ts s r

slide-1
SLIDE 1

❆ ❙t❛t❡ ❈❧❛ss ❈♦♥str✉❝t✐♦♥ ❢♦r ❈♦♠♣✉t✐♥❣ t❤❡ ■♥t❡rs❡❝t✐♦♥ ♦❢ ❚✐♠❡ P❡tr✐ ◆❡ts ▲❛♥❣✉❛❣❡s

❊r✐❝ ▲❯❇❆❚✱ ❙✐❧✈❛♥♦ ❉❆▲ ❩■▲■❖✱ ❉✐❞✐❡r ▲❊ ❇❖❚▲❆◆✱ ❨❛♥♥✐❝❦ P❊◆❈❖▲❊ ❛♥❞ ❆✉❞✐♥❡ ❙❯❇■❆❙

▲❆❆❙ ✲ ❈◆❘❙

❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶ ✴ ✷✻

slide-2
SLIDE 2

■♥❞❡①

✶

■♥tr♦❞✉❝t✐♦♥ ❇❛❝❦❣r♦✉♥❞ ♦♥ ✭♥❡t✮ ▲❛♥❣✉❛❣❡s ❛♥❞ Pr♦❞✉❝t ❈♦♠♣♦s❛❜✐❧✐t② ♦❢ ❚P◆

✷

P❚P◆ ❆r♥♦❧❞✲◆✐✈❛t Pr♦❞✉❝t ♦❢ ❚P◆ ❊①♣r❡ss✐✈❡♥❡ss ❆♣♣❧✐❝❛t✐♦♥ t♦ t❤❡ ❈♦♠♣♦s❛❜✐❧✐t② Pr♦❜❧❡♠

✸

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷ ✴ ✷✻

slide-3
SLIDE 3

■♥tr♦❞✉❝t✐♦♥

❖❜❥❡❝t✐✈❡✿ ❝♦♠♣✉t✐♥❣ ✭❡✣❝✐❡♥t❧②✮ t❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ t✐♠❡❞ ❧❛♥❣✉❛❣❡s t♦ ❝❤❡❝❦ ♣r♦♣❡rt✐❡s ♦♥ s②st❡♠s✳ ❲❤✐❝❤ ♣r♦♣❡rt✐❡s❄ ❚❡♠♣♦r❛❧ ♣r♦♣❡rt✐❡s❀ ♦❜s❡r✈❛❜✐❧✐t②❀ ✳ ✳ ✳

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✸ ✴ ✷✻

slide-4
SLIDE 4

■♥tr♦❞✉❝t✐♦♥

❚r❛❝❡s✿ t✵ t✶ t✵ t✶ . . . t✵ f t✸ t✵ t✶ . . . ❲♦r❞s ❛♥❞ ▲❛❜❡❧s✿ L(t✵) = a L(t✶) = L(t✸) = b L(f ) = ǫ ▲❛❜❡❧❧❡❞ ❚r❛❝❡s✿ a b a b . . . a b a b . . .

p1 p2 p0 t0 a t1 b t3 b f

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✹ ✴ ✷✻

slide-5
SLIDE 5

■♥tr♦❞✉❝t✐♦♥

❚r❛❝❡s✿ t✵ t✶ t✵ t✶ . . . → a b a b . . . t✵ f t✸ t✵ t✶ . . . → a b a b . . . ▲❛♥❣✉❛❣❡✿ (ab)∗ Pr♦♣❡rt②✿ ✐s ❞✐❛❣♥♦s❛❜❧❡ ❄

p1 p2 p0 t0 a t1 b t3 b f

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✺ ✴ ✷✻

slide-6
SLIDE 6

❈❤❡❝❦✐♥❣ ❞✐❛❣♥♦s❛❜✐❧✐t②

p✶ p✷ p✵ t✵.✶ ❛ t✶.✶ ❜ t✸.✶ ❜ f p✶ p✷ p✵ t✵.✷ ❛ t✶.✷ ❜ t✸.✷ ❜

❲❡ ❝❛♥ ✉s❡ ✧s②♥❝❤r♦♥♦✉s ♣r♦❞✉❝t✧ ✭✮ t♦ ❝❤❡❝❦ t❤❡ ✐♥t❡rs❡❝t✐♦♥ ❜❡t✇❡❡♥ ❧❛♥❣✉❛❣❡s✳ ❙②s ∩ ❙②s|f ≈ ❙②s ❙②s|f

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✻ ✴ ✷✻

slide-7
SLIDE 7

❚✐♠❡ P❡tr✐ ◆❡ts

❚P◆ ❛r❡ ❝♦♠♣♦s❡❞ ♦❢ ✿ ❛ P❡tr✐ ♥❡t❀ ❛♥ ✐♥✐t✐❛❧ ♠❛r❦✐♥❣ t✐♠✐♥❣ ❝♦♥str❛✐♥ts ■s(t) ✭❛❦❛ st❛t✐❝ t✐♠❡ ✐♥t❡r✈❛❧✮✳

p✶ p✷ p✵ t✵ ❛

[✷, ✹]

t✶ ❜

[✶, ✷]

t✸ ❜

[✸, ✹]

f

P♦ss✐❜❧❡ ❡①❡❝✉t✐♦♥s✿ ✷.✶ t✵ ✷ t✶ . . . ✴ ✷.✶ a ✷ b . . . ✷.✶ t✵ ✶ f ✸ t✸ . . . ✴ ✷.✶ a ✹ b . . . ▲❛♥❣✉❛❣❡✿ (ab)∗

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✼ ✴ ✷✻

slide-8
SLIDE 8

▼♦t✐✈❛t✐♦♥ ❢♦r ♦✉r ✇♦r❦

❋❛✉❧t ❞✐❛❣♥♦s✐s ❢♦r ❉✐s❝r❡t❡ ❊✈❡♥t ❙②st❡♠ ≡ ♣r♦♣❡rt✐❡s ♦♥ tr❛❝❡ ❧❛♥❣✉❛❣❡s ❬▲❛❢♦rt✉♥❡ ✲ ✾✺❪✳ ❆❞❞✐t✐♦♥ ♦❢ t✐♠❡ ❝♦♥str❛✐♥ts✳ ∆✲❞✐❛❣♥♦s❛❜✐❧✐t② ≡ ✏r❡❛❝❤❛❜✐❧✐t② ♦❢ ✭♥♦♥✲❩❡♥♦✮ r✉♥s ✐♥ ♣r♦❞✉❝t ♦❢ ❚❆✑ ❬❚r✐♣❛❦✐s ✲ ✵✷❪ τ✲❞✐❛❣♥♦s❛❜✐❧✐t② ≡ ✏s❛♠❡✑ ❢♦r ❚P◆ ❬❙✐❧✈❛ ✲ ✶✺✱ ❇❛s✐❧❡ ✲ ✶✼❪ ✭❜✉t ❛s❦ ❢♦r ❛ ✜r✐♥❣ s❡q✉❡♥❝❡✮

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✽ ✴ ✷✻

slide-9
SLIDE 9

❈♦♠♣♦s✐t✐♦♥ ♦❢ ❚P◆

❆♥❛❧②s✐♥❣ t❤❡ ✏✐♥t❡rs❡❝t✐♦♥✑ ♦❢ ❚P◆ ✐s ❤✐♥❞❡r❡❞ ❜② t✇♦ ♣r♦❜❧❡♠s✿

✶ ❙t❛t❡ ❙♣❛❝❡ ✐s ✐♥✜♥✐t❡ ✷ ❈♦♠♣♦s❛❜✐❧✐t② ♣r♦❜❧❡♠ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✾ ✴ ✷✻

slide-10
SLIDE 10

❙t❛t❡ ❙♣❛❝❡ ✐s ✐♥✜♥✐t❡

❙♦❧✉t✐♦♥✿ ✉s❡ ❛❜str❛❝t✐♦♥s ❜❛s❡❞ ♦♥ ❙t❛t❡ ❈❧❛ss❡s ❬❇❡rt❤♦♠✐❡✉ ✲ ✽✸❪✳

p✶ p✷ p✵ t✵ ❛

[✷, ✹]

t✶ ❜

[✶, ✷]

t✸ ❜

[✸, ✹]

f

★ st❛t❡s ✸❀ tr❛♥s✐t✐♦♥s ✹ ✭❝❧❛ss ✵✮ ♠❛r❦✐♥❣✿ ♣✵ ❞♦♠❛✐♥✿ ✷ ❁❂ t✵ ❁❂ ✹ s✉❝❝❡ss♦rs✿ t✵✴✶ ✭❝❧❛ss ✶✮ ♠❛r❦✐♥❣✿ ♣✶ ❞♦♠❛✐♥✿ ✶ ❁❂ t✶ ❁❂ ✷ ✵ ❁❂ ❢ ❁ ✇ s✉❝❝❡ss♦rs✿ t✶✴✵ ❢✴✷ ✭❝❧❛ss ✷✮ ♠❛r❦✐♥❣✿ ♣✷ ❞♦♠❛✐♥✿ ✸ ❁❂ t✸ ❁❂ ✹ s✉❝❝❡ss♦rs✿ t✸✴✵

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✵ ✴ ✷✻

slide-11
SLIDE 11

❈♦♠♣♦s❛❜✐❧✐t②✿ t❤✐r❞ s♦❧✉t✐♦♥

■P❚P◆ ❛r❡ ❚P◆ ✇✐t❤ ✧■♥❤✐❜✐t✧ ❛♥❞ ✧P❡r♠✐t✧ ❛r❝s ❬P❡r❡③ ✲ ✶✶❪✳ ❆❞❞s t❤❡ ♣♦ss✐❜✐❧✐t② t♦ ✐s♦❧❛t❡ ✏t✐♠✐♥❣ ❝♦♥str❛✐♥ts✑ ❢r♦♠ ✏tr❛♥s✐t✐♦♥ ❡♥❛❜❧❡❞♥❡ss✑✳

p✶ p✷ p✵ t✵.✶ ❛ tc✵.✶

[✷, ✹]

t✶.✶ ❜ tc✶.✶

[✶, ✷]

t✸.✶ ❜ tc✶.✶

[✸, ✹]

f

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✶ ✴ ✷✻

slide-12
SLIDE 12

❈♦♠♣♦s❛❜✐❧✐t② ♦❢ ❚P◆ ❊①t❡♥❞ t❤❡ ❙t❛t❡ ❈❧❛ss❡s ❝♦♥str✉❝t✐♦♥ t♦ t❤❡ ♣r♦❞✉❝t ♦❢ t✇♦✶ ❚P◆✳

✶❛❧s♦ ✇♦r❦ ✇✐t❤ t❤❡ ♣r♦❞✉❝t ♦❢ n tr❛♥s✐t✐♦♥s ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✷ ✴ ✷✻

slide-13
SLIDE 13

■♥❞❡①

✶

■♥tr♦❞✉❝t✐♦♥ ❇❛❝❦❣r♦✉♥❞ ♦♥ ✭♥❡t✮ ▲❛♥❣✉❛❣❡s ❛♥❞ Pr♦❞✉❝t ❈♦♠♣♦s❛❜✐❧✐t② ♦❢ ❚P◆

✷

P❚P◆ ❆r♥♦❧❞✲◆✐✈❛t Pr♦❞✉❝t ♦❢ ❚P◆ ❊①♣r❡ss✐✈❡♥❡ss ❆♣♣❧✐❝❛t✐♦♥ t♦ t❤❡ ❈♦♠♣♦s❛❜✐❧✐t② Pr♦❜❧❡♠

✸

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✸ ✴ ✷✻

slide-14
SLIDE 14

P❚P◆

■❞❡❛✿ ✉s❡ ❛ ♣r♦❞✉❝t✱ N✶ × N✷✱ ❛♥❞ ❢♦r❝❡ tr❛♥s✐t✐♦♥s ✇✐t❤ s❛♠❡ ❧❛❜❡❧ ✭❡✳❣✳ t✸.✶ ∈ N✶ ❛♥❞ t✶.✷ ∈ N✷✮ t♦ ✜r❡ ✏s②♥❝❤r♦♥♦✉s❧②✑✳

❊①❛♠♣❧❡

p✶ p✷ p✵ t✵.✶ ❛

[✷, ✹]

t✶.✶ ❜

[✶, ✷]

t✸.✶ ❜

[✸, ✹]

f

×

p✶ p✷ p✵ t✵.✷ ❛

[✷, ✹]

t✶.✷ ❜

[✶, ✷]

t✸.✷ ❜

[✸, ✹]

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✹ ✴ ✷✻

slide-15
SLIDE 15

P❚P◆

❊①❛♠♣❧❡

p✶ p✷ p✵ t✵.✶ ❛

[✷, ✹]

t✶.✶ ❜

[✶, ✷]

t✸.✶ ❜

[✸, ✹]

f

×

p✶ p✷ p✵ t✵.✷ ❛

[✷, ✹]

t✶.✷ ❜

[✶, ✷]

t✸.✷ ❜

[✸, ✹]

❲❡ ✜r❡ ✏❙②♥❝❤r♦♥♦✉s ❙❡ts✑ ♦❢ tr❛♥s✐t✐♦♥s ❛t t❤❡ s❛♠❡ t✐♠❡✿ {t✵.✶, t✵.✷}, {t✶.✶, t✶.✷}, {t✸.✶, t✶.✷}, {f }

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✺ ✴ ✷✻

slide-16
SLIDE 16

P❚P◆✿ ❡①❛♠♣❧❡ ♦❢ ❜❡❤❛✈✐♦✉r

p0 t0 a p1 t1 b

[1, ∞[

×

q0 t2 a t3 b

[0, 1]

q1

❚✐♠❡ ❡❧❛♣s❡ ❛s ✐♥ ✏❝❧❛ss✐❝❛❧✑ ❚P◆ ⇒ ♠✉st ✜r❡ t✵ ❜❡❢♦r❡ ✶ ✐♥✐t✐❛❧❧②✳ ❚r❛♥s✐t✐♦♥s {t✵, t✷} ❛♥❞ {t✶, t✸} ♠✉st ✜r❡ s✐♠✉❧t❛♥❡♦✉s❧② ⇒ t❤✐s ❝❛♥ ❝r❡❛t❡ ✏t✐♠❡❧♦❝❦s✑✳

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✻ ✴ ✷✻

slide-17
SLIDE 17

P❚P◆✿ ❡①♣r❡ss✐✈❡♥❡ss

❖♥ ♦♥❡ s✐❞❡✱ P❚P◆ s❡♠❛♥t✐❝s ✐♥tr♦❞✉❝❡s ♥❡✇ t✐♠❡❧♦❝❦s✳ ❖♥ t❤❡ ♦t❤❡r s✐❞❡✱ ②♦✉ ❝❛♥♥♦t ✏❧♦s❡ ❛ tr❛♥s✐t✐♦♥✑ ♦♥❧② ❜② ✇❛✐t✐♥❣✳

❚❤❡♦r❡♠

P❚P◆ ❛r❡ ❛s ❡①♣r❡ss✐✈❡ ❛s ❚P◆ ✭✉♣✲t♦ ✇t❜✿ ≈✮✿ ∀P ∈ P❚P◆ ∃N ∈ ❚P◆ . N ≈ P

✶❙❛②s ♥♦t❤✐♥❣ ❛❜♦✉t t❤❡ s✐③❡ ♦❢ N ∝ P✳ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✼ ✴ ✷✻

slide-18
SLIDE 18

P❚P◆✿ ❛♣♣❧✐❝❛t✐♦♥ t♦ t❤❡ ❝♦♠♣♦s❛❜✐❧✐t② ♣r♦❜❧❡♠

❲❡ ♣r♦✈❡ t❤❛t ✏♣r♦❞✉❝t✑ ✐s ❛ ❝♦♥❣r✉❡♥t ❝♦♠♣♦s✐t✐♦♥ ♦♣❡r❛t♦r✿ [ [N✶ × N✷] ] ≈ [ [N✶] ] [ [N✷] ] ■t ✐s ♣♦ss✐❜❧❡ t♦ ❛❞❛♣t t❤❡ ❙❈● ❝♦♥str✉❝t✐♦♥ t♦ P❚P◆ ❍❡♥❝❡ ✇❡ ❝❛♥ ❝♦♠♣✉t❡ t❤❡ ✏❙❈●✑ ❢♦r t❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ t✇♦ ❚P◆ ❚❤✐s ❤❛s ❜❡❡♥ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❛ t♦♦❧✿ ❚❲◆❆ ✭❤tt♣s✿✴✴♣r♦❥❡❝ts✳❧❛❛s✳❢r✴t✇✐♥❛✴✮

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✽ ✴ ✷✻

slide-19
SLIDE 19

❉❇▼ ❛♥❞ P❚P◆

❆ss✉♠❡ ✇❡ ✜r❡ I = {ta, tb, . . . } s②♥❝❤r♦♥♦✉s❧② ❢r♦♠ (m, D)

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✾ ✴ ✷✻

slide-20
SLIDE 20

■♥❞❡①

✶

■♥tr♦❞✉❝t✐♦♥ ❇❛❝❦❣r♦✉♥❞ ♦♥ ✭♥❡t✮ ▲❛♥❣✉❛❣❡s ❛♥❞ Pr♦❞✉❝t ❈♦♠♣♦s❛❜✐❧✐t② ♦❢ ❚P◆

✷

P❚P◆ ❆r♥♦❧❞✲◆✐✈❛t Pr♦❞✉❝t ♦❢ ❚P◆ ❊①♣r❡ss✐✈❡♥❡ss ❆♣♣❧✐❝❛t✐♦♥ t♦ t❤❡ ❈♦♠♣♦s❛❜✐❧✐t② Pr♦❜❧❡♠

✸

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✵ ✴ ✷✻

slide-21
SLIDE 21

❈♦♠♣❛r✐♥❣ s✐③❡ ♦❢ P❚P◆ ❛♥❞ ■P❚P◆

Twina IPTPN/sift Model Exp. Classes Classes Ratio jdeds plain 26 28 × 1.1 jdeds twin 544 706 × 1.3 jdeds

  • bs

57 64 × 1.1 train3 plain 3.10 · 103 5.05 · 103 × 1.6 train3 twin 1.45 · 106 4.02 · 106 × 2.8 train3

  • bs

6.20 · 103 1.01 · 104 × 1.6 train4 plain 1.03 · 104 1.68 · 104 × 1.6 train4 twin 2.10 · 107 5.76 · 107 × 2.7 train4

  • bs

2.06 · 104 3.37 · 104 × 1.6 plant plain 2.70 · 106 4.63 · 106 × 1.7 plant twin 1.30 · 103 1.63 · 103 × 1.3 plant

  • bs

5.72 · 106 9.79 · 106 × 1.7 wodes plain 2.55 · 103 5.36 · 103 × 2.1 wodes twin 5.54 · 104 1.51 · 105 × 2.7 wodes

  • bs

5.77 · 103 1.47 · 104 × 2.5 wodes232 plain 2.04 · 104 3.24 · 104 × 1.6 wodes232 twin 3.96 · 107 3.39 · 108 × 8.6 wodes232

  • bs

1.06 · 105 2.26 · 105 × 2.1

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✶ ✴ ✷✻

slide-22
SLIDE 22

❋♦❝✉s ♦♥ ❲❖❉❊❙✲✷✲✸✲✷

Twina IPTPN/sift Model Exp. Classes Classes Ratio wodes232 plain 2.0 · 104 3.2 · 104 × 1.6 wodes232 twin 4.0 · 107 3.4 · 108 × 8.6 wodes232

  • bs

1.1 · 105 2.3 · 105 × 2.1

|N × N|f | O(|N|✷)

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✷ ✴ ✷✻

slide-23
SLIDE 23

❈♦♠♣❛r✐s♦♥ ✇✐t❤ ❡♥❝♦❞✐♥❣ ✐♥t♦ ❚P◆

❘❡s✉❧ts ♦♥ ♦✉r r✉♥♥✐♥❣ ❡①❛♠♣❧❡❀ ❢♦r ❡①♣✳ t✇✐♥

p✶ p✷ p✵ t✵.✶ ❛

[✷, ✹]

t✶.✶ ❜

[✶, ✷]

t✸.✶ ❜

[✸, ✹]

f

×

p✶ p✷ p✵ t✵.✷ ❛

[✷, ✹]

t✶.✷ ❜

[✶, ✷]

t✸.✷ ❜

[✸, ✹]

Twina IPTPN/sift TPN/sift Places 6 6 25 Trans. 7 12 (6 + 6) 211 Classes 3 3 1389

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✸ ✴ ✷✻

slide-24
SLIDE 24

❈♦♥❝❧✉s✐♦♥

❲❡ ♣r♦♣♦s❡ ❛♥ ❡①t❡♥s✐♦♥ ♦❢ ❚P◆ ✇✐t❤ ✏s②♥❝❤r♦♥♦✉s ♣r♦❞✉❝t✑ ♦❢ tr❛♥s✐t✐♦♥s ❛♥❞ ❡①t❡♥❞ t❤❡ ✭▲✐♥❡❛r✮ ❙t❛t❡ ❈❧❛ss

  • r❛♣❤ ❝♦♥str✉❝t✐♦♥✳

❲❡ ❤❛✈❡ ✐♠♣❧❡♠❡♥t❡❞ t❤✐s ❝♦♥str✉❝t✐♦♥ ✐♥ ❛ t♦♦❧✳ ❚❤✐s ✐s ❛ tr✐❜✉t❡ t♦ ❇❡r♥❛r❞ ❇❡rt❤♦♠✐❡✉✬s ✇♦r❦✳ ❋✉t✉r❡ ✇♦r❦s✿ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♠♣❛r❛✐s♦♥ ✇✐t❤ ❚✳❆✳❀ ♠♦t✐❢ ❞❡t❡❝t✐♦♥ ✐♥ tr❛❝❡s❀ ✳✳✳

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✹ ✴ ✷✻

slide-25
SLIDE 25

❈♦♥❝❧✉s✐♦♥ ❚❤❛♥❦s ❢♦r ②♦✉r ❛tt❡♥t✐♦♥ ✦ ❆♥② q✉❡st✐♦♥s ❄

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✺ ✴ ✷✻

slide-26
SLIDE 26

❈♦♠♣♦s❛❜✐❧✐t② ♦❢ ❚P◆✿ r❡❧❛t❡❞ ✇♦r❦

❯s❡ ❡♥❝♦❞✐♥❣ ♦❢ ❚P◆ ✐♥t♦ ❚❆ ❬❈❛ss❡③ ✲ ✵✺✱ ❇ér❛r❞ ✲ ✵✽❪ ♣r❡s❡r✈❡s ≈ ✴ r❡str✐❝t❡❞ t♦ ✏❝❧♦s❡❞✑ t✐♠✐♥❣ ❝♦♥str❛✐♥ts s✐③❡ ∝ r❡❣✐♦♥ ❣r❛♣❤❀ s✐③❡ ♦❢ ♥❡t ✇✐t❤ |T| ❝❧♦❝❦s ❙tr✉❝t✉r❛❧ ❡♥❝♦❞✐♥❣ ♦❢ ❚P◆ ✐♥t♦ ❝♦♠♣♦s❛❜❧❡ ❚P◆ ❬P❡r❡s ✲ ✶✶❪ ♣r❡s❡r✈❡s ≈ ✴ r❡str✐❝t❡❞ t♦ ✏❧❡❢t✲❝❧♦s❡❞✑ t✐♠✐♥❣ ❝♦♥str❛✐♥ts s✐③❡ ∝ |T|× t✳❝✳ ❙tr✉❝t✉r❛❧ ❡♥❝♦❞✐♥❣ ♦❢ ❚P◆ ✐♥t♦ ❚P◆ ✇✐t❤ ✏♣r✐♦r✐t✐❡s✑ ✭■P❚P◆✮ ❬P❡r❡s ✲ ✶✶❪❀ ♣r❡s❡r✈❡s ≈ ✴ r❡q✉✐r❡s t❤❡ ✉s❡ ♦❢ ✏str♦♥❣ ❝❧❛ss❡s✑ s✐③❡ ∝ s✐③❡ ♦❢ ♥❡t

❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷✻ ✴ ✷✻