p r t r
play

Prt r Prt - PowerPoint PPT Presentation

Prt Prt r Pr t Prt r Prt


  1. P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥

  2. ❙✉♠♠❛r② P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❬❈❤❛♥❣✲▲❡❡ ✽✳✸❪ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛t✐♦♥ ❬❈❤❛♥❣✲▲❡❡ ✽✳✻❪

  3. ❲❤② ❛ ♥❡✇ ✐♥❢❡r❡♥❝❡ r✉❧❡ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ◆❡❡❞ ♦❢ ❛ ♥❡✇ ✐♥❢❡r❡♥❝❡ r✉❧❡ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ ❊q✉❛❧✐t② ❘❡❧❛t✐♦♥✿ r❡✢❡①✐✈✐t②✱ s✐♠♠❡tr②✱ tr❛♥s✐t✐✈✐t②✱ s✉❜s ♦❢ t✐♦♥ ❡q✉❛❧s ◆❡❡❞ ❡①tr❛ ❡q✉❛❧✐t② ❛①✐♦♠s ❑ t♦ r❡♣r❡s❡♥t t❤♦s❡ ♣r♦♣❡rt✐❡s ❆♣♣❧②✐♥❣ st❛♥❞❛r❞ r❡s♦❧✉t✐♦♥ t♦ ❙ ∪ ❑ ✐s ✐♥❡✣❝✐❡♥t ◆❡❡❞ ❛ s♣❡❝✐✜❝ ✐♥❢❡r❡♥❝❡ r✉❧❡ t♦ ❤❛♥❞❧❡ ❡q✉❛❧✐t②✿ P❛r❛♠♦❞✉❧❛t✐♦♥

  4. P❛r❛♠♦❞✉❧❛t✐♦♥✿ ❊①❛♠♣❧❡ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r ❊①❛♠♣❧❡ ✭✉♥✐t ❝❧❛✉s❡✮ P❛r❛♠♦❞✉❧❛✲ t✐♦♥ ❈♦♥s✐❞❡r t❤❡ ❢♦❧❧♦✇✐♥❣ ❝❧❛✉s❡s✿ ❈ ✶ : P ( ❛ ) ❈ ✷ : ❛ = ❜ ❇② ❊①♣❧♦✐t✐♥❣ t❤❡ ❡q✉❛❧✐t② ❛①✐♦♠s✱ ✇❡ ❝❛♥ ✐♥❢❡r ❈ ✸ : P ( ❜ ) ✳

  5. ❊q✉❛❧✐t② s✉❜st✐t✉t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ t✐♦♥ ❉❡✜♥✐t✐♦♥ ✭❊q✉❛❧✐t② s✉❜st✐t✉t✐♦♥✮ ■❢ ❛ ❝❧❛✉s❡ ❈ ❝♦♥t❛✐♥s ❛ t❡r♠ t ✭ ❈ [ t ] ✮ ❛♥❞ ✐❢ ❛ ✉♥✐t ❝❧❛✉s❡ ✐s t = s t❤❡♥ ✇❡ ❝❛♥ ✐♥❢❡r ❛ ♥❡✇ ❝❧❛✉s❡ ❜② s✉❜st✐t✉t✐♥❣ s ❢♦r ❛ s✐♥❣❧❡ ♦❝❝✉rr❡♥❝❡ ♦❢ t ✭❞❡♥♦t❡❞ ❜② ❈ [ s ] ✮✳

  6. P❛r❛♠♦❞✉❧❛t✐♦♥ ❢♦r ●r♦✉♥❞ ❝❧❛✉s❡s P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r ●r♦✉♥❞ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛✲ t✐♦♥ ❈ ✶ : ▲ [ t ] ∨ ❈ ′ ✶ ❈ ✷ : t = s ∨ ❈ ′ ✷ ❲❡ ❝❛♥ ✐♥❢❡r t❤❡ ♣❛r❛♠♦❞✉❧❛♥t ▲ [ s ] ∨ ❈ ′ ✶ ∨ ❈ ′ ✷

  7. P❛r❛♠♦❞✉❧❛t✐♦♥✿ ❊①❛♠♣❧❡ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ ❊①❛♠♣❧❡ ✭●r♦✉♥❞✮ t✐♦♥ ❈ ✶ : P ( ❛ ) ∨ ◗ ( ❜ ) ❈ ✷ : ❛ = ❜ ∨ ❘ ( ❜ ) ❲❡ ❝❛♥ ✐♥❢❡r t❤❡ ♣❛r❛♠♦❞✉❧❛♥t✿ P ( ❜ ) ∨ ◗ ( ❜ ) ∨ ❘ ( ❜ )

  8. P❛r❛♠♦❞✉❧❛t✐♦♥ ❢♦r ●❡♥❡r❛❧ ❝❧❛✉s❡s P❛r❛♠♦❞✉❧❛t✐♦♥ ●❡♥❡r❛❧ ❈❧❛✉s❡s P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ t♦ ❣❡♥❡r❛❧ ❝❧❛✉s❡s ▲✐♥❡❛r ■♥st❛♥t✐❛t❡ ❜❡❢♦r❡ ♣❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛✲ t✐♦♥ ❊①❛♠♣❧❡ ❈ ✶ : P ( ① ) ∨ ◗ ( ❜ ) ❈ ✷ : ❛ = ❜ ∨ ❘ ( ❜ ) σ = { ❛ / ① } ❛♥❞ ❈ ′ ✶ : ❈ ✶ σ = P ( ❛ ) ∨ ◗ ( ❜ ) ❈ ′ ✸ : P ( ❜ ) ∨ ◗ ( ❜ ) ∨ ❘ ( ❜ ) ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❈ ✶ ❛♥❞ ❈ ✷

  9. P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❉❡✜♥✐t✐♦♥ ✭P❛r❛♠♦❞✉❧❛t✐♦♥✮ ❈ ✶ : ▲ [ t ] ∨ ❈ ′ ✶ P❛r❛♠♦❞✉❧❛t✐♦♥ ❈ ✷ : r = s ∨ ❈ ′ ▲✐♥❡❛r ✷ P❛r❛♠♦❞✉❧❛✲ ❈ ✶ ❛♥❞ ❈ ✷ ❤❛✈❡ ♥♦ ✈❛r✐❛❜❧❡s ✐♥ ❝♦♠♠♦♥✱ ❛♥❞ σ ▼●❯ ❢♦r t t✐♦♥ ❛♥❞ r ✳ ❲❡ ❝❛♥ ✐♥❢❡r t❤❡ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ▲ σ [ s σ ] ∨ ❈ ′ ✶ σ ∨ ❈ ′ ✷ σ ❲❤❡r❡ ▲ σ [ s σ ] ✐s ♦❜t❛✐♥❡❞ ❜② r❡♣❧❛❝✐♥❣ ❛ s✐♥❣❧❡ ♦❝❝✉rr❡♥❝❡ ♦❢ t σ ✐♥ ▲ σ ❜② s σ ✳ ❚❤❡ ✐♥❢❡rr❡❞ ❝❧❛✉s❡ ✐s ❛ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❈ ✶ ❛♥❞ ❈ ✷ ▲ ❛♥❞ r = s ❛r❡ t❤❡ ❧✐t❡r❛❧s ♣❛r❛♠♦❞✉❧❛t❡❞ ✉♣♦♥ ♣❛r❛♠♦❞✉❧❛t✐♦♥ ❢r♦♠ ❈ ✷ ✐♥t♦ ❈ ✶

  10. P❛r❛♠♦❞✉❧❛t✐♦♥✿ ❊①❛♠♣❧❡ P❛r❛♠♦❞✉❧❛t✐♦♥ ❊①❛♠♣❧❡ ✭P❛r❛♠♦❞✉❧❛t✐♦♥✮ P❛r❛♠♦❞✉❧❛t✐♦♥ ▲✐♥❡❛r ❈ ✶ : P ( ❣ ( ❢ ( ① ))) ∨ ◗ ( ① ) P❛r❛♠♦❞✉❧❛✲ t✐♦♥ ❈ ✷ : ❢ ( ❣ ( ❜ )) = ❛ ∨ ❘ ( ❣ ( ❝ )) ❆♣♣❧②✐♥❣ ♣❛r❛♠♦❞✉❧❛t✐♦♥ t : ❢ ( ① ) ✱ ▲ [ t ] : P ( ❣ ( ❢ ( ① ))) r : ❢ ( ❣ ( ❜ )) ✱ r = s : ❢ ( ❣ ( ❜ )) = ❛ σ = { ❣ ( ❜ ) / ① } P ( ❣ ( ❛ )) ∨ ◗ ( ❣ ( ❜ )) ∨ ❘ ( ❣ ( ❝ ))

  11. P❛r❛♠♦❞✉❧❛t✐♦♥✿ ❊①❛♠♣❧❡ ■■ P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❊①❛♠♣❧❡ ✭P❛r❛♠♦❞✉❧❛t✐♦♥✮ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ ❈ ✶ : P ( ❢ ( ① , ❛ ) , ② ) ∨ ❘ ( ② ) t✐♦♥ ❈ ✷ : ❢ ( ❝ , ❛ ) = ❣ ( ❜ ) ∨ ❘ ( ❣ ( ❜ )) P❛r❛♠♦❞✉❧❛♥ts P ( ❣ ( ❜ ) , ② ) ∨ ❘ ( ② ) ∨ ❘ ( ❣ ( ❜ )) P ( ❢ ( ① , ❛ ) , ❣ ( ❜ )) ∨ ❘ ( ❢ ( ❝ , ❛ )) ∨ ❘ ( ❣ ( ❜ )) P ( ❢ ( ① , ❛ ) , ❢ ( ❝ , ❛ )) ∨ ❘ ( ❣ ( ❜ ))

  12. P❛r❛♠♦❞✉❧❛♥t P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❉❡✜♥✐t✐♦♥ ✭P❛r❛♠♦❞✉❧❛♥t✮ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ ❆ ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ✭♣❛r❡♥t✮ ❝❧❛✉s❡s ❈ ✶ ❛♥❞ ❈ ✷ ✐s ♦♥❡ ♦❢ t❤❡ t✐♦♥ ❢♦❧❧♦✇✐♥❣ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t✿ ✶ ❆ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❈ ✶ ❛♥❞ ❈ ✷ ❀ ✷ ❆ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❛ ❢❛❝t♦r ♦❢ ❈ ✶ ❛♥❞ ❈ ✷ ❀ ✸ ❆ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❈ ✶ ❛♥❞ ❛ ❢❛❝t♦r ♦❢ ❈ ✷ ❀ ✹ ❆ ❜✐♥❛r② ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❛ ❢❛❝t♦r ♦❢ ❈ ✶ ❛♥❞ ❛ ❢❛❝t♦r ♦❢ ❈ ✷ ❀

  13. P❛r❛♠♦❞✉❧❛t✐♦♥✿ ❝❤❛r❛❝t❡r✐st✐❝s P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❝❤❛r❛❝t❡r✐st✐❝s ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ P❛r❛♠♦❞✉❧❛t✐♦♥ ❝♦♠❜✐♥❡❞ ✇✐t❤ r❡s♦❧✉t✐♦♥ ✐s r❡❢✉t❛t✐♦♥❛❧❧② t✐♦♥ ❝♦♠♣❧❡t❡ ❢♦r ❊✲❙❛t✐s✜❛❜❧✐t② ❯s✐♥❣ ♣❛r❛♠♦❞✉❧❛t✐♦♥ ❛♥❞ r❡s♦❧✉t✐♦♥ ✇❡ ❝❛♥ ❛❧✇❛②s ❣❡♥❡r❛t❡ � ❢r♦♠ ❛♥ ❊✲✉♥s❛t✐s✜❛❜❧❡ s❡t ♦❢ ❝❧❛✉s❡s ▼❛♥② r❡✜♥❡♠❡♥ts ❛r❡ st✐❧❧ ❝♦♠♣❧❡t❡✿ ❡✳❣✳✱ ❧✐♥❡❛r ♣❛r❛♠♦❞✉❧❛t✐♦♥

  14. ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛t✐♦♥ P❛r❛♠♦❞✉❧❛t✐♦♥ ❉❡✜♥✐t✐♦♥ ✭▲✐♥❡❛r ♣❛r❛♠♦❞✉❧❛t✐♦♥✮ P❛r❛♠♦❞✉❧❛t✐♦♥ ❙ ✿ s❡t ♦❢ ❝❧❛✉s❡s✱ ❈ ✵ ✿ ❝❧❛✉s❡ ✐♥ ❙ ▲✐♥❡❛r P❛r❛♠♦❞✉❧❛✲ ❆ ❧✐♥❡❛r ❞❡❞✉❝t✐♦♥ ♦❢ ❈ ♥ ❢r♦♠ ❙ ✇✐t❤ ❛ t♦♣ ❝❧❛✉s❡ ❈ ✵ ❜② t✐♦♥ r❡s♦❧✉t✐♦♥ ❛♥❞ ♣❛r❛♠♦❞✉❧❛t✐♦♥ ✐s ❛ s❡q✉❡♥❝❡ ♦❢ ❝❧❛✉s❡s ❘ ✶ , · · · , ❘ ♥ ✇❤❡r❡ ❘ ♥ = ❈ ♥ ❛♥❞✿ ❘ ✵ = ❈ ✵ ❢♦r ✐ = ✵ , · · · , ♥ − ✶ ❘ ✐ + ✶ ✐s ❛ r❡s♦❧✈❡♥t ♦r ❛ ♣❛r❛♠♦❞✉❧❛♥t ♦❢ ❈ ✐ ✭❝❛❧❧❡❞ ❝❡♥t❡r ❝❧❛✉s❡✮ ❛♥❞ ❇ ✐ ✭❝❛❧❧❡❞ s✐❞❡ ❝❧❛✉s❡✮ ❡❛❝❤ ❇ ✐ ✐s ❡✐t❤❡r ❛ ❝❧❛✉s❡ ✐♥ ❙ ♦r ✐s ❛ ❈ ❥ ❢♦r ❥ < ✐ ❆ ❧✐♥❡❛r r❡❢✉t❛t✐♦♥ ❜② r❡s♦❧✉t✐♦♥ ❛♥❞ ♣❛r❛♠♦❞✉❧❛t✐♦♥ ✐s ❛ ❧✐♥❡❛r ❞❡❞✉❝t✐♦♥ ♦❢ � ❜② r❡s♦❧✉t✐♦♥ ❛♥❞ ♣❛r❛♠♦❞✉❧❛t✐♦♥✳

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend