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P ttt Prtts rt r tt rtr r

  1. ❆P❊✿ ❆✉t❤❡♥t✐❝❛t❡❞ P❡r♠✉t❛t✐♦♥✲❇❛s❡❞ ❊♥❝r②♣t✐♦♥ ❢♦r ▲✐❣❤t✇❡✐❣❤t ❈r②♣t♦❣r❛♣❤② ❊❧❡♥❛ ❆♥❞r❡❡✈❛✱ ❇❡❣ü❧ ❇✐❧❣✐♥✱ ❆♥❞r❡② ❇♦❣❞❛♥♦✈✱ ❆t✉❧ ▲✉②❦①✱ ❇❛rt ▼❡♥♥✐♥❦✱ ◆✐❝❦② ▼♦✉❤❛✱ ❑❛♥ ❨❛s✉❞❛ ❑❯ ▲❡✉✈❡♥✱ ❯❚✇❡♥t❡✱ ❉❚❯✱ ◆❚❚ ❋❙❊ ✷✵✶✹ ✖ ▼❛r❝❤ ✸✱ ✷✵✶✹ ✶ ✴ ✶✹

  2. ▲✐❣❤t✇❡✐❣❤t ❈♦♥str❛✐♥❡❞ ❡♥✈✐r♦♥♠❡♥ts ❖♥❧✐♥❡ ◆♦♥❝❡✲r❡✉s❡ Pr✐♠✐t✐✈❡ ❇❧♦❝❦ ❝✐♣❤❡r P❡r♠✉t❛t✐♦♥ ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ ❢♦r ▲✐❣❤t✇❡✐❣❤t ❈r②♣t♦❣r❛♣❤② ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ • Pr✐✈❛❝② • ❆✉t❤❡♥t✐❝✐t② ✷ ✴ ✶✹

  3. Pr✐♠✐t✐✈❡ ❇❧♦❝❦ ❝✐♣❤❡r P❡r♠✉t❛t✐♦♥ ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ ❢♦r ▲✐❣❤t✇❡✐❣❤t ❈r②♣t♦❣r❛♣❤② ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ • Pr✐✈❛❝② • ❆✉t❤❡♥t✐❝✐t② ▲✐❣❤t✇❡✐❣❤t • ❈♦♥str❛✐♥❡❞ ❡♥✈✐r♦♥♠❡♥ts • ❖♥❧✐♥❡ • ◆♦♥❝❡✲r❡✉s❡ ✷ ✴ ✶✹

  4. ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ ❢♦r ▲✐❣❤t✇❡✐❣❤t ❈r②♣t♦❣r❛♣❤② ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ • Pr✐✈❛❝② • ❆✉t❤❡♥t✐❝✐t② ▲✐❣❤t✇❡✐❣❤t • ❈♦♥str❛✐♥❡❞ ❡♥✈✐r♦♥♠❡♥ts • ❖♥❧✐♥❡ • ◆♦♥❝❡✲r❡✉s❡ Pr✐♠✐t✐✈❡ • ❇❧♦❝❦ ❝✐♣❤❡r • P❡r♠✉t❛t✐♦♥ ✷ ✴ ✶✹

  5. ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ ❢♦r ▲✐❣❤t✇❡✐❣❤t ❈r②♣t♦❣r❛♣❤② ❆✉t❤❡♥t✐❝❛t❡❞ ❊♥❝r②♣t✐♦♥ • Pr✐✈❛❝② • ❆✉t❤❡♥t✐❝✐t② ▲✐❣❤t✇❡✐❣❤t • ❈♦♥str❛✐♥❡❞ ❡♥✈✐r♦♥♠❡♥ts • ❖♥❧✐♥❡ • ◆♦♥❝❡✲r❡✉s❡ Pr✐♠✐t✐✈❡ • ❇❧♦❝❦ ❝✐♣❤❡r ✗ • P❡r♠✉t❛t✐♦♥ ✓ ✷ ✴ ✶✹

  6. ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ ❖♥❧✐♥❡ ♠✐s✉s❡ r❡s✐st❛♥❝❡ ❙❡❝✉r✐t② ✉♣ t♦ ❝♦♠♠♦♥ ♣r❡✜① ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ M 1 M 1 M 3 AE K AE K AE K N 1 N 2 N 3 C 1 C 2 C 3 ✳ ◆♦♥❝❡ • ❈♦✉♥t❡r ♦r r❛♥❞♦♠ ♥✉♠❜❡r • ❘❡q✉✐r❡s ♥♦♥✲✈♦❧❛t✐❧❡ ♠❡♠♦r② ♦r ❤❛r❞✇❛r❡ r❛♥❞♦♠♥❡ss ✸ ✴ ✶✹

  7. ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ ❖♥❧✐♥❡ ♠✐s✉s❡ r❡s✐st❛♥❝❡ ❙❡❝✉r✐t② ✉♣ t♦ ❝♦♠♠♦♥ ♣r❡✜① ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ M 1 M 1 M 3 AE K AE K AE K N N N C 1 C 2 C 3 ✳ ◆♦♥❝❡ • ❈♦✉♥t❡r ♦r r❛♥❞♦♠ ♥✉♠❜❡r • ❘❡q✉✐r❡s ♥♦♥✲✈♦❧❛t✐❧❡ ♠❡♠♦r② ♦r ❤❛r❞✇❛r❡ r❛♥❞♦♠♥❡ss ✸ ✴ ✶✹

  8. ❖♥❧✐♥❡ ♠✐s✉s❡ r❡s✐st❛♥❝❡ ❙❡❝✉r✐t② ✉♣ t♦ ❝♦♠♠♦♥ ♣r❡✜① ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ M 1 M 1 M 3 AE K AE K AE K N N N C 1 C 1 C 3 ✳ ◆♦♥❝❡ • ❈♦✉♥t❡r ♦r r❛♥❞♦♠ ♥✉♠❜❡r • ❘❡q✉✐r❡s ♥♦♥✲✈♦❧❛t✐❧❡ ♠❡♠♦r② ♦r ❤❛r❞✇❛r❡ r❛♥❞♦♠♥❡ss ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ ✸ ✴ ✶✹

  9. ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ M 1 M 2 a M 1 M 2 b M 3 AE K AE K AE K N N N C 1 C 2 a C 1 C 2 b C 3 ✳ ◆♦♥❝❡ • ❈♦✉♥t❡r ♦r r❛♥❞♦♠ ♥✉♠❜❡r • ❘❡q✉✐r❡s ♥♦♥✲✈♦❧❛t✐❧❡ ♠❡♠♦r② ♦r ❤❛r❞✇❛r❡ r❛♥❞♦♠♥❡ss ▼✐s✉s❡ ❘❡s✐st❛♥❝❡ • ❖♥❧✐♥❡ ♠✐s✉s❡ r❡s✐st❛♥❝❡ • ❙❡❝✉r✐t② ✉♣ t♦ ❝♦♠♠♦♥ ♣r❡✜① ✸ ✴ ✶✹

  10. ❆P❊ ❙t❛t❡ ♦❢ t❤❡ ❆rt ♥♦♥❝❡✲❞❡♣❡♥❞❡♥t ♠✐s✉s❡ r❡s✐st❛♥t ■❆P▼ ❵✵✵✱ ❖❈❇ ❵✵✶ ❙■❱ ❵✵✻✱ ❇❚▼ ❵✵✾ ❜❧♦❝❦ ❝✐♣❤❡r ❳❊❈❇ ❵✵✶✱ ❈❈▼ ❵✵✸ ▼❝❖❊✲● ❵✶✶✱ ❈❖P❆ ✬✶✸ ●❈▼ ❵✵✹✱ ❈▲❖❈ ❵✶✹ P❖❊❚ ✬✶✹✱ ❈❖❇❘❆ ✬✶✹ ❙♣♦♥❣❡❲r❛♣ ❵✶✶ ♣❡r♠✉t❛t✐♦♥ ❑❡②❛❦✫❑❡t❥❡ ✬✶✹ ◆❖❘❳ ✬✶✹ ✹ ✴ ✶✹

  11. ❙t❛t❡ ♦❢ t❤❡ ❆rt ♥♦♥❝❡✲❞❡♣❡♥❞❡♥t ♠✐s✉s❡ r❡s✐st❛♥t ■❆P▼ ❵✵✵✱ ❖❈❇ ❵✵✶ ❙■❱ ❵✵✻✱ ❇❚▼ ❵✵✾ ❜❧♦❝❦ ❝✐♣❤❡r ❳❊❈❇ ❵✵✶✱ ❈❈▼ ❵✵✸ ▼❝❖❊✲● ❵✶✶✱ ❈❖P❆ ✬✶✸ ●❈▼ ❵✵✹✱ ❈▲❖❈ ❵✶✹ P❖❊❚ ✬✶✹✱ ❈❖❇❘❆ ✬✶✹ ❙♣♦♥❣❡❲r❛♣ ❵✶✶ ❆P❊ ♣❡r♠✉t❛t✐♦♥ ❑❡②❛❦✫❑❡t❥❡ ✬✶✹ ◆❖❘❳ ✬✶✹ ✹ ✴ ✶✹

  12. ❆P❊ C [1] C [2] C [3] C [4] M [1] M [2] M [3] M [4] 0 + + + + 1 K p p p p K T + + ✳ ✺ ✴ ✶✹

  13. ❆P❊✿ ❆ss♦❝✐❛t❡❞ ❉❛t❛ A [1] A [2] A [3] A [4] 0 IV r + + + + p p p p IV c K C [1] C [2] C [3] C [4] M [1] M [2] M [3] M [4] IV r + + + + 1 K p p p p IV c T + + ✳ ✻ ✴ ✶✹

  14. ❆P❊✿ ❉❡❝r②♣t✐♦♥ ❛♥❞ ❱❡r✐✜❝❛t✐♦♥ M [1] M [2] M [3] M [4] C [1] C [2] C [3] C [4] + + + 1 K p –1 p –1 p –1 p –1 K ? T + + ✼ ✴ ✶✹

  15. ❆P❊✿ ❋r❛❝t✐♦♥❛❧ ▼❡ss❛❣❡s ❛♥❞ ❆ss♦❝✐❛t❡❞ ❉❛t❛ A [1] A [2] A [3] A [4] � 10 ∗ 0 IV r + + + p p p p + IV c K C [1] C [2] ⌈ C [3] ⌉ , | M [4] | C [4] M [1] M [2] M [3] M [4] � 10 ∗ IV r + + + 1 K p p p p + IV c T + + ✳ ✽ ✴ ✶✹

  16. ❙t❛♥❞❛r❞ ❈✐♣❤❡r ▼♦❞❡❧ Pr✐✈❛❝②✿ ■♥t❡❣r✐t②✿ Pr✐✈❛❝②✿ ✰ s♣r♣ ■♥t❡❣r✐t②✿ ✰ s♣r♣ ❆P❊✿ ❙❡❝✉r✐t② C [1] C [2] C [3] C [4] M [1] M [2] M [3] M [4] 0 + + + + 1 K p p p p K T + + ■❞❡❛❧ P❡r♠✉t❛t✐♦♥ ▼♦❞❡❧ ✾ ✴ ✶✹

  17. ❙t❛♥❞❛r❞ ❈✐♣❤❡r ▼♦❞❡❧ Pr✐✈❛❝②✿ ✰ s♣r♣ ■♥t❡❣r✐t②✿ ✰ s♣r♣ ❆P❊✿ ❙❡❝✉r✐t② C [1] C [2] C [3] C [4] M [1] M [2] M [3] M [4] 0 + + + + 1 K p p p p K T + + ■❞❡❛❧ P❡r♠✉t❛t✐♦♥ ▼♦❞❡❧ • Pr✐✈❛❝②✿ 2 c/ 2 • ■♥t❡❣r✐t②✿ 2 c/ 2 ✾ ✴ ✶✹

  18. ❆P❊✿ ❙❡❝✉r✐t② C [1] C [2] C [3] C [4] M [1] M [2] M [3] M [4] 0 + + + + p p p p 1 T + + + + + + + + K K K K K K K K ■❞❡❛❧ P❡r♠✉t❛t✐♦♥ ▼♦❞❡❧ ❙t❛♥❞❛r❞ ❈✐♣❤❡r ▼♦❞❡❧ • Pr✐✈❛❝②✿ 2 c/ 2 • E := ⊕ 0 � K ◦ p ◦ ⊕ 0 � K • Pr✐✈❛❝②✿ 2 c/ 2 ✰ s♣r♣ ( E ) • ■♥t❡❣r✐t②✿ 2 c/ 2 • ■♥t❡❣r✐t②✿ 2 c/ 2 ✰ s♣r♣ ( E ) ✾ ✴ ✶✹

  19. P❡r♠✉t❛t✐♦♥ P❡r♠✉t❛t✐♦♥ ❢r♦♠ P❤♦t♦♥✴◗✉❛r❦✴❙♣♦♥❣❡♥t ❆P❊ ❡♥❝✴❞❡❝ P❛r❛♠❡t❡rs ❙❡❝✉r✐t②✿ ✽✵✱ ✶✷✽ ❜✐ts ❘❛t❡✿ ✶✻✱ ✸✷ ❜✐ts ❆P❊✿ ❍❛r❞✇❛r❡ ■♠♣❧❡♠❡♥t❛t✐♦♥ ❚✇♦ ♣❧❛t❢♦r♠s • ❋❛r❛❞❛② ❙t❛♥❞❛r❞ ❈❡❧❧ ▲✐❜r❛r② ♦♥ ❯▼❈ ✶✽✵♥♠ • ❖♣❡♥✲❝❡❧❧ ✹✺♥♠ ◆❆◆●❆❚❊ ❧✐❜r❛r② ✶✵ ✴ ✶✹

  20. P❛r❛♠❡t❡rs ❙❡❝✉r✐t②✿ ✽✵✱ ✶✷✽ ❜✐ts ❘❛t❡✿ ✶✻✱ ✸✷ ❜✐ts ❆P❊✿ ❍❛r❞✇❛r❡ ■♠♣❧❡♠❡♥t❛t✐♦♥ ❚✇♦ ♣❧❛t❢♦r♠s • ❋❛r❛❞❛② ❙t❛♥❞❛r❞ ❈❡❧❧ ▲✐❜r❛r② ♦♥ ❯▼❈ ✶✽✵♥♠ • ❖♣❡♥✲❝❡❧❧ ✹✺♥♠ ◆❆◆●❆❚❊ ❧✐❜r❛r② P❡r♠✉t❛t✐♦♥ • P❡r♠✉t❛t✐♦♥ ❢r♦♠ P❤♦t♦♥✴◗✉❛r❦✴❙♣♦♥❣❡♥t • ❆P❊ ❡♥❝✴❞❡❝ ✶✵ ✴ ✶✹

  21. ❆P❊✿ ❍❛r❞✇❛r❡ ■♠♣❧❡♠❡♥t❛t✐♦♥ ❚✇♦ ♣❧❛t❢♦r♠s • ❋❛r❛❞❛② ❙t❛♥❞❛r❞ ❈❡❧❧ ▲✐❜r❛r② ♦♥ ❯▼❈ ✶✽✵♥♠ • ❖♣❡♥✲❝❡❧❧ ✹✺♥♠ ◆❆◆●❆❚❊ ❧✐❜r❛r② P❡r♠✉t❛t✐♦♥ • P❡r♠✉t❛t✐♦♥ ❢r♦♠ P❤♦t♦♥✴◗✉❛r❦✴❙♣♦♥❣❡♥t • ❆P❊ ❡♥❝✴❞❡❝ P❛r❛♠❡t❡rs • ❙❡❝✉r✐t②✿ ✽✵✱ ✶✷✽ ❜✐ts • ❘❛t❡✿ ✶✻✱ ✸✷ ❜✐ts ✶✵ ✴ ✶✹

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