❆✉t❡♥t✐❝❛çã♦ ❡ ❝♦♠✉♥✐❝❛çã♦ s❡❣✉r❛
❡♠ ❞✐s♣♦s✐t✐✈♦s ♠ó✈❡✐s ❞❡ ♣♦❞❡r
❝♦♠♣✉t❛❝✐♦♥❛❧ r❡str✐t♦
❘❛❢❛❡❧ ❲✐❧❧ ▼❛❝❡❞♦ ❞❡ ❆r❛✉❥♦
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛
❛♦
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
❞❛
❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
♣❛r❛
♦❜t❡♥çã♦ ❞♦ tít✉❧♦
❞❡
▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s
Pr♦❣r❛♠❛✿ ▼❡str❛❞♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❘♦✉t♦ ❚❡r❛❞❛
❉✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ♦ ❛✉t♦r r❡❝❡❜❡✉ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ❞♦ ❈◆Pq
❆✉t❡♥t✐❝❛çã♦ ❡ ❝♦♠✉♥✐❝❛çã♦ s❡❣✉r❛
❡♠ ❞✐s♣♦s✐t✐✈♦s ♠ó✈❡✐s ❞❡ ♣♦❞❡r
❝♦♠♣✉t❛❝✐♦♥❛❧ r❡str✐t♦
❊st❛ ❞✐ss❡rt❛çã♦ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ r❡❛❧✐③❛❞❛ ♣♦r ❘❛❢❛❡❧ ❲✐❧❧ ▼❛❝❡❞♦ ❞❡ ❆r❛✉❥♦ ❡♠ ✸✶✴✶✵✴✷✵✶✸✳ ❖ ♦r✐❣✐♥❛❧ ❡♥❝♦♥tr❛✲s❡ ❞✐s♣♦♥í✈❡❧ ♥♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳
❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s✱ ♣❡❧❛ s❛ú❞❡ ❡ s❛❜❡❞♦r✐❛ q✉❡ ♣❡r♠✐t✐r❛♠ ❛ ❝♦♥❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦s ♠❡✉s ♣❛✐s ◆❛✉♠ ❡ ❲â♥❡r✱ ♣❡❧♦ s✉♣♦rt❡ ❝♦♥tí♥✉♦✱ ♣♦r s❡♠♣r❡ ❛❝r❡❞✐t❛r❡♠ ❡♠ ♠✐♠ ❡ ♣❡❧❛ ❞❡❞✐❝❛çã♦ q✉❡ tê♠ ♠❡ ❞❛❞♦ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❞❡ ♠✐♥❤❛ ✈✐❞❛✱ ❡ ❛ t♦❞♦s ♦s ❢❛♠✐❧✐❛r❡s q✉❡ ♠❡ ❛♣♦✐❛r❛♠✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ▲✐❧✐❛♥✱ ♣♦r s❡✉ ❛♠♦r✱ ❛❢❡t♦ ❡ ♣❛❧❛✈r❛s ❞❡ ❝❛r✐♥❤♦ q✉❡ ❢♦r❛♠ ❢✉♥❞❛♠❡♥t❛✐s ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❞♦ ♠❡str❛❞♦✱ ❡ ❛♦s s❡✉s ♣❛✐s ❱❛❧❞s♦♥ ❡ ▲❡♥✐❧❞❡✱ ♣❡❧♦ ❛♣♦✐♦ ❡ ♣❛❧❛✈r❛s ❞❡ ♠♦t✐✈❛çã♦✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❡ ♣r♦❢❡ss♦r ❘♦✉t♦ ❚❡r❛❞❛✱ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❡ ♣♦r ❣✉✐❛r✲♠❡ ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ❝♦♠ s✉❛ ♣❛❝✐ê♥❝✐❛✱ ❡①♣❡r✐ê♥❝✐❛ ❡ ❝♦♥❤❡❝✐♠❡♥t♦✳
❆♦s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛ ❞❡ q✉❛❧✐✜❝❛çã♦ ❡ ❞❛ ❝♦♠✐ssã♦ ❥✉❧❣❛❞♦r❛ ✭♣r♦❢❡ss♦r❡s ▼❛r❝♦ ❆✉ré❧✐♦ ●❡r♦s❛✱ ❈í♥t✐❛ ❇♦r❣❡s ▼❛r❣✐✱ ❘♦❜❡rt♦ ❍✐r❛t❛ ❏✉♥✐♦r✮✱ ♣❡❧❛s ✈❛❧✐♦s❛s s✉❣❡stõ❡s✱ q✉❡st✐♦♥❛♠❡♥t♦s ❡ ❝♦♠❡♥tár✐♦s✳
❆♦s ❛♠✐❣♦s ❡ ♠❡♠❜r♦s ❞♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❙❡❣✉r❛♥ç❛ ❞❡ ❉❛❞♦s ✭▲❙❉✮ ❞♦ ■▼❊✲❯❙P✱ ♣❡❧❛s ❞✐s❝✉s✲ sõ❡s ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳ ❊♠ ❡s♣❡❝✐❛❧✱ ❛ ❉❡♥✐s❡ ●♦②❛ ♣❡❧❛ ♣❛r❝❡r✐❛ ❡ ❝♦♥❤❡❝✐♠❡♥t♦s ❝♦♠♣❛rt✐❧❤❛❞♦s✳ ❆♦s ❞❡♠❛✐s ❛♠✐❣♦s ❞❛ ❯❙P q✉❡ ❡st✐✈❡r❛♠ ❝♦♠✐❣♦ ❞❡s❞❡ ❛ é♣♦❝❛ ❞❛s ❞✐s❝✐♣❧✐♥❛s ❡ ❣r✉♣♦s ❞❡ ❡st✉❞♦✳
❆♦s ❛♠✐❣♦s ❞❡ ❧♦♥❣❛ ❞❛t❛ ❞❡ ❆r❛❝❛❥✉✱ q✉❡ ❛♣❡s❛r ❞❛ ❞✐stâ♥❝✐❛ ❝♦♥t✐♥✉❛r❛♠ ♠❡ ❛♣♦✐❛♥❞♦ ❡ t♦r❝❡♥❞♦ ♣❡❧♦ ♠❡✉ s✉❝❡ss♦✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❡ ❢✉♥❝✐♦♥ár✐♦s ❞♦ ■▼❊✲❯❙P✱ q✉❡ ❝♦❧❛❜♦r❛r❛♠ ❝♦♠ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❡ ✈✐❛❜✐❧✐③❛r❛♠ ❛ ♣r♦❞✉çã♦ ❞❡st❛ ♦❜r❛✳
❆♦ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❈✐❡♥tí✜❝♦ ❡ ❚❡❝♥♦❧ó❣✐❝♦ ✭❈◆Pq✮✱ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥✲ ❝❡✐r♦✳
❆ t♦❞♦s✱ ♠❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s✦
❘❡s✉♠♦
Pr♦t♦❝♦❧♦s ❞❡ ❛✉t❡♥t✐❝❛çã♦ ❡ ❞❡ ❡st❛❜❡❧❡❝✐♠❡♥t♦ ❞❡ ❝❤❛✈❡s sã♦ ♣❡ç❛s ❢✉♥❞❛♠❡♥t❛✐s ❡♠ ✐♠♣❧❡✲ ♠❡♥t❛çõ❡s ❞❡ s❡❣✉r❛♥ç❛ ♣❛r❛ ❝♦♠✉♥✐❝❛çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s✳ ❊♠ ❛♣❧✐❝❛çõ❡s q✉❡ ❡♥✈♦❧✈❛♠ ❞✐s♣♦s✐t✐✈♦s ❝♦♠ ♣♦❞❡r ❝♦♠♣✉t❛❝✐♦♥❛❧ r❡str✐t♦ ✭t❛✐s ❝♦♠♦ s♠❛rt♣❤♦♥❡s ♦✉ t❛❜❧❡ts✮ ❝♦♠✉♥✐❝❛♥❞♦✲s❡ ❝♦♠ ✉♠ s❡r✈✐❞♦r✱ é ♣r✐♠♦r❞✐❛❧ ❛ ❡s❝♦❧❤❛ ❞❡ ♣r♦t♦❝♦❧♦s ❡✜❝✐❡♥t❡s ❡ q✉❡ ♥❡❝❡ss✐t❡♠ ❞❡ ✉♠❛ ✐♥❢r❛❡s✲ tr✉t✉r❛ ♠❛✐s s✐♠♣❧❡s✳ ◆❡st❡ tr❛❜❛❧❤♦ s❡❧❡❝✐♦♥❛♠♦s ❡ ✐♠♣❧❡♠❡♥t❛♠♦s ♣r♦t♦❝♦❧♦s ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ s❡❣✉r♦s ♥♦s ♠♦❞❡❧♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ✭■❉✲❜❛s❡❞✮ ❡ s❡♠ ❝❡rt✐✲ ✜❝❛❞♦ ✭❈❡rt✐✜❝❛t❡❧❡ss✮ ❡♠ ♣❧❛t❛❢♦r♠❛s ❝♦♠ ♣r♦❝❡ss❛❞♦r❡s ❆❘▼✳ ❈♦♠♣❛r❛♠♦s t❡♠♣♦s ❞❡ ❡①❡❝✉çã♦✱ ✉t✐❧✐③❛çã♦ ❞❡ ♠❡♠ór✐❛ ❡ ✉s♦ ❞♦ ❝❛♥❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♣r♦t♦❝♦❧♦ ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡✱ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞❛ ❡♠ ✐❞❡♥t✐❞❛❞❡✱ ❝r✐♣t♦❣r❛✜❛ s❡♠ ❝❡rt✐✜❝❛❞♦✱ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❜✐❧✐♥❡❛r✱ ❝r✐♣t♦❣r❛✜❛ s♦❜r❡ ❝✉r✈❛ ❡❧í♣t✐❝❛✱ ❞✐s♣♦s✐t✐✈♦s ♠ó✈❡✐s✳
❆❜str❛❝t
Pr♦t♦❝♦❧s ❢♦r ❛✉t❤❡♥t✐❝❛t✐♦♥ ❛♥❞ ❦❡② ❡st❛❜❧✐s❤♠❡♥t ❛r❡ ❢✉♥❞❛♠❡♥t❛❧ ♣❛rts ✐♥ s❡❝✉r✐t② ✐♠♣❧❡✲ ♠❡♥t❛t✐♦♥s ❢♦r ❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s ❝♦♠♠✉♥✐❝❛t✐♦♥✳ ■♥ ❛♣♣❧✐❝❛t✐♦♥s ✐♥✈♦❧✈✐♥❣ ❞❡✈✐❝❡s ✇✐t❤ ❧✐♠✐t❡❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ♣♦✇❡r ✭s✉❝❤ ❛s s♠❛rt♣❤♦♥❡s ❛♥❞ t❛❜❧❡ts✮ ❝♦♠♠✉♥✐❝❛t✐♥❣ ✇✐t❤ ❛ s❡r✈❡r✱ t❤❡ ❝❤♦✐❝❡ ♦❢ ❡✣❝✐❡♥t ♣r♦t♦❝♦❧s t❤❛t r❡q✉✐r❡ ❛ s✐♠♣❧❡r ✐♥❢r❛str✉❝t✉r❡ ✐s ❡ss❡♥t✐❛❧✳ ■♥ t❤✐s ✇♦r❦ ✇❡ s❡❧❡❝t ❛♥❞ ✐♠♣❧❡♠❡♥t s❡❝✉r❡ ❦❡② ❛❣r❡❡♠❡♥t ♣r♦t♦❝♦❧s ✐♥ ■❉✲❜❛s❡❞ ❛♥❞ ❈❡rt✐✜❝❛t❡❧❡ss ♣✉❜❧✐❝ ❦❡② ❝r②♣t♦❣r❛♣❤② ♠♦❞❡❧s ♦♥ ❆❘▼ ♣r♦❝❡ss♦r ♣❧❛t❢♦r♠s✳ ❲❡ ❛❧s♦ ❝♦♠♣❛r❡ r✉♥♥✐♥❣ t✐♠❡s✱ ♠❡♠♦r② ❛♥❞ ♥❡t✇♦r❦ ✉s❛❣❡✳
❑❡②✇♦r❞s✿ ❦❡② ❛❣r❡❡♠❡♥t ♣r♦t♦❝♦❧✱ ■❉✲❜❛s❡❞ ❝r②♣t♦❣r❛♣❤②✱ ❝❡rt✐✜❝❛t❡❧❡ss ❝r②♣t♦❣r❛♣❤②✱ ❜✐❧✐♥❡❛r ♣❛✐r✐♥❣✱ ❡❧❧✐♣t✐❝ ❝✉r✈❡ ❝r②♣t♦❣r❛♣❤②✱ ♠♦❜✐❧❡ ❞❡✈✐❝❡s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ✐①
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶
✷ ❋✉♥❞❛♠❡♥t♦s ❞❡ ❈r✐♣t♦❣r❛✜❛ ✸
✷✳✶ ❚❡r♠✐♥♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷✳✷ Pr♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷✳✸ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ s❡❝r❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✹ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✹✳✶ ❆ss✐♥❛t✉r❛ ❞✐❣✐t❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✹✳✷ ■♥❢r❛❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✸ ❊♠♣❛r❡❧❤❛♠❡♥t♦s ❇✐❧✐♥❡❛r❡s ✾
✸✳✶ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❛❧❣♦r✐t♠♦s ❡ ♣r♦❜❧❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❞❡ ✐♥t❡r❡ss❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✸✳✶✳✶ Pr♦❜❧❡♠❛ ❞♦ ❧♦❣❛r✐t♠♦ ❞✐s❝r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸✳✶✳✷ Pr♦❜❧❡♠❛ ❞♦ ❧♦❣❛r✐t♠♦ ❞✐s❝r❡t♦ s♦❜r❡ ❝✉r✈❛s ❡❧í♣t✐❝❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸✳✶✳✸ ❖✉tr♦s ♣r♦❜❧❡♠❛s r❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✹ ▼♦❞❡❧♦s ❆❧t❡r♥❛t✐✈♦s ❞❡ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❈❤❛✈❡ Pú❜❧✐❝❛ ✶✸
✹✳✶ ▼♦❞❡❧♦ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✹✳✷ ▼♦❞❡❧♦ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ s❡♠ ❝❡rt✐✜❝❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✹✳✸ ❈♦♠♣r✐♠❡♥t♦ ❞❛s ❝❤❛✈❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✹✳✹ Pr♦t♦❝♦❧♦s ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✹✳✹✳✶ ❆tr✐❜✉t♦s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✹✳✹✳✷ ▼♦❞❡❧♦s ❞❡ s❡❣✉r❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✺ Pr♦t♦❝♦❧♦s ❊st✉❞❛❞♦s ✷✶
✺✳✶ ❊s❝♦❧❤❛ ❞♦s ♣r♦t♦❝♦❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✺✳✷ Pr♦t♦❝♦❧♦s ♥♦ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✺✳✷✳✶ Pr♦t♦❝♦❧♦ ❍✉❛♥❣✲❈❛♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✈✐✐✐ ❙❯▼➪❘■❖
✺✳✷✳✷ Pr♦t♦❝♦❧♦ ❍✉✲▲✐✉✲❩❤❛♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✺✳✷✳✸ Pr♦t♦❝♦❧♦ ❈❤♦✇✲❈❤♦♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✺✳✷✳✹ Pr♦t♦❝♦❧♦ ◆✐✲❈❤❡♥✲▲✐✲❍❛♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✺✳✷✳✺ Pr♦t♦❝♦❧♦ ◆✐✲❈❤❡♥✲▲✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✺✳✸ Pr♦t♦❝♦❧♦s ♥♦ ♠♦❞❡❧♦ s❡♠ ❝❡rt✐✜❝❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✺✳✸✳✶ Pr♦t♦❝♦❧♦ ▲✐♣♣♦❧❞✲❇♦②❞✲●♦♥③á❧❡③ ◆✐❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✺✳✸✳✷ Pr♦t♦❝♦❧♦ ●♦②❛✲❖❦✐❞❛✲❚❡r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✺✳✸✳✸ Pr♦t♦❝♦❧♦ ●♦②❛✲◆❛❦❛♠✉r❛✲❚❡r❛❞❛✲✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✺✳✸✳✹ Pr♦t♦❝♦❧♦ ●♦②❛✲◆❛❦❛♠✉r❛✲❚❡r❛❞❛✲✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✺✳✸✳✺ Pr♦t♦❝♦❧♦ ●♦②❛✲◆❛❦❛♠✉r❛✲❚❡r❛❞❛✲✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✺✳✸✳✻ Pr♦t♦❝♦❧♦ ●♦②❛✲◆❛❦❛♠✉r❛✲❚❡r❛❞❛✲✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✺✳✹ ❆❞❛♣t❛çã♦ ♣❛r❛ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❛ss✐♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✻ ❊①♣❡r✐♠❡♥t♦s ✸✺
✻✳✶ ❈❡♥ár✐♦ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✻✳✷ ❆♠❜✐❡♥t❡ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✻✳✸ ❈✉r✈❛s ❡❧í♣t✐❝❛s ❡ ❝✉st♦ ❞❛s ♦♣❡r❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✻✳✹ ❆❞❛♣t❛çã♦ ❡✜❝✐❡♥t❡ ♣❛r❛ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❛ss✐♠étr✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✻✳✺ ❈♦♠♣❛r❛çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡♥tr❡ ♦s ♣r♦t♦❝♦❧♦s ❛♥❛❧✐s❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✻✳✻ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s s♦❜r❡ ♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✼ ❈♦♥❝❧✉sõ❡s ✺✸
✼✳✶ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✼✳✷ ❙✉❣❡stõ❡s ♣❛r❛ ♣❡sq✉✐s❛s ❢✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
❆ ❋✉♥❞❛♠❡♥t♦s ▼❛t❡♠át✐❝♦s ✺✺
❆✳✶ ●r✉♣♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❆✳✷ ❆♥é✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❆✳✸ ❈♦r♣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❆✳✸✳✶ ❈♦r♣♦s ✜♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❆✳✹ ❈✉r✈❛s ❡❧í♣t✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❆✳✹✳✶ ❖r❞❡♠ ❞❡ ❝✉r✈❛s ❡❧í♣t✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❆✳✹✳✷ ▲❡✐ ❞❡ ❣r✉♣♦s ❡♠ ❝✉r✈❛s ❡❧í♣t✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❇ ■♥t❡r✈❛❧♦s ❞❡ ❈♦♥✜❛♥ç❛ ❞♦s ❊①♣❡r✐♠❡♥t♦s ✺✾
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s
❆❊❙ ❆❞✈❛♥❝❡❞ ❊♥❝r✐♣t✐♦♥ ❙t❛♥❞❛r❞ ✭❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✮ ❉❊❙ ❉❛t❛ ❊♥❝r✐♣t✐♦♥ ❙t❛♥❞❛r❞ ✭❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✮ ❉▲P Pr♦❜❧❡♠❛ ❞♦ ❧♦❣❛r✐t♠♦ ❞✐s❝r❡t♦ ✭❉✐s❝r❡t❡ ▲♦❣❛r✐t❤♠ Pr♦❜❧❡♠✮
❊❈❈ ❈r✐♣t♦ss✐st❡♠❛ ❞❡ ❈✉r✈❛s ❊❧í♣t✐❝❛s ✭❊❧❧✐♣t✐❝ ❈✉r✈❡ ❈r②♣t♦s②st❡♠✮ ■❇❊ ❊♥❝r✐♣t❛çã♦ ❜❛s❡❛❞❛ ❡♠ ✐❞❡♥t✐❞❛❞❡s ✭■❞❡♥t✐t②✲❇❛s❡❞ ❊♥❝r②♣t✐♦♥✮ ■❈P ■♥❢r❛❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s
❑●❈ ❈❡♥tr♦ ❣❡r❛❞♦r ❞❡ ❝❤❛✈❡s ✭❑❡② ●❡♥❡r❛t✐♦♥ ❈❡♥t❡r✮
❏◆■ ❏❛✈❛ ◆❛t✐✈❡ ■♥t❡r❢❛❝❡ ✭♣❡r♠✐t❡ q✉❡ ❛ ♠áq✉✐♥❛ ✈✐rt✉❛❧ ❏❛✈❛ ❛❝❡ss❡ ❝ó❞✐❣♦ ♥❛t✐✈♦✮ P❑■ ■♥❢r❛❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ✭P✉❜❧✐❝ ❑❡② ■♥❢r❛str✉❝t✉r❡✮
P❑● ●❡r❛❞♦r ❞❡ ❝❤❛✈❡s ♣r✐✈❛❞❛s ✭Pr✐✈❛t❡ ❑❡② ●❡♥❡r❛t♦r✮
❘❙❆ ❆❝rô♥✐♠♦ ❞❡ ❘✐✈❡st✱ ❙❤❛♠✐r✱ ❆❞❧❡♠❛♥ ✭❛❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛✮
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❊①❡♠♣❧♦ ❞❡ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✷ ▼♦❞❡❧♦ ❞❡ ❝❡rt✐✜❝❛çã♦ ❡♠ ár✈♦r❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✸ ▼♦❞❡❧♦ ❞❡ ❝❡rt✐✜❝❛çã♦ ❡♠ ✢♦r❡st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✸✳✶ ■❧✉str❛çã♦ ❞❡ ✉♠ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❇✐❧✐♥❡❛r ✭❈❡s❡♥❛✱✷✵✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✹✳✶ ❉✐str✐❜✉çã♦ ❞❡ ❝❤❛✈❡s ♥❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❜❛s❡❛❞❛ ❡♠ ✐❞❡♥t✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✶✹
✹✳✷ ❉✐str✐❜✉çã♦ ❞❡ ❝❤❛✈❡s ♥❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ s❡♠ ❝❡rt✐✜❝❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✹✳✸ Pr♦t♦❝♦❧♦ ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ ❉✐✣❡✲❍❡❧❧♠❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✹✳✹ ❍✐❡r❛rq✉✐❛ ❞♦s ♠♦❞❡❧♦s ❞❡ s❡❣✉r❛♥ç❛ ♣❛r❛ ♣r♦t♦❝♦❧♦s ♥♦ ♠♦❞❡❧♦ s❡♠ ❝❡rt✐✜❝❛❞♦ ✭●♦②❛✱✷✵✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✺✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❣❡♥ér✐❝❛ ❞❡ ✉♠ ♣r♦t♦❝♦❧♦ ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ ♥♦ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✺✳✷ Pr♦t♦❝♦❧♦ ❍❈✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✺✳✸ Pr♦t♦❝♦❧♦ ❍▲❩✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✺✳✹ Pr♦t♦❝♦❧♦ ❈❈✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✺✳✺ Pr♦t♦❝♦❧♦ ◆▲❈❍✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✺✳✻ Pr♦t♦❝♦❧♦ ◆▲❈❍✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✺✳✼ Pr♦t♦❝♦❧♦ ◆▲❈✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✺✳✽ ❘❡♣r❡s❡♥t❛çã♦ ❣❡♥ér✐❝❛ ❞❡ ✉♠ ♣r♦t♦❝♦❧♦ ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡s ♥♦ ♠♦❞❡❧♦ s❡♠ ❝❡rt✐✜❝❛❞♦ ✷✼
✺✳✾ Pr♦t♦❝♦❧♦ ▲❇●✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✺✳✶✵ Pr♦t♦❝♦❧♦ ▲❇●✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✺✳✶✶ Pr♦t♦❝♦❧♦ ●❖❚✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✺✳✶✷ Pr♦t♦❝♦❧♦ ●❖❚✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✺✳✶✸ Pr♦t♦❝♦❧♦ ●◆❚✸✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✺✳✶✹ Pr♦t♦❝♦❧♦ ●◆❚✹✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ❇❉❍✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✺✳✶✺ Pr♦t♦❝♦❧♦ ●◆❚✶✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✺✳✶✻ Pr♦t♦❝♦❧♦ ●◆❚✷✱ s❡❣✉r♦ s♦❜ ♦ ♣r♦❜❧❡♠❛ ●❛♣✲❇❉❍✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✻✳✶ ❈❡♥ár✐♦ ❞♦s ❡①♣❡r✐♠❡♥t♦s ❡ ❝♦♠✉♥✐❝❛çã♦ ❡♥tr❡ ♦s ❞✐s♣♦s✐t✐✈♦s✿ ❛✮ ❘❛s♣❜❡rr② P✐✱ ❜✮ ▼♦t♦r♦❧❛ ▼✐❧❡st♦♥❡ ✶✱ ❝✮ ●♦♦❣❧❡ ◆❡①✉s ✼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✻✳✷ ◆í✈❡❧ ❞❡ s❡❣✉r❛♥ç❛ ❞❛s ❝✉r✈❛s ❡❧í♣t✐❝❛s ❡s❝♦❧❤✐❞❛s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✻✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s t❡♠♣♦s ❞❡ ❝❛❞❛ ♦♣❡r❛çã♦ ❡♠ ❝✉r✈❛s ❜✐♥ár✐❛s ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✳ ✸✾
✻✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s t❡♠♣♦s ❞❡ ❝❛❞❛ ♦♣❡r❛çã♦ ❡♠ ❝✉r✈❛s ♣r✐♠❛s ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✳ ✹✵
✻✳✺ Pr♦t♦❝♦❧♦ ❍✉❛♥❣✲❈❛♦ ❛ss✐♠étr✐❝♦ ✲ ❝❛s♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
①✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✻✳✻ Pr♦t♦❝♦❧♦ ❍✉❛♥❣✲❈❛♦ ❛ss✐♠étr✐❝♦ ✲ ❝❛s♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✻✳✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♣r♦t♦❝♦❧♦s ❜❛s❡❛❞♦s ❡♠ ✐❞❡♥t✐❞❛❞❡✱ ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✱ ♣❛r❛ ♦ ❝❛s♦ s❡♠ ♣ré✲❝♦♠♣✉t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✻✳✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♣r♦t♦❝♦❧♦s s❡♠ ❝❡rt✐✜❝❛❞♦✱ ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✱ ♣❛r❛ ♦ ❝❛s♦ s❡♠ ♣ré✲❝♦♠♣✉t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✻✳✾ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♣r♦t♦❝♦❧♦s ❜❛s❡❛❞♦s ❡♠ ✐❞❡♥t✐❞❛❞❡✱ ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✱ ♣❛r❛ ♦ ❝❛s♦ ❝♦♠ ♣ré✲❝♦♠♣✉t❛çã♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✻✳✶✵ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♣r♦t♦❝♦❧♦s s❡♠ ❝❡rt✐✜❝❛❞♦✱ ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✱ ♣❛r❛ ♦ ❝❛s♦ ❝♦♠ ♣ré✲❝♦♠♣✉t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✹✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❝♦♠♣r✐♠❡♥t♦s ♠í♥✐♠♦s ❞❡ ❝❤❛✈❡s ✭❡♠ ❜✐ts✮ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛ ✭❇❛r❦❡r ❡t ❛❧✳✱✷✵✵✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✻✳✶ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞❛s ♦♣❡r❛çõ❡s ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✱ ❡♠ ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐t✐✈♦s ❡ ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✻✳✷ ❘❡❧❛çã♦ ❡♥tr❡ ♣r♦t♦❝♦❧♦s ♥♦ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ❡ ♠♦❞❡❧♦s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✹✷
✻✳✸ ❘❡❧❛çã♦ ❡♥tr❡ ♣r♦t♦❝♦❧♦s ♥♦ ♠♦❞❡❧♦ s❡♠ ❝❡rt✐✜❝❛❞♦ ❡ ♠♦❞❡❧♦s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✻✳✹ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♦♣❡r❛çõ❡s ♥♦s ♣r♦t♦❝♦❧♦s ✐♠♣❧❡♠❡♥t❛❞♦s ✭❡♠♣❛r❡❧❤❛♠❡♥t♦ s✐♠étr✐❝♦✮✳ ✹✸
✻✳✺ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♦♣❡r❛çõ❡s ♥♦s ♣r♦t♦❝♦❧♦s ✐♠♣❧❡♠❡♥t❛❞♦s ✭❡♠♣❛r❡❧❤❛♠❡♥t♦ ❛ss✐♠étr✐❝♦✮✳ ✹✸
✻✳✻ ❚❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ❞♦s ♣r♦t♦❝♦❧♦s ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✱ s❡♠ ♣ré✲❝♦♠♣✉t❛çã♦✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✻✳✼ ❚❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ❞♦s ♣r♦t♦❝♦❧♦s ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✱ ❝♦♠ ♣ré✲❝♦♠♣✉t❛çã♦✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✻✳✽ ❯s♦ ❞❡ ♠❡♠ór✐❛ ✭❡♠ ❜②t❡s✮ ❞♦s ♣r♦t♦❝♦❧♦s ❛♥❛❧✐s❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉✲ r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✻✳✾ ❈♦♠♣r✐♠❡♥t♦ ❞❛s ♠❡♥s❛❣❡♥s tr♦❝❛❞❛s ✭❡♠ ❜②t❡s✮ ❞♦s ♣r♦t♦❝♦❧♦s ❛♥❛❧✐s❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
❇✳✶ ■♥t❡r✈❛❧♦ ❞❡ ❝♦♥✜❛♥ç❛ ✭95%✮ ❞♦s t❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ❞♦s ♣r♦t♦❝♦❧♦s ✭❡♠ ♠✐❧✐ss❡❣✉♥✲ ❞♦s✮✱ s❡♠ ♣ré✲❝♦♠♣✉t❛çã♦✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
❇✳✷ ■♥t❡r✈❛❧♦ ❞❡ ❝♦♥✜❛♥ç❛ ✭95%✮ ❞♦s t❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ❞♦s ♣r♦t♦❝♦❧♦s ✭❡♠ ♠✐❧✐ss❡❣✉♥✲ ❞♦s✮✱ ❝♦♠ ♣ré✲❝♦♠♣✉t❛çã♦✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
❇✳✸ ■♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ✭95%✮ ❞♦s t❡♠♣♦s ❞❡ ❡①❡❝✉çã♦ ♣♦r ♦♣❡r❛çã♦ ✭❡♠ ♠✐❧✐ss❡❣✉♥❞♦s✮✳ ✻✷
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❝♦♥❝❡✐t♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ s✉r❣✐✉ ❛tr❛✈és ❞❛ ❜✉s❝❛ ♣♦r s♦❧✉çõ❡s ♣❛r❛ ❞♦✐s ♣r♦❜❧❡♠❛s ✐♥tr✐♥s❡❝❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✿ ♦ ❞❡ ❞✐str✐❜✉✐r ✉♠❛ ❝❤❛✈❡ s❡❝r❡t❛ ❡ ❛✉t❡♥t✐❝❛çã♦ ❞❡ ✉s✉ár✐♦s✱ ❝♦♠ ❣❛r❛♥t✐❛ ❞❡ ✐rr❡tr❛t❛❜✐❧✐❞❛❞❡✳ ❆♠❜♦s ♦s ♣r♦❜❧❡♠❛s ❢♦r❛♠ tr❛t❛❞♦s ♣♦r ✭❉✐✣❡ ❡ ❍❡❧❧♠❛♥✱✶✾✼✻✮✱ q✉❛♥❞♦ ♥❛s❝❡✉ ✉♠ ♥♦✈♦ t✐♣♦ ❞❡ ❝r✐♣t♦❣r❛✜❛✿ ❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛✳
❊st❡ ♥♦✈♦ ♣❛r❛❞✐❣♠❛ ❢❛③ ✉s♦ ❞❡ ❞✉❛s ❝❤❛✈❡s r❡❧❛❝✐♦♥❛❞❛s ♠❛t❡♠❛t✐❝❛♠❡♥t❡✱ ❡ ♣♦r ✐ss♦ é t❛♠❜é♠ ❝❤❛♠❛❞♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛✳ ❊♥q✉❛♥t♦ ✉♠❛ ❞❛s ❝❤❛✈❡s ❞❡✈❡ s❡r ♠❛♥t✐❞❛ s♦❜ s✐❣✐❧♦ ♣❡❧♦ s❡✉ ♣r♦♣r✐❡tár✐♦✱ ❛ ♦✉tr❛ é ❞✐✈✉❧❣❛❞❛ ♣✉❜❧✐❝❛♠❡♥t❡ ♣❛r❛ q✉❡ ♣♦ss❛ s❡r ✉t✐❧✐③❛❞❛ ♣♦r q✉❡♠ ❞❡s❡❥❛ s❡ ❝♦♠✉♥✐❝❛r ❝♦♠ ✉s✉ár✐♦ ❞♦♥♦ ❞❛q✉❡❧❛ ❝❤❛✈❡✳
◆♦ ❡♥t❛♥t♦✱ ❡st❡ ♥♦✈♦ ♣❛r❛❞✐❣♠❛ tr♦✉①❡ ❝♦♥s✐❣♦ ❛❧❣✉♥s ❞❡s❛✜♦s✳ ❯♠ ♣r♦❜❧❡♠❛ ❝❡♥tr❛❧ ❞❡ss❡ ♠♦❞❡❧♦ é ♦ ❞❡ ❧❡❣✐t✐♠❛çã♦ ❞❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛✳ ❆ s♦❧✉çã♦ ❡♥❝♦♥tr❛❞❛ ♣❛r❛ ❡st❡ ♣r♦❜❧❡♠❛ ❢♦✐ ❛ ❝❡rt✐✲ ✜❝❛çã♦ ❞❛s ❝❤❛✈❡s ♣ú❜❧✐❝❛s✱ ♣❡r❛♥t❡ ✉♠❛ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛ ✐❞ô♥❡❛✱ ❛tr❛✈és ❞❛ ✐♠♣❧❛♥t❛çã♦ ❞❡ ✉♠❛ ✐♥❢r❛✲❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ✭■❈P ♦✉ P❑■ ✲ P✉❜❧✐❝ ❑❡② ■♥❢r❛str✉❝t✉r❡✮✳ ❚♦❞❛✈✐❛✱ ❡st❛ s♦❧✉çã♦ ❝r✐♦✉ ✉♠❛ sér✐❡ ❞❡ ♥♦✈❛s ❞✐✜❝✉❧❞❛❞❡s✱ ❝♦♠♦ ♦s ❝✉st♦s ♣❛r❛ ✐♠♣❧❛♥t❛çã♦ ❡ ♠❛♥✉t❡♥çã♦ ❞❛ ■❈P✱ ♠❛✐♦r ❝♦♠♣❧❡①✐❞❛❞❡ ♣❛r❛ r❡❝✉♣❡r❛r ❡ ✈❛❧✐❞❛r ❝❡rt✐✜❝❛❞♦s✱ ❛❧é♠ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ r❡✈♦❣❛çã♦ ❞♦s ❝❡rt✐✜❝❛❞♦s✳
◆❡st❡ tr❛❜❛❧❤♦ ♥♦s ❝♦♥❝❡♥tr❛♠♦s ❡♠ ❞♦✐s ♠♦❞❡❧♦s ❛❧t❡r♥❛t✐✈♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú✲ ❜❧✐❝❛ q✉❡ ♥ã♦ ❢❛③❡♠ ✉s♦ ❞❡ ❝❡rt✐✜❝❛❞♦s ❞✐❣✐t❛✐s✿ ♦ ♠♦❞❡❧♦ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡s✱ ♣r♦♣♦st♦ ♣♦r
❙❤❛♠✐r ✭✶✾✽✹✮ ❡ ♦ ♠♦❞❡❧♦ s❡♠ ❝❡rt✐✜❝❛❞♦✱ ♣r♦♣♦st♦ ♣♦r❆❧✲❘✐②❛♠✐ ❡ P❛t❡rs♦♥ ✭✷✵✵✸✮✳ ❉❡♥tr♦ ❞♦s
❝r✐♣t♦ss✐st❡♠❛s ❡①✐st❡♥t❡s ♥❡ss❡s ❞♦✐s ♠♦❞❡❧♦s✱ ❞❡st❛❝❛♠♦s ✉♠❛ ❝❧❛ss❡ ❡s♣❡❝í✜❝❛✱ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♣r♦t♦❝♦❧♦s ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡✳
✶✳✶ ❖❜❥❡t✐✈♦s
❊st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❢❛③❡r ✉♠ ❧❡✈❛♥t❛♠❡♥t♦ ❞❡ ♣r♦t♦❝♦❧♦s ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ ❝♦♠ ❛✉t❡♥t✐❝❛çã♦✱ ♥♦s ♠♦❞❡❧♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ❡ s❡♠ ❝❡rt✐✜❝❛❞♦✳ ❏✉♥t♦ ❛ ❡ss❡ ❧❡✈❛♥t❛♠❡♥t♦✱ ♦❜❥❡t✐✈❛✲s❡ ✉♠ ♠❛♣❡❛♠❡♥t♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛✳ P♦r ✜♠✱ ✐♠♣❧❡♠❡♥t❛çõ❡s ❡ ♠❡❞✐çõ❡s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❝♦♥tr✐❜✉❡♠ ❝♦♠ ✉♠ ♣❛✐♥❡❧ ❝♦♠♣❛r❛t✐✈♦ s♦❜r❡ ❡♠ q✉❡ ❝♦♥t❡①t♦ ❞❡ ❛♣❧✐❝❛çã♦ ❝❛❞❛ ♣r♦t♦❝♦❧♦ é ♠❛✐s ❛❞❡q✉❛❞♦✳
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦
◆♦ ❈❛♣ít✉❧♦ ✷ é ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❞♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛ ❡ ❛ss✐♠étr✐❝❛✱ ❛ss✐♥❛t✉r❛ ❡ ❝❡rt✐✜❝❛❞♦s ❞✐❣✐t❛✐s✳ ❖ ❈❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛ ♦s ❢✉♥❞❛♠❡♥t♦s ♠❛t❡♠át✐❝♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❝♦♥❝❡✐t♦s q✉❡ s❡rã♦ ❡①♣♦st♦s ♥♦ ❞❡❝♦rr❡r ❞♦ t❡①t♦✳ ◆♦ ❈❛♣ít✉❧♦ ✹ t❡♠♦s ✉♠❛ ✐♥tr♦❞✉çã♦ ❜ás✐❝❛ ❛♦s ♠♦❞❡❧♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ❡♠ ✐❞❡♥t✐❞❛❞❡ ❡ s❡♠ ❝❡rt✐✜❝❛❞♦✱ s✉❛s ✈❛♥t❛❣❡♥s ❡ ❞❡s✈❛♥t❛❣❡♥s✱ ❛❧é♠ ❞❡ ✉♠❛ r❡✈✐sã♦ s♦❜r❡ ♣r♦t♦❝♦❧♦s ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡ ❡ ♠♦❞❡❧♦s ❞❡ s❡❣✉r❛♥ç❛✳ ❖ ❈❛♣ít✉❧♦ ✺❞❡s❝r❡✈❡ ♦s ♣r♦t♦❝♦❧♦s s❡❧❡❝✐♦♥❛❞♦s ♣❛r❛ r❡❛❧✐③❛çã♦ ❞♦s ❡①♣❡r✐♠❡♥t♦s ❡ ♦s
✷ ■◆❚❘❖❉❯➬➹❖ ✶✳✷
❈❛♣ít✉❧♦ ✷
❋✉♥❞❛♠❡♥t♦s ❞❡ ❈r✐♣t♦❣r❛✜❛
❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❝r✐♣t♦❣r❛✜❛✱ ✐♥❞✐s♣❡♥sá✈❡✐s ♣❛r❛ ♦ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
✷✳✶ ❚❡r♠✐♥♦❧♦❣✐❛
◆♦ ❞❡❝♦rr❡r ❞❡st❡ tr❛❜❛❧❤♦ s❡rã♦ ✉t✐❧✐③❛❞♦s ✉♠❛ sér✐❡ ❞❡ t❡r♠♦s ♣r❡s❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❡s♣❡❝✐❛✲ ❧✐③❛❞❛ ❡♠ ❝r✐♣t♦❣r❛✜❛✳ ❉❡✜♥✐r❡♠♦s ❛❧❣✉♥s ❞♦s t❡r♠♦s ♠❛✐s ❡ss❡♥❝✐❛✐s ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❡st❡ ❡ ❞♦s ♣ró①✐♠♦s ❝❛♣ít✉❧♦s ❛ s❡❣✉✐r✳
• P❛rt✐❝✐♣❛♥t❡✱ ❡♥t✐❞❛❞❡ ♦✉ ✉s✉ár✐♦✿ é ❛❧❣✉é♠ ♦✉ ❛❧❣♦ ✭♣♦r ❡①❡♠♣❧♦✿ ✉♠❛ ♣❡ss♦❛✱ ✉♠
❝♦♠♣✉t❛❞♦r✱ ❡t❝✮ q✉❡ ❡♥✈✐❛✱ r❡❝❡❜❡✱ ♦✉ ♠❛♥✐♣✉❧❛ ✐♥❢♦r♠❛çã♦✳ ◗✉❛♥❞♦ r❡♣r❡s❡♥t❛r♠♦s ❞✉❛s ♣❡ss♦❛s q✉❡ ❞❡s❡❥❛♠ s❡ ❝♦♠✉♥✐❝❛r✱ ❝❤❛♠❛r❡♠♦s ❡ss❛s ❞✉❛s ❡♥t✐❞❛❞❡s ❞❡ Alice ❡ Beto✱ ♦✉
s✐♠♣❧❡s♠❡♥t❡ ❞❡ ❡♥t✐❞❛❞❡s A❡ B✳
• ❆❞✈❡rsár✐♦✱ ❛t❛❝❛♥t❡✱ ✉s✉ár✐♦ ♠❛❧✲✐♥t❡♥❝✐♦♥❛❞♦✱ ✐♥tr✉s♦ ♦✉ ❡s♣✐ã♦✿ é ✉♠❛ ❡♥t✐❞❛❞❡
q✉❡ ♥ã♦ é ♥❡♠ ♦ r❡♠❡t❡♥t❡ ♥❡♠ ♦ ❞❡st✐♥❛tár✐♦ ❞❛ ✐♥❢♦r♠❛çã♦ q✉❡ ❡stá s❡♥❞♦ tr❛♥s♠✐t✐❞❛✳ ❙❡✉ ♦❜❥❡t✐✈♦ é t❡♥t❛r ❛♥✉❧❛r ♦ s❡r✈✐ç♦ ❞❡ s❡❣✉r❛♥ç❛ ❞❡ ✐♥❢♦r♠❛çã♦ ❡st❛❜❡❧❡❝✐❞♦ ❡♥tr❡ ❞✉❛s ❡♥t✐❞❛❞❡s ❧❡❣ít✐♠❛s q✉❡ ❞❡s❡❥❛♠ s❡ ❝♦♠✉♥✐❝❛r✳ ❈❤❛♠❛r❡♠♦s ❡ss❛ ❡♥t✐❞❛❞❡ ♠❛❧✲✐♥t❡♥❝✐♦♥❛❞❛ ❞❡ Carlos✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡C✳
• ❈❛♥❛❧ ✭♦✉ ❧✐♥❤❛✮ ❞❡ ❝♦♠✉♥✐❝❛çã♦✿ ♠❡✐♦ ✭♣♦r ❡①❡♠♣❧♦✿ ❧✐♥❤❛ t❡❧❡❢ô♥✐❝❛✱ ♦♥❞❛s ❞❡ rá❞✐♦✱
■♥t❡r♥❡t✱ ▲❆◆✶✱ ❡t❝✮ ♣♦r ♦♥❞❡ tr❛❢❡❣❛♠ ❛s ✐♥❢♦r♠❛çõ❡s tr♦❝❛❞❛s ♣♦r ♣❛rt✐❝✐♣❛♥t❡s ❞❡ ✉♠❛
❝♦♠✉♥✐❝❛çã♦✳
• ❈❤❛✈❡✿ s❡q✉ê♥❝✐❛ ❞❡ sí♠❜♦❧♦s q✉❡ ❝♦♥tr♦❧❛ ❛ ♦♣❡r❛çã♦ ❞❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❝r✐♣t♦❣rá✜❝❛✳
• ❚❡①t♦ ❧❡❣í✈❡❧✿ ♠❡♥s❛❣❡♠ ♦✉ ✐♥❢♦r♠❛çã♦ q✉❡ ✉♠❛ ❡♥t✐❞❛❞❡ A ✭r❡♠❡t❡♥t❡✮ ❞❡s❡❥❛ ❡♥✈✐❛r ❛
✉♠❛ ❡♥t✐❞❛❞❡ B ✭❞❡st✐♥❛tár✐♦✮✳
• ❚❡①t♦ ❝✐❢r❛❞♦ ♦✉ t❡①t♦ ✐❧❡❣í✈❡❧✿ r❡s✉❧t❛❞♦ ❞❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❝r✐♣t♦❣rá✜❝❛ ❛♣❧✐❝❛❞❛ ❛♦
t❡①t♦ ❧❡❣í✈❡❧✱ ❞❡ ♠❛♥❡✐r❛ q✉❡ ♥ã♦ s❡ ❝♦♥s✐❣❛ t❡r ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ✐♥❢♦r♠❛çã♦ s❡♠ ♦ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ ❞❛ ❝❤❛✈❡ ❛❞❡q✉❛❞❛✳
✷✳✷ Pr♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛
P❛r❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❝♦♠✉♥✐❝❛çã♦ ❞❡ ❢♦r♠❛ s❡❣✉r❛✱ é ♣r❡❝✐s♦ ❣❛r❛♥t✐r q✉❡ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛ s❡❥❛♠ ❛t❡♥❞✐❞❛s ♣❡❧♦ s✐st❡♠❛ ❝r✐♣t♦❣rá✜❝♦ ✉t✐❧✐③❛❞♦✳ ❆ ❞❡♣❡♥❞❡r ❞♦ ♥í✈❡❧ ❞❡ s❡❣✉r❛♥ç❛ q✉❡ s❡ ❞❡s❡❥❛ ❛❧❝❛♥ç❛r ❡ ❞♦ ❝❡♥ár✐♦ ♣♦r ♦♥❞❡ ✈❛✐ tr❛❢❡❣❛r ❛ ❝♦♠✉♥✐❝❛çã♦✱ s❡ ❢❛③ ♥❡❝❡ssár✐❛ ❛ ❣❛r❛♥t✐❛ ❞❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s✿
✶❉♦ ✐♥❣❧ês ▲♦❝❛❧ ❆r❡❛ ◆❡t✇♦r❦✳
✹ ❋❯◆❉❆▼❊◆❚❖❙ ❉❊ ❈❘■P❚❖●❘❆❋■❆ ✷✳✹
• ❆✉t❡♥t✐❝✐❞❛❞❡✿ ❣❛r❛♥t✐❛ ❞❡ q✉❡ ♦s ♣❛rt✐❝✐♣❛♥t❡s ❞❡ ✉♠❛ ❝♦♠✉♥✐❝❛çã♦ sã♦ ❛✉tê♥t✐❝♦s✱ ♦✉
s❡❥❛✱ ✉♠ ✐♥tr✉s♦ ♥ã♦ ❞❡✈❡ s❡ ♣❛ss❛r ♣♦r ♦✉tr♦ ✉s✉ár✐♦✳
• ❈♦♥✜❞❡♥❝✐❛❧✐❞❛❞❡✿ ❣❛r❛♥t✐❛ ❞❡ q✉❡ t♦❞❛s ❛s ✐♥❢♦r♠❛çõ❡s tr❛❢❡❣❛❞❛s ♦✉ ❛r♠❛③❡♥❛❞❛s ❡♠ ✉♠
s✐st❡♠❛ ❞❡ ❝♦♠♣✉t❛çã♦ s❡❥❛♠ ❛❝❡ss❛❞❛s ♦✉ ♠❛♥✐♣✉❧❛❞❛s ❛♣❡♥❛s ♣♦r ✉s✉ár✐♦s ❛✉t♦r✐③❛❞♦s✳
• ■♥t❡❣r✐❞❛❞❡✿ ❣❛r❛♥t✐❛ ❞❡ q✉❡ ❛ ✐♥❢♦r♠❛çã♦ tr❛❢❡❣❛❞❛ ❞✉r❛♥t❡ ❛ ❝♦♠✉♥✐❝❛çã♦ ❝❤❡❣❛rá ❛♦ s❡✉
❞❡st✐♥♦ ❡①❛t❛♠❡♥t❡ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♣❛rt✐✉ ❞❛ ♦r✐❣❡♠✱ ✐st♦ é✱ ♥❡♥❤✉♠ ❞❛❞♦ ♣♦❞❡ s❡r ❛❞✉❧t❡r❛❞♦✳
• ■rr❡tr❛t❛❜✐❧✐❞❛❞❡ ✭♦✉ ♥ã♦ r❡♣ú❞✐♦✮✿ ❣❛r❛♥t✐❛ ❞❡ q✉❡ ♥❡♠ ♦ r❡♠❡t❡♥t❡ ♥❡♠ ♦ r❡❝❡♣t♦r ❞❛s
✐♥❢♦r♠❛çõ❡s ♣♦ss❛♠ ♥❡❣❛r✱ ♣♦st❡r✐♦r♠❡♥t❡✱ s✉❛ tr❛♥s♠✐ssã♦✱ r❡❝❡♣çã♦ ♦✉ ♣♦ss❡✳
❆❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s ♣♦❞❡♠ r❡q✉❡r❡r ♣r♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛ ❛❞✐❝✐♦♥❛✐s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ❛♥♦♥✐♠❛t♦ ❞♦s ♣❛rt✐❝✐♣❛♥t❡s ❞❛ ❝♦♠✉♥✐❝❛çã♦✱ ♦✉ ❝♦♥tr♦❧❡ ❞❡ ❛❝❡ss♦ ✭r❡str✐♥❣✐r ♦ ❛❝❡ss♦ ❞❡ r❡❝✉rs♦s à ❡♥t✐❞❛❞❡s ♣r✐✈✐❧❡❣✐❛❞❛s✮✳ ❆ ❞❡s❝r✐çã♦ ❞❡ss❛s ❡ ❞❡ ♦✉tr❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ s❡❣✉r❛♥ç❛ ✈ã♦ ❛❧é♠ ❞♦ ❡s❝♦♣♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊♠▼❡♥❡③❡s ❡t ❛❧✳ ✭✶✾✾✻✮ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ♦✉tr❛s ♣r♦♣r✐❡❞❛❞❡s ❝♦♠ ♠❛✐s ❞❡t❛❧❤❡s✳
✷✳✸ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ s❡❝r❡t❛
❆ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ s❡❝r❡t❛✱ t❛♠❜é♠ ❝❤❛♠❛❞❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✱ é ❛ ❢♦r♠❛ ♠❛✐s tr❛❞✐❝✐♦♥❛❧ ❞❡ ❝r✐♣t♦❣r❛✜❛✳ ◆❡❧❛✱ ❞✉❛s ❡♥t✐❞❛❞❡s A ❡ B ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ú♥✐❝❛ ❝❤❛✈❡ s❡❝r❡t❛ k ♣❛r❛ ❝✐❢r❛r ❡ ❞❡❝✐❢r❛r ♠❡♥s❛❣❡♥s✳ ❙✉❛ ♣r✐♥❝✐♣❛❧ ❝❛r❛❝t❡ríst✐❝❛ é ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❝❛♥❛❧ ❞❡
❝♦♠✉♥✐❝❛çã♦ t♦t❛❧♠❡♥t❡ s❡❣✉r♦✱ ♦ q✉❛❧ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ tr❛♥s♠✐t✐r ❛ ❝❤❛✈❡ q✉❡ s❡rá ✉s❛❞❛ ♥❛s ❢✉t✉r❛s ❝♦♠✉♥✐❝❛çõ❡s ❝✐❢r❛❞❛s✳
❖✉tr❛ ❝❛r❛❝t❡ríst✐❝❛ r❡❧❡✈❛♥t❡ é q✉❡ ♦ ♥ú♠❡r♦ ❞❡ ❝❤❛✈❡s ♥❡❝❡ssár✐❛s ❝r❡s❝❡ ❡♠ ♦r❞❡♠ ❞❡ ❣r❛♥❞❡③❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ q✉❛❞r❛❞♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♣❛rt✐❝✐♣❛♥t❡s ❞❛ ❝♦♠✉♥✐❝❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❝❤❛✈❡ ✉t✐❧✐③❛❞❛ ♣♦r ❝❛❞❛ ♣❛r ❞❡ ✉s✉ár✐♦s é ú♥✐❝❛✱ ❡ ♥ã♦ ♣♦❞❡ s❡r ✉s❛❞❛ ♣♦r ✉♠ t❡r❝❡✐r♦ ✉s✉ár✐♦✳ P❛r❛ ✉♠ ✉♥✐✈❡rs♦ ❞❡ n ♣❛rt✐❝✐♣❛♥t❡s✱ ♣♦❞❡♠♦s ✐♠❛❣✐♥❛r ✉♠ ❣r❛❢♦ ❝♦♠ n ✈ért✐❝❡s✱ r❡♣r❡s❡♥t❛♥❞♦ ❝❛❞❛ ♣❛rt✐❝✐♣❛♥t❡✱
❡♠ q✉❡ ❝❛❞❛ ♣❛r ❞✐st✐♥t♦ ❞❡ ✈ért✐❝❡s ❡stá ❧✐❣❛❞♦ ♣♦r ✉♠❛ ú♥✐❝❛ ❛r❡st❛✱ ❡ ❝❛❞❛ ✉♠❛ ❞❡ss❛s ❛r❡st❛s r❡♣r❡s❡♥t❛ ✉♠❛ ❝❤❛✈❡ s❡❝r❡t❛✳ ❆ss✐♠ s❡♥❞♦✱ ♦ ♥ú♠❡r♦ ❞❡ ❝❤❛✈❡s ♥❡❝❡ssár✐❛s ♣❛r❛ q✉❡n♣❛rt✐❝✐♣❛♥t❡s
♣♦ss❛♠ s❡ ❝♦♠✉♥✐❝❛r é ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s ❡♠ ✉♠ ❣r❛❢♦ ❝♦♠♣❧❡t♦ ❝♦♠n✈ért✐❝❡s✱ ♣♦rt❛♥t♦✿
◗✉❛♥t✐❞❛❞❡ ❞❡ ❝❤❛✈❡s ♥❡❝❡ssár✐❛s ❂ n(n−1)
2 ✭✷✳✶✮
➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ♥ã♦ ❡①✐st❡ ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ✐rr❡tr❛t❛❜✐❧✐❞❛❞❡ ❡♠ s✐st❡♠❛s ❞❡ ❝r✐♣t♦✲ ❣r❛✜❛ s✐♠étr✐❝❛✱ ♣♦✐s ❝♦♠♦ ♦s ❞♦✐s ❡①tr❡♠♦s ❞❛ ❝♦♠✉♥✐❝❛çã♦ ❝♦♠♣❛rt✐❧❤❛♠ ❛ ♠❡s♠❛ ❝❤❛✈❡ s❡❝r❡t❛✱ é ✐♠♣♦ssí✈❡❧ ❞✐st✐♥❣✉✐r q✉❛❧ ❞♦s ❞♦✐s ❝r✐♣t♦❣r❛❢♦✉ ❞❡t❡r♠✐♥❛❞❛ ♠❡♥s❛❣❡♠✳
❯♠❛ ❞❛s ✈❛♥t❛❣❡♥s ❞❛ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛ é q✉❡ ♣❛r❛ ✉♠ ♠❡s♠♦ ♥í✈❡❧ ❞❡ s❡❣✉r❛♥ç❛✱ s❡✉s ❛❧❣♦r✐t♠♦s sã♦✱ ❡♠ ❣❡r❛❧✱ ♠❛✐s rá♣✐❞♦s ❞♦ q✉❡ ❛❧❣♦r✐t♠♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛✳ ❉❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛ ♠❛✐s ❞✐❢✉♥❞✐❞♦s✱ ❡stã♦ ♦ ❉❊❙ ✭❉❛t❛ ❊♥❝r✐♣t✐♦♥ ❙t❛♥❞❛r❞✮ ❡ ♦ ❆❊❙ ✭❆❞✈❛♥❝❡❞ ❊♥❝r✐♣t✐♦♥ ❙t❛♥❞❛r❞✮✳
✷✳✹ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛
❆ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛✱ t❡✈❡ ♦r✐✲ ❣❡♠ ❛ ♣❛rt✐r ❞❛ ♣✉❜❧✐❝❛çã♦ ❞♦ ❛rt✐❣♦ ◆❡✇ ❉✐r❡❝t✐♦♥s ✐♥ ❈r②♣t♦❣r❛♣❤② ✭❉✐✣❡ ❡ ❍❡❧❧♠❛♥✱ ✶✾✼✻✮✳ ◆❡ss❡ ❛rt✐❣♦ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ♦ ♣r✐♠❡✐r♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝♦r❞♦ ❞❡ ❝❤❛✈❡✱ ♦♥❞❡ ❞♦✐s ♣❛rt✐❝✐♣❛♥t❡s ❞❡ ✉♠❛ ❝♦♠✉♥✐❝❛çã♦ ♣♦❞❡r✐❛♠ ✏❝♦♠❜✐♥❛r✑ ✉♠❛ ❝❤❛✈❡ s❡❝r❡t❛ ✉s❛♥❞♦ s♦♠❡♥t❡ ✉♠ ❝❛♥❛❧ ♣ú❜❧✐❝♦✳
✷✳✹ ❈❘■P❚❖●❘❆❋■❆ ❉❊ ❈❍❆❱❊ PÚ❇▲■❈❆ ✺
❝❤❛✈❡ ♣ú❜❧✐❝❛✱ ❞❡♥tr❡ ♦s q✉❛✐s ♦ ❛❧❣♦r✐t♠♦ ❊❧●❛♠❛❧✱ ♦s ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ❝✉r✈❛s ❡❧í♣t✐❝❛s✱ ❡ ♦s ❛❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ❡♠♣❛r❡❧❤❛♠❡♥t♦s ❜✐❧✐♥❡❛r❡s s♦❜r❡ ❝✉r✈❛s ❡❧í♣t✐❝❛s✳ ❊ss❡s ú❧t✐♠♦s s❡rã♦ ❡st✉❞❛❞♦s ♠❛✐s ❞❡t❛❧❤❛❞❛♠❡♥t❡ ♥♦ ❞❡❝♦rr❡r ❞❡st❡ tr❛❜❛❧❤♦✳
◆♦s ❝r✐♣t♦ss✐st❡♠❛s ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛✱ ❝❛❞❛ ♣❛rt✐❝✐♣❛♥t❡ ❞❛ ❝♦♠✉♥✐❝❛çã♦ ♣♦ss✉✐ ✉♠ ♣❛r ❞❡ ❝❤❛✈❡s
(S, P)r❡❧❛❝✐♦♥❛❞❛s ♠❛t❡♠❛t✐❝❛♠❡♥t❡✱ s❡♥❞♦Ss✉❛ ❝❤❛✈❡ ♣❛rt✐❝✉❧❛r✱ q✉❡ ❞❡✈❡ s❡r ♠❛♥t✐❞❛ s❡❝r❡t❛✱
❡ P s✉❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛✱ q✉❡ ❞❡✈❡ s❡r ❝♦♥❤❡❝✐❞❛ ♣♦r t♦❞♦s ♦s ♣❛rt✐❝✐♣❛♥t❡s ❞❛ ❝♦♠✉♥✐❝❛çã♦✳ ❉❡ss❛
❢♦r♠❛✱ é ♣♦ssí✈❡❧ s✉♣❧❛♥t❛r ♦ ♣r♦❜❧❡♠❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❤❛✈❡s ✐♥❡r❡♥t❡ à ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✱ ❤❛❥❛ ✈✐st❛ q✉❡ ♥ã♦ ❤á ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ❝❛♥❛❧ s❡❣✉r♦ ♣❛r❛ ❞✐str✐❜✉✐çã♦ ❞❛s ❝❤❛✈❡s ♣ú❜❧✐❝❛s✳
❈r✐♣t♦ss✐st❡♠❛s ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ sã♦ ❜❛s❡❛❞♦s ❡♠ ❢✉♥çõ❡s ♠❛t❡♠át✐❝❛s ❝❤❛♠❛❞❛s ❢✉♥çõ❡s ✉♥✐❞✐r❡❝✐♦♥❛✐s ❝♦♠ s❡❣r❡❞♦✷✳ ❯♠❛ ❢✉♥çã♦ ✉♥✐❞✐r❡❝✐♦♥❛❧ é ✉♠❛ ❢✉♥çã♦ ♠❛t❡♠át✐❝❛ ❝♦♠♣✉t❛❝✐✲
♦♥❛❧♠❡♥t❡ ❢á❝✐❧ ❞❡ s❡r ❝❛❧❝✉❧❛❞❛ ❡♠ ✉♠❛ ❞✐r❡çã♦✱ ♠❛s ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ❞✐❢í❝✐❧ ❞❡ s❡r ❝❛❧❝✉❧❛❞❛ ♥❛ ❞✐r❡çã♦ ♦♣♦st❛✳ ❯♠❛ ❢✉♥çã♦ ✉♥✐❞✐r❡❝✐♦♥❛❧ ❝♦♠ s❡❣r❡❞♦✱ ♣♦r s✉❛ ✈❡③✱ é ✉♠❛ ❢✉♥çã♦ ✉♥✐❞✐r❡❝✐♦✲ ♥❛❧ ❝✉❥❛ ✐♥✈❡rs❛ ♣♦❞❡ s❡r ❢❛❝✐❧♠❡♥t❡ ❝❛❧❝✉❧❛❞❛ ❞❛❞❛ ✉♠❛ ✐♥❢♦r♠❛çã♦ ✭tr❛♣❞♦♦r✮✱ ❡ ❞✐❢í❝✐❧ s❡♠ ❡ss❛ ✐♥❢♦r♠❛çã♦✳
❚❛♥t♦ ❛ ❝❤❛✈❡ ♣r✐✈❛❞❛S❝♦♠♦ ❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛P sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❝r✐♣t♦❣r❛❢❛r ❡ ❞❡❝r✐♣t♦❣r❛❢❛r
♠❡♥s❛❣❡♥s✳ ❙✉♣♦♥❤❛ q✉❡ x ❞❡♥♦t❡ ✉♠ t❡①t♦ ❧❡❣í✈❡❧ ❡ S() ❞❡♥♦t❡ ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❝❤❛✈❡ ♣r✐✈❛❞❛S✱
q✉❡ tr❛♥s❢♦r♠❛ x ❡♠ S(x) = y✳ ❙❡♥❞♦ P() ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛P✱ t❡♠✲s❡ q✉❡ P(y) = x✱
♦✉ s❡❥❛✱ ❛ ❝❤❛✈❡S é ❛ ✐♥✈❡rs❛ ❞❛ ❝❤❛✈❡ P✱ ✐✳❡✳✱ P(S(x)) =x ✭❚❡r❛❞❛✱✷✵✵✽✮✳
❯♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ❡①✐stê♥❝✐❛ ❞❛s ❝❤❛✈❡s (S, P)✱ é q✉❡ q✉❛♥❞♦ ✉t✐❧✐③❛♠♦s ❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛
P ❞❡ ✉♠❛ ❡♥t✐❞❛❞❡ ✭❞✐❣❛♠♦s ❆❧✐❝❡✮ ♣❛r❛ ❝r✐♣t♦❣r❛❢❛r ✉♠❛ ♠❡♥s❛❣❡♠✱ ❣❛r❛♥t✐♠♦s ❛ ❛✉t❡♥t✐❝✐❞❛❞❡
♥♦ ❞❡st✐♥♦✱ ♣♦✐s s♦♠❡♥t❡ ❆❧✐❝❡✱ ❝♦♠ s✉❛ ❝❤❛✈❡ ♣r✐✈❛❞❛ S✱ ♣♦❞❡ r❡❝✉♣❡r❛r ❛ ♠❡♥s❛❣❡♠ ♦r✐❣✐♥❛❧✳
❊♠ ❝♦♥tr❛♣❛rt✐❞❛✱ q✉❛♥❞♦ ❆❧✐❝❡ ✉t✐❧✐③❛ s✉❛ ❝❤❛✈❡ ♣r✐✈❛❞❛ S ♣❛r❛ ❝r✐♣t♦❣r❛❢❛r ✉♠❛ ♠❡♥s❛❣❡♠✱ é
❣❛r❛♥t✐❞❛ ❛ ❛✉t❡♥t✐❝✐❞❛❞❡ ♥❛ ♦r✐❣❡♠✱ ♣♦✐s s♦♠❡♥t❡ ❆❧✐❝❡✱ q✉❡ ♣♦ss✉✐ ❛ ❝❤❛✈❡ ♣r✐✈❛❞❛S✱ ♣♦❞❡r✐❛ t❡r
♣r♦❞✉③✐❞♦ ♦ t❡①t♦ ❝✐❢r❛❞♦✳ P❛r❛ ❣❛r❛♥t✐r ❛ ❛✉t❡♥t✐❝✐❞❛❞❡ ❡♠ ❛♠❜♦s ♦s ❡①tr❡♠♦s ❞❛ ❝♦♠✉♥✐❝❛çã♦✱ é ♥❡❝❡ssár✐♦ ❡♠♣r❡❣❛r ✉♠ ❡sq✉❡♠❛ ❝♦♠❜✐♥❛❞♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❡ ❛ss✐♥❛t✉r❛ ✭❏ú♥✐♦r✱✷✵✵✸✮✳
✷✳✹✳✶ ❆ss✐♥❛t✉r❛ ❞✐❣✐t❛❧
❆ss✐♥❛t✉r❛s ❞✐❣✐t❛✐s ❢♦r♥❡❝❡♠ ✉♠ ♠❡✐♦ ❞❡ ✈✐♥❝✉❧❛r ❛ ✐❞❡♥t✐❞❛❞❡ ❞❡ ✉♠❛ ❡♥t✐❞❛❞❡ ❛ ✉♠ ♣❡❞❛ç♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❡♥✈✐❛❞❛ ♣♦r ❡❧❛✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❛ss✐♥❛r ✐♠♣❧✐❝❛ ❡♠ tr❛♥s❢♦r♠❛r ✉♠❛ ♠❡♥s❛❣❡♠ ❡ ❛❧❣✉♠❛ ✐♥❢♦r♠❛çã♦ s❡❝r❡t❛ ❞❡ ♣♦ss❡ ❞♦ r❡♠❡t❡♥t❡ ❞❡ss❛ ♠❡♥s❛❣❡♠ ❡♠ ✉♠❛ ❡s♣é❝✐❡ ❞❡ ✏♠❛r❝❛✑ ú♥✐❝❛✱ ❞❡♥♦♠✐♥❛❞❛ ❛ss✐♥❛t✉r❛ ✭▼❡♥❡③❡s ❡t ❛❧✳✱✶✾✾✻✮✳
❆tr❛✈és ❞❡ ❛ss✐♥❛t✉r❛s ❞✐❣✐t❛✐s ♦ r❡❝❡♣t♦r ❞❛ ♠❡♥s❛❣❡♠ t❡rá ❛ ❝❡rt❡③❛ ❞❡ q✉❡ ❡❧❛ ❢♦✐ ❡♥✈✐❛❞❛ ♣♦r q✉❡♠ r❡❛❧♠❡♥t❡ ❞✐③ tê✲❧❛ ❡♥✈✐❛❞♦✱ ❣❛r❛♥t✐♥❞♦ ❛✉t❡♥t✐❝❛çã♦ ❞❛ ♦r✐❣❡♠✳ ❚❛♠❜é♠ ❤á ❣❛r❛♥t✐❛ ❞❡ q✉❡ ❛ ♠❡♥s❛❣❡♠ ♥ã♦ ❢♦✐ ❛❧t❡r❛❞❛ ♣♦r ❛❧❣✉♠❛ ❡♥t✐❞❛❞❡ ♠❛❧✲✐♥t❡♥❝✐♦♥❛❞❛ ♦✉ ❛❧❣✉♠❛ ❢❛❧❤❛ ♥❛ ❧✐♥❤❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❞✉r❛♥t❡ s✉❛ tr❛♥s♠✐ssã♦✱ ❣❛r❛♥t✐♥❞♦ ✐♥t❡❣r✐❞❛❞❡ ❞❛ ♠❡♥s❛❣❡♠✳
P❛r❛ ❞❡✜♥✐r ❣❡♥❡r✐❝❛♠❡♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❛ss✐♥❛t✉r❛ ❞✐❣✐t❛❧✱ ❝♦♥s✐❞❡r❡✿
• M♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s ♠❡♥s❛❣❡♥s q✉❡ ♣♦❞❡♠ s❡r ❛ss✐♥❛❞❛s✳
• S ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s ❝❛❞❡✐❛s ❞❡ ❝❛r❛❝t❡r❡s ❞❡ t❛♠❛♥❤♦ ✜①♦✱ ❝❤❛♠❛❞❛s ❞❡ ❛ss✐♥❛t✉r❛s✳ • SA()✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ♠❡♥s❛❣❡♥s M♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛ss✐♥❛t✉r❛sS✳
• VA()✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❞♦ ❝♦♥❥✉♥t♦M × S ♣❛r❛ ♦ ❝♦♥❥✉♥t♦ {verdadeiro, f also}✳
❙✉♣♦♥❤❛♠♦s q✉❡ ❛ ❡♥t✐❞❛❞❡A❞❡s❡❥❛ ❡♥✈✐❛r ✉♠❛ ♠❡♥s❛❣❡♠m✱ ❛ss✐♥❛❞❛ ♣♦r ❡❧❛✱ ♣❛r❛ ❛ ❡♥t✐❞❛❞❡ B✳ ❆ ❡♥t✐❞❛❞❡A ❞❡✈❡✱ ❡♥tã♦✿
✶✳ ❈❛❧❝✉❧❛r✿ s=SA(m)✳
✷✳ ❚r❛♥s♠✐t✐r ♦ ♣❛r(m, s) ♣❛r❛B✳sé ❛ ❛ss✐♥❛t✉r❛ ❞❛ ♠❡♥s❛❣❡♠ m✳
✻ ❋❯◆❉❆▼❊◆❚❖❙ ❉❊ ❈❘■P❚❖●❘❆❋■❆ ✷✳✹
✶✳ ❈❛❧❝✉❧❛r✿ u=VA(m, s)✳
✷✳ ❆❝❡✐t❛r ❛ ❛ss✐♥❛t✉r❛ ❝♦♠♦ s✐❞♦ ❝r✐❛❞❛ ♣♦r A s❡ u = verdadeiro✱ ♦✉ r❡❥❡✐t❛r ❛ ❛ss✐♥❛t✉r❛ s❡ u=f also✳
❉❡✈❡ s❡r ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ✐♥✈✐á✈❡❧ ♣❛r❛ q✉❛❧q✉❡r ♦✉tr❛ ❡♥t✐❞❛❞❡ q✉❡ ♥ã♦ s❡❥❛ A✱ ❝❛❧❝✉❧❛r
✉♠❛ ♠❡♥s❛❣❡♠ m ❡ ❛❧❣✉♠❛ ❝❛❞❡✐❛ ❞❡ ❝❛r❛❝t❡r❡s s t❛❧ q✉❡ VA(m, s) = verdadeiro✳ ◆❛ ♣rát✐❝❛✱ ❛ tr❛♥s❢♦r♠❛çã♦SA()é ✐♠♣❧❡♠❡♥t❛❞❛ ✉t✐❧✐③❛♥❞♦✲s❡ ❢✉♥çõ❡s ❞❡ ❤❛s❤✸ ❝r✐♣t♦❣rá✜❝❛s✳
➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ♦ ✉s♦ ❞❡ ❛ss✐♥❛t✉r❛s ❞✐❣✐t❛✐s só é ♣♦ssí✈❡❧ ♥❛ ❝r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛✱ ✉♠❛ ✈❡③ q✉❡ ♥❛ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛✱ ❝♦♠♦ t♦❞♦s ♦s ♣❛rt✐❝✐♣❛♥t❡s ❞❛ ❝♦♠✉♥✐❝❛çã♦ ❝♦♠♣❛rt✐❧❤❛♠ ❛ ♠❡s♠❛ ❝❤❛✈❡✱ ♥ã♦ é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r q✉❛❧ ♣❛rt✐❝✐♣❛♥t❡ ❡♥✈✐♦✉ ❛ ♠❡♥s❛❣❡♠✳
✷✳✹✳✷ ■♥❢r❛❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s
P❛r❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ❛ ❝♦♠✉♥✐❝❛çã♦ ❡♥tr❡ ❛s ❡♥t✐❞❛❞❡sA❡B✉t✐❧✐③❛♥❞♦ ❝r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛✱
é ♥❡❝❡ssár✐♦ q✉❡ ♦ r❡♠❡t❡♥t❡ ❞❛ ♠❡♥s❛❣❡♠ ❝♦♥❤❡ç❛ ❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❞❛ ❡♥t✐❞❛❞❡ ❝♦♠ ❛ q✉❛❧ ❡❧❡ ❞❡s❡❥❛ s❡ ❝♦♠✉♥✐❝❛r✳ ❊♥tr❡t❛♥t♦✱ ❝♦♠♦ ❛s ❝❤❛✈❡s ♣ú❜❧✐❝❛s sã♦ ❞✐ss❡♠✐♥❛❞❛s ❡♠ ✉♠ ❝❛♥❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♣ú❜❧✐❝♦ ✭♥ã♦ s❡❣✉r♦✮✱ t❛✐s ❝❤❛✈❡s ♣♦❞❡♠ s❡r ❢❛❧s✐✜❝❛❞❛s ♣♦r ✉♠ ✐♠♣♦st♦r✱ ✐st♦ é✱ ✉♠❛ ❡♥t✐❞❛❞❡
C ♠❛❧✲✐♥t❡♥❝✐♦♥❛❞❛✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ✉♠❛ ♦❢❡♥s✐✈❛ ❝♦♥❤❡❝✐❞❛ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ❛t❛q✉❡ ♠❛♥✲✐♥✲t❤❡✲
♠✐❞❞❧❡ ✭♦✉ ❛t❛q✉❡ ❞♦ ✏❤♦♠❡♠ ♥♦ ♠❡✐♦✑✮✳ ❊ss❡ ❢❛❧s♦ ✉s✉ár✐♦ ♣❡rs♦♥✐✜❝❛ ♦ r❡❝❡♣t♦r ♣❡r❛♥t❡ ♦ ❡♠✐ss♦r ❡ ❛✐♥❞❛ s❡ ❢❛③ ♣❛ss❛r ♣❡❧♦ ❡♠✐ss♦r ♣❡r❛♥t❡ ♦ r❡❝❡♣t♦r✳ ❉❡ss❛ ❢♦r♠❛✱ ❡❧❡ é ❝❛♣❛③ ❞❡ ❞❡❝✐❢r❛r t♦❞❛s ❛s ♠❡♥s❛❣❡♥s tr♦❝❛❞❛s ❡♥tr❡A ❡ B ✭●♦②❛✱✷✵✵✻✮✳
❉❡✈✐❞♦ à ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠ ♠❡❝❛♥✐s♠♦ ♣❛r❛ ❛✉t❡♥t✐❝❛r ❝❤❛✈❡s ♣ú❜❧✐❝❛s✱ ❝r✐♦✉✲s❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧✳ ❉❡ ♠❛♥❡✐r❛ s✐♠♣❧✐✜❝❛❞❛✱ ✉♠ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧ é ❛♥á❧♦❣♦ ❛ ✉♠ ❞♦❝✉♠❡♥t♦ r❡❣✐str❛❞♦ ❡♠ ❝❛rtór✐♦✱ q✉❡ ❝♦♠♣r♦✈❛ q✉❡ ✉♠❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛ r❡❛❧♠❡♥t❡ ♣❡rt❡♥❝❡ à ❞❡t❡r♠✐♥❛❞❛ ❡♥t✐❞❛❞❡✳ ❖ ❝❛rtór✐♦✱ ♥❡st❡ ❝❛s♦✱ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠❛ ❡♥t✐❞❛❞❡ ❥✉rí❞✐❝❛✱ q✉❡ ♣♦ss✉✐ ❢é ♣ú❜❧✐❝❛✱ ❝❤❛♠❛❞❛ ❞❡ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛ ✭❆❈✮✳
❖ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧ é ✉♠ ❞♦❝✉♠❡♥t♦ ♣❛❞r♦♥✐③❛❞♦ ✭❳✲✺✵✾✮✱ ❛ss✐♥❛❞♦ ♣♦r ✉♠❛ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✲ ✜❝❛❞♦r❛✱ ❡ ❝♦♥té♠ ♦s s❡❣✉✐♥t❡s ❝❛♠♣♦s ♣r✐♥❝✐♣❛✐s✿
• ❱❡rsã♦ ❞♦ ❝❡rt✐✜❝❛❞♦
• ◆♦♠❡ ❞❛ ✐♥st✐t✉✐çã♦
• ❈❤❛✈❡ ♣ú❜❧✐❝❛ ❞❛ ✐♥st✐t✉✐çã♦ • ◆♦♠❡ ❞❛ ❡♥t✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛
• ❉❛t❛ ❞❡ ❡♠✐ssã♦
• ❉❛t❛ ❞❡ ❡①♣✐r❛çã♦
• ◆ú♠❡r♦ ❞❡ sér✐❡
• ❆❧❣♦r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ss✐♥❛r
◆❛ ✜❣✉r❛ ✷✳✶ é ❡①✐❜✐❞♦ ✉♠ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧ r❡t✐r❛❞♦ ❞♦ sít✐♦ ❤tt♣✿✴✴✇❡❜♠❛✐❧✳✐♠❡✳✉s♣✳❜r✱ ♦❜t✐❞♦ ♥♦ ❞✐❛ ✷✽✴✵✷✴✷✵✶✷✳
✷✳✹ ❈❘■P❚❖●❘❆❋■❆ ❉❊ ❈❍❆❱❊ PÚ❇▲■❈❆ ✼
❋✐❣✉r❛ ✷✳✶✿ ❊①❡♠♣❧♦ ❞❡ ❝❡rt✐✜❝❛❞♦ ❞✐❣✐t❛❧✳
◆❛ ♣rát✐❝❛✱ ✉♠❛ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛ é ✉♠ s❡r✈✐❞♦r q✉❡ ❛❞♠✐♥✐str❛ ✉♠❛ ❜❛s❡ ❞❡ ❞❛❞♦s q✉❡ ❛ss♦❝✐❛ ✉♠❛ ❞❛❞❛ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ❛♦s ❛tr✐❜✉t♦s ❞♦ s❡✉ ♣r♦♣r✐❡tár✐♦✳ ❉❡♣❡♥❞❡♥❞♦ ❞♦ t❛♠❛♥❤♦ ❞♦ s✐st❡♠❛✱ ♣♦❞❡ s❡r ♥❡❝❡ssár✐♦ ❤❛✈❡r ♠❛✐s ❞❡ ✉♠❛ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛✱ ❢♦r♠❛♥❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞✐str✐❜✉í❞♦ ❞❡ s❡r✈✐❞♦r❡s✱ ❝❤❛♠❛❞♦ ✐♥❢r❛✲❡str✉t✉r❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ✭■❈P ♦✉ P❑■ ✲ P✉❜❧✐❝ ❑❡② ■♥❢r❛str✉❝t✉r❡✮ ✭❚❡r❛❞❛✱✷✵✵✽✮✳ ❊ss❛s ❛✉t♦r✐❞❛❞❡s ❝❡rt✐✜❝❛❞♦r❛s sã♦ ♦r❣❛♥✐③❛❞❛s ❤✐❡r❛rq✉✐❝❛♠❡♥t❡✱ ❢♦r♠❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ❝❡rt✐✜❝❛çã♦✳ ❖s ❞♦✐s ♠♦❞❡❧♦s ❞❡ ❝❡rt✐✜❝❛çã♦ ♠❛✐s ❝♦♠✉♥s sã♦ ♦s ♠♦❞❡❧♦s ❡♠ ár✈♦r❡ ❡ ❡♠ ✢♦r❡st❛ ❞❡ ár✈♦r❡s✳ ❈♦♠♦ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ✜❣✉r❛ ✷✳✷✱ ❡①✐st❡ ✉♠❛ ❛✉t♦r✐❞❛❞❡ ❝❡rt✐✜❝❛❞♦r❛ r❛✐③✱ q✉❡ ❝❡rt✐✜❝❛ ❡❧❛ ♠❡s♠❛✳ ❖✉tr❛s ❛✉t♦r✐❞❛❞❡s ❝❡rt✐✜❝❛❞♦r❛s ❡stã♦ s✉❜♦r❞✐♥❛❞❛s à ❛✉t♦r✐❞❛❞❡ r❛✐③ ❡ t❛♠❜é♠ ♣♦❞❡♠ ❝❡rt✐✜❝❛r ♦✉tr❛s ❛✉t♦r✐❞❛❞❡s ❝❡rt✐✜❝❛❞♦r❛s s✉❜♦r❞✐♥❛❞❛s ❛ ❡❧❛s✳
❋✐❣✉r❛ ✷✳✷✿ ▼♦❞❡❧♦ ❞❡ ❝❡rt✐✜❝❛çã♦ ❡♠ ár✈♦r❡✳
✽ ❋❯◆❉❆▼❊◆❚❖❙ ❉❊ ❈❘■P❚❖●❘❆❋■❆ ✷✳✹
❋✐❣✉r❛ ✷✳✸✿ ▼♦❞❡❧♦ ❞❡ ❝❡rt✐✜❝❛çã♦ ❡♠ ✢♦r❡st❛✳
❈❛♣ít✉❧♦ ✸
❊♠♣❛r❡❧❤❛♠❡♥t♦s ❇✐❧✐♥❡❛r❡s
❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ✐♥tr♦❞✉çã♦ ❛♦s ❡♠♣❛r❡❧❤❛♠❡♥t♦s ❜✐❧✐♥❡❛r❡s ❡ ♣r♦❜❧❡♠❛s ❝♦♠♣✉✲ t❛❝✐♦♥❛✐s r❡❧❛❝✐♦♥❛❞♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❞❡✜♥✐çõ❡s ❛♣r❡s❡♥t❛❞❛s ♥♦ ❆♣ê♥❞✐❝❡ ❆✳
❉❛❞♦s três ❣r✉♣♦s G1✱ G2 ❡ GT ❞❡ ♦r❞❡♠ ♣r✐♠❛ q✱ t❛❧ q✉❡ G1 ❡ G2 sã♦ ❣r✉♣♦s ❛❞✐t✐✈♦s ❡ GT é ✉♠ ❣r✉♣♦ ♠✉❧t✐♣❧✐❝❛t✐✈♦✱ ✉♠ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❜✐❧✐♥❡❛r é ❞❡✜♥✐❞♦ ❝♦♠♦ ✉♠ ♠❛♣❡❛♠❡♥t♦
e : G1 ×G2 → GT q✉❡ ♣♦ss✉✐ ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s ✭❝♦♥s✐❞❡r❡ P, R ∈ G1✱ Q, S ∈ G2 ❡
a, b∈Zq✮✿
✶✳ ❇✐❧✐♥❡❛r✐❞❛❞❡✿ ✉♠ ❡♠♣❛r❡❧❤❛♠❡♥t♦ eé ❞✐t♦ ❜✐❧✐♥❡❛r s❡ ✈❛❧❡♠ ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s✿
✭❛✮ Pr♦♣r✐❡❞❛❞❡ ❞✐str✐❜✉t✐✈❛ ❡♠ r❡❧❛çã♦ ❛♦ ♣r✐♠❡✐r♦ ❛r❣✉♠❡♥t♦
e(P +R, Q) =e(P, Q)·e(R, Q) ✭✸✳✶✮
✭❜✮ Pr♦♣r✐❡❞❛❞❡ ❞✐str✐❜✉t✐✈❛ ❡♠ r❡❧❛çã♦ ❛♦ s❡❣✉♥❞♦ ❛r❣✉♠❡♥t♦
e(P, Q+S) =e(P, Q)·e(P, S) ✭✸✳✷✮
✭❝✮ ❉❛s ♣r♦♣r✐❡❞❛❞❡s✸✳✶❡ ✸✳✷✱ t❡♠✲s❡ q✉❡
e(aP, bQ) =e(P, bQ)a=e(aP, Q)b=e(P, Q)ab ✭✸✳✸✮
❆ ❋✐❣✉r❛ ✸✳✶✐❧✉str❛ ✉♠ ♠❛♣❡❛♠❡♥t♦ ❜✐❧✐♥❡❛r✳
✷✳ ◆ã♦✲❞❡❣❡♥❡r❛çã♦✿ ✉♠ ❡♠♣❛r❡❧❤❛♠❡♥t♦ e é ❞✐t♦ ♥ã♦✲❞❡❣❡♥❡r❛❞♦ s❡ ♥ã♦ ♠❛♣❡✐❛ t♦❞♦s ♦s
♣❛r❡sG1×G2 ♣❛r❛ ♦ ❡❧❡♠❡♥t♦ ✐❞❡♥t✐❞❛❞❡ ❞❡GT✳ ❈♦♠♦G1 ❡ G2 sã♦ ❣r✉♣♦s ❞❡ ♦r❞❡♠ ♣r✐♠❛
q✱ s❡P é ✉♠ ❣❡r❛❞♦r ❞❡G1✱ ❡ Qé ✉♠ ❣❡r❛❞♦r ❞❡G2✱ ❡♥tã♦ e(P, Q) é ✉♠ ❣❡r❛❞♦r ❞❡GT✳ ✸✳ ❈♦♠♣✉t❛❜✐❧✐❞❛❞❡✿ ✉♠ ♠❛♣❡❛♠❡♥t♦ é ❝♦♠♣✉tá✈❡❧ s❡ ❡①✐st❡ ✉♠ ❛❧❣♦r✐t♠♦ ❡✜❝✐❡♥t❡ ✭✐✳❡✳✱ ❞❡
t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧✮✱ ♣❛r❛ ❝❛❧❝✉❧❛r e(P, Q)✱ ♣❛r❛ t♦❞♦ P ∈G1 ❡Q∈G2✳
