tt ss strt r t t - PowerPoint PPT Presentation

❆ ❙t❛t❡ ❈❧❛ss ❈♦♥str✉❝t✐♦♥ ❢♦r ❈♦♠♣✉t✐♥❣ t❤❡ ■♥t❡rs❡❝t✐♦♥ ♦❢ ❚✐♠❡ P❡tr✐ ◆❡ts ▲❛♥❣✉❛❣❡s ❊r✐❝ ▲❯❇❆❚ ✱ ❙✐❧✈❛♥♦ ❉❆▲ ❩■▲■❖✱ ❉✐❞✐❡r ▲❊ ❇❖❚▲❆◆✱ ❨❛♥♥✐❝❦ P❊◆❈❖▲❊ ❛♥❞ ❆✉❞✐♥❡ ❙❯❇■❆❙ ▲❆❆❙ ✲ ❈◆❘❙ ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶ ✴ ✷✻

■♥❞❡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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✷ ✴ ✷✻

■♥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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✸ ✴ ✷✻

■♥tr♦❞✉❝t✐♦♥ t ✵ t ✶ t ✵ t ✶ . . . ❚r❛❝❡s✿ t ✵ f t ✸ t ✵ t ✶ . . . p 0 L ( t ✵ ) = a ❲♦r❞s ❛♥❞ ▲❛❜❡❧s✿ L ( t ✶ ) = L ( t ✸ ) = b t 3 b L ( f ) = ǫ t 1 t 0 a a b a b . . . ▲❛❜❡❧❧❡❞ ❚r❛❝❡s✿ b a b a b . . . f p 1 p 2 ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✹ ✴ ✷✻

■♥tr♦❞✉❝t✐♦♥ t ✵ t ✶ t ✵ t ✶ . . . → a b a b . . . ❚r❛❝❡s✿ t ✵ f t ✸ t ✵ t ✶ . . . → a b a b . . . p 0 ▲❛♥❣✉❛❣❡✿ ( ab ) ∗ t 3 b t 1 t 0 a Pr♦♣❡rt②✿ ✐s ❞✐❛❣♥♦s❛❜❧❡ ❄ b f p 1 p 2 ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✺ ✴ ✷✻

❈❤❡❝❦✐♥❣ ❞✐❛❣♥♦s❛❜✐❧✐t② p ✵ p ✵ t ✸ . ✶ ❜ t ✸ . ✷ ❜ ❛ ❛ t ✶ . ✶ t ✵ . ✶ t ✶ . ✷ t ✵ . ✷ ❜ ❜ f p ✶ p ✷ p ✶ p ✷ ❲❡ ❝❛♥ ✉s❡ ✧s②♥❝❤r♦♥♦✉s ♣r♦❞✉❝t✧ ✭ � ✮ t♦ ❝❤❡❝❦ t❤❡ ✐♥t❡rs❡❝t✐♦♥ ❜❡t✇❡❡♥ ❧❛♥❣✉❛❣❡s✳ � ❙②s � ∩ � ❙②s | f � ≈ � ❙②s � ❙②s | f � ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✻ ✴ ✷✻

❚✐♠❡ P❡tr✐ ◆❡ts ❚P◆ ❛r❡ ❝♦♠♣♦s❡❞ ♦❢ ✿ ❛ P❡tr✐ ♥❡t❀ ❛♥ ✐♥✐t✐❛❧ ♠❛r❦✐♥❣ t✐♠✐♥❣ ❝♦♥str❛✐♥ts ■ s ( t ) ✭ ❛❦❛ st❛t✐❝ t✐♠❡ ✐♥t❡r✈❛❧✮✳ p ✵ [ ✸ , ✹ ] P♦ss✐❜❧❡ ❡①❡❝✉t✐♦♥s✿ t ✸ ❜ ✷ . ✶ t ✵ ✷ t ✶ . . . ✴ ✷ . ✶ a ✷ b . . . t ✶ t ✵ ❛ ✷ . ✶ t ✵ ✶ f ✸ t ✸ . . . ✴ ✷ . ✶ a ✹ b . . . [ ✶ , ✷ ] [ ✷ , ✹ ] ❜ ▲❛♥❣✉❛❣❡✿ ( ab ) ∗ f p ✶ p ✷ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✼ ✴ ✷✻

▼♦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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✽ ✴ ✷✻

❈♦♠♣♦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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✾ ✴ ✷✻

❙t❛t❡ ❙♣❛❝❡ ✐s ✐♥✜♥✐t❡ ❙♦❧✉t✐♦♥✿ ✉s❡ ❛❜str❛❝t✐♦♥s ❜❛s❡❞ ♦♥ ❙t❛t❡ ❈❧❛ss❡s ❬❇❡rt❤♦♠✐❡✉ ✲ ✽✸❪✳ ★ st❛t❡s ✸❀ tr❛♥s✐t✐♦♥s ✹ ✭❝❧❛ss ✵✮ ♠❛r❦✐♥❣✿ ♣✵ p ✵ [ ✸ , ✹ ] ❞♦♠❛✐♥✿ ✷ ❁❂ t✵ ❁❂ ✹ t ✸ s✉❝❝❡ss♦rs✿ t✵✴✶ ❜ ✭❝❧❛ss ✶✮ ♠❛r❦✐♥❣✿ ♣✶ [ ✶ , ✷ ] t ✶ [ ✷ , ✹ ] t ✵ ❛ ❞♦♠❛✐♥✿ ✶ ❁❂ t✶ ❁❂ ✷ ❜ ✵ ❁❂ ❢ ❁ ✇ s✉❝❝❡ss♦rs✿ t✶✴✵ ❢✴✷ f ✭❝❧❛ss ✷✮ ♠❛r❦✐♥❣✿ ♣✷ p ✶ p ✷ ❞♦♠❛✐♥✿ ✸ ❁❂ t✸ ❁❂ ✹ s✉❝❝❡ss♦rs✿ t✸✴✵ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✵ ✴ ✷✻

❈♦♠♣♦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 ✵ ❜ t ✸ . ✶ tc ✶ . ✶ [ ✸ , ✹ ] [ ✶ , ✷ ] tc ✶ . ✶ t ✶ . ✶ ❛ t ✵ . ✶ tc ✵ . ✶ [ ✷ , ✹ ] ❜ f p ✶ p ✷ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✶ ✴ ✷✻

❈♦♠♣♦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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✷ ✴ ✷✻

■♥❞❡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 ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✸ ✴ ✷✻

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 ✵ [ ✸ , ✹ ] [ ✸ , ✹ ] t ✸ . ✶ t ✸ . ✷ ❜ ❜ × [ ✶ , ✷ ] t ✶ . ✶ [ ✷ , ✹ ] t ✵ . ✶ ❛ [ ✶ , ✷ ] t ✶ . ✷ [ ✷ , ✹ ] t ✵ . ✷ ❛ ❜ ❜ f p ✶ p ✷ p ✶ p ✷ ❊r✐❝ ▲❯❇❆❚ ✭▲❆❆❙ ✲ ❈◆❘❙✮ ❚P◆ ▲❛♥❣✉❛❣❡s ❆✉❣✉st ✷✵✶✾ ✴ ❋❖❘▼❆❚❙ ✶✹ ✴ ✷✻