❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛
■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❯♠ ❋r❛♠❡✇♦r❦ ♣❛r❛ Pr♦❝❡ss❛♠❡♥t♦ P❛r❛❧❡❧♦ ❞❡
❆❧❣♦r✐t♠♦s ❞❡ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ❱í❞❡♦s
P❡❞r♦ ●❛r❝✐❛ ❋r❡✐t❛s
❉♦❝✉♠❡♥t❛çã♦ ❛♣r❡s❡♥t❛❞♦ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❛ ♦ ❡①❛♠❡ ❞❡ q✉❛❧✐✜❝❛çã♦ ✿ ▼❡str❛❞♦ ❡♠ ■♥❢♦r♠át✐❝❛
❖r✐❡♥t❛❞♦r❛
Pr♦❢✳❛ ❉r✳❛ ▼②❧❡♥❡ ❈❤r✐st✐♥❡ ◗✉❡✐r♦③ ❞❡ ❋❛r✐❛s
❈♦♦r✐❡♥t❛❞♦r❛
Pr♦❢✳❛ ❉r✳❛ ❆❧❡té✐❛ P❛trí❝✐❛ ❋❛✈❛❝❤♦ ❞❡ ❆r❛ú❥♦
❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛ ✖ ❯♥❇ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ▼❡str❛❞♦ ❡♠ ■♥❢♦r♠át✐❝❛
❈♦♦r❞❡♥❛❞♦r✿ Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ P❡③③✉♦❧ ❏❛❝♦❜✐
❇❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛ ❝♦♠♣♦st❛ ♣♦r✿
Pr♦❢✳❛ ❉r✳❛ ▼②❧❡♥❡ ❈❤r✐st✐♥❡ ◗✉❡✐r♦③ ❞❡ ❋❛r✐❛s ✭❖r✐❡♥t❛❞♦r❛✮ ✖ ❊◆❊✴❯♥❇
Pr♦❢✳ ❉r✳ ❊❞✉❛r❞♦ ❆✳ ❇✳ ❞❛ ❙✐❧✈❛ ✖ ❉❊▲✴P❖▲■✴❯❋❘❏ Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ P❡③③✉♦❧ ❏❛❝♦❜✐ ✖ ❈■❈✴❯♥❇
❈■P ✖ ❈❛t❛❧♦❣❛çã♦ ■♥t❡r♥❛❝✐♦♥❛❧ ♥❛ P✉❜❧✐❝❛çã♦
❋r❡✐t❛s✱ P❡❞r♦ ●❛r❝✐❛✳
❯♠ ❋r❛♠❡✇♦r❦ ♣❛r❛ Pr♦❝❡ss❛♠❡♥t♦ P❛r❛❧❡❧♦ ❞❡ ❆❧❣♦r✐t♠♦s ❞❡ ❆✉✲ ♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ❱í❞❡♦s ✴ P❡❞r♦ ●❛r❝✐❛ ❋r❡✐t❛s✳ ❇r❛sí❧✐❛ ✿ ❯♥❇✱ ✷✵✶✸✳
✶✹✹ ♣✳ ✿ ✐❧✳ ❀ ✷✾✱✺ ❝♠✳
❊①❛♠❡ ❞❡ ◗✉❛❧✐✜❝❛çã♦ ✭▼❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛✱ ❇r❛sí❧✐❛✱ ✷✵✶✸✳
✶✳ ❆✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦✱ ✷✳ ❙✉♣❡r✲r❡s♦❧✉çã♦✱ ✸✳ ❈♦♠♣✉t❛çã♦ P❛r❛❧❡❧❛
❈❉❯ ✶✶✴✵✵✻✽✹✵✽
❊♥❞❡r❡ç♦✿ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛
❈❛♠♣✉s ❯♥✐✈❡rs✐tár✐♦ ❉❛r❝② ❘✐❜❡✐r♦ ✖ ❆s❛ ◆♦rt❡ ❈❊P ✼✵✾✶✵✲✾✵✵
❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛
■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❯♠ ❋r❛♠❡✇♦r❦ ♣❛r❛ Pr♦❝❡ss❛♠❡♥t♦ P❛r❛❧❡❧♦ ❞❡
❆❧❣♦r✐t♠♦s ❞❡ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ❱í❞❡♦s
P❡❞r♦ ●❛r❝✐❛ ❋r❡✐t❛s
❉♦❝✉♠❡♥t❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❝♦♥❝❧✉sã♦ ❞♦ ▼❡str❛❞♦ ❡♠ ■♥❢♦r♠át✐❝❛
Pr♦❢✳❛ ❉r✳❛ ▼②❧❡♥❡ ❈❤r✐st✐♥❡ ◗✉❡✐r♦③ ❞❡ ❋❛r✐❛s ✭❖r✐❡♥t❛❞♦r❛✮ ❊◆❊✴❯♥❇
Pr♦❢✳ ❉r✳ ❊❞✉❛r❞♦ ❆✳ ❇✳ ❞❛ ❙✐❧✈❛ Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ P❡③③✉♦❧ ❏❛❝♦❜✐
❉❊▲✴P❖▲■✴❯❋❘❏ ❈■❈✴❯♥❇
Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ P❡③③✉♦❧ ❏❛❝♦❜✐ ❈♦♦r❞❡♥❛❞♦r ❞♦ ▼❡str❛❞♦ ❡♠ ■♥❢♦r♠át✐❝❛
❘❡s✉♠♦
❖ ❛✉♠❡♥t♦ ❞✐♠❡♥s✐♦♥❛❧ ❞❡ s✐♥❛✐s ✈✐s✉❛✐s ❝♦♥s✐st❡ ♥❛ ❛❧t❡r❛çã♦ ❞♦ t❛♠❛♥❤♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ♦✉ ❞❡ ✉♠ ✈í❞❡♦ ♣❛r❛ ❞✐♠❡♥sõ❡s ❡s♣❛❝✐❛✐s ♠❛✐♦r❡s✱ ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❞❡ ♣r♦❝❡ss❛✲ ♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ s✐♥❛✐s✳ ●❡r❛❧♠❡♥t❡✱ ❡ss❡ ❛✉♠❡♥t♦ é ❢❡✐t♦ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✳ ❈♦♥t✉❞♦✱ ❡ss❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣r♦❞✉③❡♠ ❞✐st♦rçõ❡s ♥❛s ✐♠❛❣❡♥s ❛✉✲ ♠❡♥t❛❞❛s✳ ❚❛✐s ❞✐st♦rçõ❡s ♦❝♦rr❡♠ ♣♦rq✉❡ ❛ ✐♠❛❣❡♠ ❛✉♠❡♥t❛❞❛ ♣♦ss✉✐ ❛♣❡♥❛s ❛s ❛♠♦str❛s ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧✱ ❞❡ ❞✐♠❡♥sõ❡s ♠❡♥♦r❡s✱ q✉❡ sã♦ ✐♥s✉✜❝✐❡♥t❡s ♣❛r❛ r❡❝♦♥str✉çã♦ ❡①❛t❛ ❞♦ s✐♥❛❧✱ ♦ q✉❡ ❣❡r❛ ❡❢❡✐t♦s ❞❡ ❛❧✐❛s✐♥❣✳ ❆ss✐♠ s❡♥❞♦✱ ❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ❛♣❡♥❛s ❡st✐♠❛♠ ♦s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s ❞♦ s✐♥❛❧✱ ♦ q✉❡ ♠✉✐t❛s ✈❡③❡s ♣r♦❞✉③ r❡s✉❧t❛❞♦s ✐♥s❛t✐s❢❛tór✐♦s ♣❛r❛ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s✱ ♥❡❝❡ss✐t❛♥❞♦ ❞❡ ♦✉tr❛s té❝♥✐❝❛s ♣❛r❛ r❡❝♦♥st✐t✉✐r ♦s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s ❝♦♠ ♠❛✐♦r ♣r❡❝✐sã♦✳
P❛r❛ ♠❡❧❤♦r❛r ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❡st✐♠❛❞❛ ❝♦♠ r❡❧❛çã♦ à ✐♠❛❣❡♠ ♦r✐❣✐✲ ♥❛❧✱ ❡①✐st❡♠ té❝♥✐❝❛s q✉❡ r❡❝♦♥str♦❡♠ ♦s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s✳ ❊ss❛s té❝♥✐❝❛s sã♦ ❝❤❛♠❛❞❛s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✳ ❊❧❛s ❝♦♥s✐st❡♠ ❡♠ ❛✉♠❡♥t❛r ❛ r❡s♦❧✉çã♦ ✉t✐❧✐③❛♥❞♦✱ ❣❡r❛❧✲ ♠❡♥t❡✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ♦✉tr❛s ✐♠❛❣❡♥s ❡♠ ❜❛✐①❛ ♦✉ ❛❧t❛✲r❡s♦❧✉çã♦ ♣❛r❛ ❡st✐♠❛r ❛ ✐♥❢♦r♠❛çã♦ ❢❛❧t❛♥t❡ ♥❛ ✐♠❛❣❡♠ q✉❡ s❡ ❞❡s❡❥❛ ❛♠♣❧✐❛r✳
❙✉♣❡r✲r❡s♦❧✉çã♦ é ✉♠ ♣r♦❝❡ss♦ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ✐♥t❡♥s♦✱ ♦♥❞❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ❛❧❣♦r✐t♠♦s sã♦✱ ❣❡r❛❧♠❡♥t❡✱ ❞❡ ♦r❞❡♠ ❡①♣♦♥❡♥❝✐❛❧ ♥♦ t❡♠♣♦ ❡♠ ❢✉♥çã♦ ❞♦ ❜❧♦❝♦ ♦✉ ❞♦ ❢❛✲ t♦r ❞❡ ❛♠♣❧✐❛çã♦✳ P♦rt❛♥t♦✱ q✉❛♥❞♦ ❡ss❛s té❝♥✐❝❛s sã♦ ❛♣❧✐❝❛❞❛s ♣❛r❛ ✈í❞❡♦s✱ é ♥❡❝❡ssár✐♦ q✉❡ ♦ ❛❧❣♦r✐t♠♦ s❡❥❛ ❡①tr❡♠❛♠❡♥t❡ rá♣✐❞♦✳ ❖ ♣r♦❜❧❡♠❛ é q✉❡ ♦s ❛❧❣♦r✐t♠♦s ♠❛✐s ❝♦♠✲ ♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ❡✜❝✐❡♥t❡s✱ ♥❡♠ s❡♠♣r❡ sã♦ ❛q✉❡❧❡s q✉❡ ♣r♦❞✉③❡♠ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ✈✐s✉❛✐s✳
❙❡♥❞♦ ❛ss✐♠✱ ❡st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠ ❢r❛♠❡✇♦r❦ ♣❛r❛ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ ❛tr❛✈és ❞❡ ❡str❛té❣✐❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ s❡❧❡t✐✈♦ ❡ ♣❛r❛❧❡❧♦✳ P❛r❛ ✐ss♦✱ ♥❡st❛ ❞✐ss❡rt❛çã♦ sã♦ ❡①❛♠✐♥❛❞❛s ❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦s r❡s✉❧t❛❞♦s ♣r♦❞✉③✐❞♦s ♣❡❧♦s ❛❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ ❡ ♦s r❡s✉❧t❛❞♦s ♣r♦❞✉③✐❞♦s ✉t✐❧✐③❛♥❞♦✲s❡ té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✳ ❈♦♠ ❡ss❛s ♣r♦♣r✐❡❞❛❞❡s✱ é ❡♥❝♦♥tr❛❞♦ ✉♠ ❝r✐tér✐♦ ♣❛r❛ ❝❧❛ss✐✜❝❛r ❛s r❡❣✐õ❡s ❡♠ q✉❡ ♦s r❡s✉❧t❛❞♦s ♣r♦❞✉③✐❞♦s s❡❥❛♠ ✈✐s✉❛❧♠❡♥t❡ ❡q✉✐✈❛❧❡♥t❡s✱ ♥ã♦ ✐♠♣♦rt❛♥❞♦ ♦ ♠ét♦❞♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛♠♣❧✐❛çã♦✳ ◆❡ss❛s r❡❣✐õ❡s ❞❡ ❡q✉✐✈❛❧ê♥❝✐❛ ✉t✐❧✐③❛✲s❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦✱ q✉❡ é ♠✉✐t♦ ♠❛✐s ✈❡❧♦③ ❞♦ q✉❡ ♦s ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ❝♦♠♣❧❡①♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✳ ❆ss✐♠✱ ❝♦♥s❡❣✉❡✲s❡ r❡❞✉③✐r ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ s❡♠ ♣r❡❥✉❞✐❝❛r ❛ q✉❛❧✐❞❛❞❡ ✈✐s✉❛❧ ❞♦ ✈í❞❡♦ ❛♠♣❧✐❛❞♦✳
❆❧é♠ ❞❡ss❛ ❛❜♦r❞❛❣❡♠✱ ❡st❡ tr❛❜❛❧❤♦ t❛♠❜é♠ ♣r♦♣õ❡ ✉♠❛ ❡str❛té❣✐❛ ❞❡ ❞✐✈✐sã♦ ❞❡ ❞❛❞♦s ❡♥tr❡ ❞✐❢❡r❡♥t❡s t❛r❡❢❛s ♣❛r❛ q✉❡ ❛ ♦♣❡r❛çã♦ ❞❡ ❛✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦ s❡❥❛ r❡❛❧✐③❛❞❛
❞❡ ❢♦r♠❛ ♣❛r❛❧❡❧❛✳ ❯♠ r❡s✉❧t❛❞♦ ✐♥t❡r❡ss❛♥t❡ ❞♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ é q✉❡ ❡❧❡ ❞❡s❛❝♦♣❧❛ ❛ ❛❜str❛çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛ ❞❛ ❢✉♥çã♦ ❞❡ ❛✉♠❡♥t♦ ❞✐♠❡♥s✐♦♥❛❧✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ ♣♦❞❡♠ ❡①♣❧♦r❛r ♦s r❡❝✉rs♦s ❞♦ ❢r❛♠❡✇♦r❦ s❡♠ q✉❡ ♣❛r❛ ✐ss♦ s❡✉s ❛❧❣♦r✐t♠♦s ♣r❡❝✐s❡♠ s❡r ♠♦❞✐✜❝❛❞♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ♣❛r❛❧❡❧✐s♠♦✳ ■ss♦ t♦r♥❛ ♦ ❢r❛♠❡✇♦r❦ ♣♦rtá✈❡❧✱ ❡s❝❛❧á✈❡❧ ❡ r❡✉sá✈❡❧ ♣♦r ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❆✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦✱ ❙✉♣❡r✲r❡s♦❧✉çã♦✱ ❈♦♠♣✉t❛çã♦ P❛r❛❧❡❧❛
❆❜str❛❝t
❚❤❡ ♠❛❣♥✐✜❝❛t✐♦♥ ♦❢ ✈✐s✉❛❧ s✐❣♥❛❧s ❝♦♥s✐sts ♦❢ ❝❤❛♥❣✐♥❣ t❤❡ s✐③❡ ♦❢ ❛♥ ✐♠❛❣❡ ♦r ❛ ✈✐❞❡♦ t♦ ❧❛r❣❡r s♣❛t✐❛❧ ❞✐♠❡♥s✐♦♥s✱ ✉s✐♥❣ ❞✐❣✐t❛❧ s✐❣♥❛❧ ♣r♦❝❡ss✐♥❣ t❡❝❤♥✐q✉❡s✳ ❯s✉❛❧❧②✱ t❤✐s ♠❛❣✲ ♥✐✜❝❛t✐♦♥ ✐s ❞♦♥❡ ✉s✐♥❣ ♥✉♠❡r✐❝❛❧ ✐♥t❡r♣♦❧❛t✐♦♥ ♠❡t❤♦❞s✳ ❍♦✇❡✈❡r✱ t❤❡s❡ ✐♥t❡r♣♦❧❛t✐♦♥ ♠❡t❤♦❞s t❡♥❞ t♦ ♣r♦❞✉❝❡ s♦♠❡ ❞✐st♦rt✐♦♥s ✐♥ t❤❡ ✐♥❝r❡❛s❡❞ ✐♠❛❣❡s✳ ❙✉❝❤ ❞✐st♦rt✐♦♥s ♦❝✲ ❝♦✉rs ❜❡❝❛✉s❡ t❤❡ ✐♥t❡r♣♦❧❛t❡❞ ✐♠❛❣❡ ✐s r❡❝♦♥str✉❝t❡❞ ✉s✐♥❣ ♦♥❧② t❤❡ ♦r✐❣✐♥❛❧ ✐♠❛❣❡ s❛♠♣❧❡s✱ ✇❤✐❝❤ ❛r❡ ✐♥s✉✣❝✐❡♥ts ❢♦r t❤❡ ❛❝❝✉r❛t❡ s✐❣♥❛❧ r❡❝♦♥str✉❝t✐♦♥✱ ❣❡♥❡r❛t✐♥❣ ❛❧✐❛s✐♥❣ ❡✛❡❝ts✳ ❚❤❡s❡ ✐♥t❡r♣♦❧❛t✐♦♥ t❡❝❤♥✐q✉❡s ♦♥❧② ❛♣♣r♦①✐♠❛t❡ t❤❡ ♥♦♥✲s❛♠♣❧❡❞ s✐❣♥❛❧ ❝♦❡✣❝✐❡♥ts✱ ♣r♦✲ ❞✉❝✐♥❣ ✉♥s❛t✐s❢❛❝t♦r② r❡s✉❧ts ❢♦r ♠❛♥② ❛♣♣❧✐❝❛t✐♦♥s✳ ❚❤✉s✱ ❢♦r t❤❡s❡ ❛♣♣❧✐❝❛t✐♦♥s✱ ♦t❤❡rs t❡❝❤♥✐q✉❡s t♦ ❡st✐♠❛t❡ t❤❡ ♥♦♥✲s❛♠♣❧❡❞ ❝♦❡✣❝✐❡♥ts ❛r❡ ♥❡❡❞❡❞✳
❚♦ ✐♠♣r♦✈❡ t❤❡ ❡st✐♠❛t✐♦♥ ❛❝❝✉r❛❝② ♦❢ ❛♥ ✐♠❛❣❡ ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ♦r✐❣✐♥❛❧✱ t❤❡ s✉♣❡r✲ r❡s♦❧✉t✐♦♥ t❡❝❤♥✐q✉❡s ❛r❡ ✉s❡❞ t♦ r❡❝♦♥str✉❝t t❤❡ ♥♦♥✲s❛♠♣❧❡❞ ❝♦❡✣❝✐❡♥ts✳ ●❡♥❡r❛❧❧②✱ t❤❡s❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ t❡❝❤♥✐q✉❡s ❡♥❤❛♥❝❡ t❤❡ ✐♥❝r❡❛s❡❞ ✐♠❛❣❡ ✉s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ♦❢ ♦t❤❡r ✐♠❛❣❡s t♦ ❡st✐♠❛t❡ t❤❡ ♠✐ss✐♥❣ ✐♥❢♦r♠❛t✐♦♥✳
❙✉♣❡r✲r❡s♦❧✉t✐♦♥ ✐s ❛ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ✐♥t❡♥s✐✈❡ ♣r♦❝❡ss✱ ✇❤❡r❡ t❤❡ ❛❧❣♦r✐t❤♠s ❝♦♠✲ ♣❧❡①✐t② ❛r❡✱ ❣❡♥❡r❛❧❧②✱ ❡①♣♦♥❡♥t✐❛❧ ✐♥ t✐♠❡ ❛s ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ❜❧♦❝❦ s✐③❡ ♦r ♠❛❣♥✐✜❝❛t✐♦♥ ❢❛❝t♦r✳ ❚❤❡r❡❢♦r❡✱ ✇❤❡♥ t❤❡s❡ t❡❝❤♥✐q✉❡s ❛r❡ ❛♣♣❧✐❡❞ ❢♦r ✈✐❞❡♦s✱ ✐t ✐s r❡q✉✐r❡❞ t❤❛t t❤❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠ ❜❡ ❡①tr❡♠❡❧② ❢❛st✳ ❍♦✇❡✈❡r✱ ♠♦r❡ ❝♦♠♣✉t❛t✐♦♥❛❧❧② ❡✣❝✐❡♥t ❛❧❣♦r✐t❤♠s ❛r❡ ♥♦t ❛❧✇❛②s t❤♦s❡ t❤❛t ♣r♦❞✉❝❡ t❤❡ ❜❡st ✈✐s✉❛❧ r❡s✉❧ts✳
❚❤❡r❡❢♦r❡✱ t❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛ ❢r❛♠❡✇♦r❦ t♦ ✐♠♣r♦✈❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ✈❛r✐♦✉s s✉♣❡r✲ r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠s ✉s✐♥❣ s❡❧❡❝t✐✈❡ ♣r♦❝❡ss✐♥❣ ❛♥❞ ♣❛r❛❧❧❡❧ ♣r♦❝❡ss✐♥❣ str❛t❡❣✐❡s✳ ❚❤✉s✱ t❤✐s ❞✐ss❡rt❛t✐♦♥ ❡①❛♠✐♥❡s t❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ r❡s✉❧ts ♣r♦❞✉❝❡❞ ❜② t❤❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠s ❛♥❞ t❤❡ r❡s✉❧ts ♣r♦❞✉❝❡❞ ❜② ✉s✐♥❣ ✐♥t❡r♣♦❧❛t✐♦♥ t❡❝❤♥✐q✉❡s✳ ❋r♦♠ t❤❡s❡ ♣r♦♣❡r✲ t✐❡s✱ ✐s ❛❝❤✐❡✈❡❞ ❛ ❝r✐t❡r✐♦♥ t♦ ❝❧❛ss✐❢② r❡❣✐♦♥s ✇❤❡r❡✐♥ t❤❡ r❡s✉❧ts ♣r♦❞✉❝❡❞ ❛r❡ ❡q✉✐✈❛❧❡♥t ✭✉s✐♥❣ ❜♦t❤ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ♦r ✐♥t❡r♣♦❧❛t✐♦♥✮✳ ■♥ t❤❡s❡ r❡❣✐♦♥s ♦❢ ❡q✉✐✈❛❧❡♥❝❡✱ t❤❡ ✐♥✲ t❡r♣♦❧❛t✐♦♥ ❛❧❣♦r✐t❤♠s ❛r❡ ✉s❡❞ t♦ ✐♥❝r❡❛s❡ t❤❡ ❞✐♠❡♥s✐♦♥s✳ ■♥ t❤❡ ❛♥♦t❤❡rs r❡❣✐♦♥s✱ t❤❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠s ❛r❡ ✉s❡❞✳ ❆s ✐♥t❡r♣♦❧❛t✐♦♥ ❛❧❣♦r✐t❤♠s ❛r❡ ❢❛st❡r t❤❛♥ t❤❡ ❝♦♠✲ ♣✉t❛t✐♦♥❛❧❧② ❝♦♠♣❧❡① s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠s✱ t❤❡ ✐❞❡❛ ✐s ❞❡❝r❡❛s❡ t❤❡ ♣r♦❝❡ss✐♥❣ t✐♠❡ ✇✐t❤♦✉t ❛✛❡❝t✐♥❣ t❤❡ ✈✐s✉❛❧ q✉❛❧✐t② ♦❢ ❛♠♣❧✐✜❡❞ ✈✐❞❡♦✳
❇❡s✐❞❡s t❤✐s ❛♣♣r♦❛❝❤✱ t❤✐s ♣❛♣❡r ❛❧s♦ ♣r♦♣♦s❡s ❛ str❛t❡❣② t♦ ❞✐✈✐❞❡ t❤❡ ❞❛t❛ ❛♠♦♥❣ ✈❛r✐♦✉s ♣r♦❝❡ss❡s t♦ ♣❡r❢♦r♠ t❤❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ♦♣❡r❛t✐♦♥ ✐♥ ♣❛r❛❧❧❡❧✳ ❆♥ ✐♥t❡r❡st✐♥❣ r❡✲ s✉❧t ♦❢ t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧ ✐s t❤❡ ❞❡❝♦✉♣❧✐♥❣ ♦❢ t❤❡ s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ ♣❛r❛❧❧❡❧ ♣r♦❝❡ss✐♥❣ str❛t❡❣②✳ ■♥ ♦t❤❡r ✇♦r❞s✱ ❞✐✛❡r❡♥t s✉♣❡r✲r❡s♦❧✉t✐♦♥ ❛❧❣♦r✐t❤♠s ❝❛♥ ❡①✲ ♣❧♦r❡ t❤❡ ❢❡❛t✉r❡s ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❢r❛♠❡✇♦r❦ ✇✐t❤♦✉t ❛❧❣♦r✐t❤♠✐❝ ♠♦❞✐✜❝❛t✐♦♥s t♦ ❛❝❤✐❡✈❡
t❤❡ ♣❛r❛❧❧❡❧✐s♠✳ ❚❤✉s✱ t❤❡ ❢r❛♠❡✇♦r❦ ✐s ♣♦rt❛❜❧❡✱ s❝❛❧❛❜❧❡ ❛♥❞ ❝❛♥ ❜❡ r❡✉s❛❜❧❡ ❜② ❞✐✛❡r❡♥t s✉♣❡r✲r❡s♦❧✉t✐♦♥ ♠❡t❤♦❞s✳
❑❡②✇♦r❞s✿ ■♥❝r❡❛s❡❞ r❡s♦❧✉t✐♦♥✱ ❙✉♣❡r✲r❡s♦❧✉t✐♦♥✱ P❛r❛❧❧❡❧ ❈♦♠♣✉t✐♥❣
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦ ✹
✷✳✶ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ■♠❛❣❡♥s ❡ ❱í❞❡♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✷ Pr♦❝❡ss❛♠❡♥t♦ ❙✐♠♣❧✐✜❝❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✷✳✶ ❙✐♠♣❧✐✜❝❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡♠ ◆í✈❡❧ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✷✳✷ ❙✐♠♣❧✐✜❝❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡♠ ◆í✈❡❧ ❞❡ ■♥str✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✸ ❈♦♠♣✉t❛çã♦ P❛r❛❧❡❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸✳✶ ❆rq✉✐t❡t✉r❛s P❛r❛❧❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✷✳✸✳✷ Pr♦❝❡ss❛❞♦r❡s ❞❡ Pr♦♣ós✐t♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✷✳✸✳✸ ■♠♣❧❡♠❡♥t❛çã♦ ♣❛r❛ ❆rq✉✐t❡t✉r❛s P❛r❛❧❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✹ P❛r❛❧❡❧✐s♠♦ ❡♠ Pr♦❝❡ss❛♠❡♥t♦ ❞❡ ❱í❞❡♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷✳✹✳✶ P❛r❛❧❡❧✐s♠♦ ❡♠ ◆í✈❡❧ ❞❡ P✐①❡❧s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✷✳✹✳✷ P❛r❛❧❡❧✐s♠♦ ❡♠ ◆í✈❡❧ ❞❡ ❈❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✷✳✹✳✸ P❛r❛❧❡❧✐s♠♦ ❡♠ ◆í✈❡❧ ❞❡ ❈♦♥tr♦❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✷✳✺ ▼étr✐❝❛s ❞❡ ❆♥á❧✐s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✷✳✺✳✶ ▼étr✐❝❛s ❞❡ ❉❡s❡♠♣❡♥❤♦ ❞❡ ❆❧❣♦r✐t♠♦s P❛r❛❧❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✷✳✺✳✷ ▼étr✐❝❛s ❞❡ ❉❡s❡♠♣❡♥❤♦ ♣❛r❛ ❙✐♠♣❧✐✜❝❛çõ❡s ❞❡ ■♠♣❧❡♠❡♥t❛çã♦ ✳ ✳ ✷✾
✷✳✺✳✸ ▼étr✐❝❛s ❖❜❥❡t✐✈❛s ❞❡ ◗✉❛❧✐❞❛❞❡ ❱✐s✉❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✷✳✻ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸ ❆❧❣♦r✐t♠♦s ❞❡ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ✸✺
✸✳✶ ❘❡❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ■♠❛❣❡♥s ❯s❛♥❞♦ ■♥t❡r♣♦❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✷ ❙✉♣❡r✲r❡s♦❧✉çã♦ ✈✐❛ ▼ét♦❞♦s ❇❛②❡s✐❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✷✳✶ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✸✳✸ ❙✉♣❡r✲r❡s♦❧✉çã♦ ✈✐❛ ❈♦❞✐✜❝❛çã♦ ❊s♣❛rs❛ ✭❙❘✈❙❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✸✳✸✳✶ ●❡r❛çã♦ ❞♦s ❉✐❝✐♦♥ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹ ❋r❛♠❡✇♦r❦ P❛r❛❧❡❧♦ ❡ ❙✐♠♣❧✐✜❝❛❞♦ ♣❛r❛ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❡♠ ❱í❞❡♦s ✻✷ ✹✳✶ ❙✐♠♣❧✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✶✳✶ ❙❡❧❡çã♦ ❞❡ ■♥❢♦r♠❛çã♦ ❱✐s✉❛❧ ❙✐❣♥✐✜❝❛♥t❡ ✭❙■❱❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✶✳✷ Pr♦❝❡ss❛♠❡♥t♦ ●✉✐❛❞♦ ♣♦r ❈♦♥t♦r♥♦ ✭P●❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✹✳✶✳✸ ❈♦❞✐✜❝❛çã♦ ❉✐❢❡r❡♥❝✐❛❧ ✭❈❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✹✳✷ Pr♦❝❡ss❛♠❡♥t♦ P❛r❛❧❡❧♦ ❞♦ ❋r❛♠❡✇♦r❦ Pr♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✹✳✷✳✶ ❊t❛♣❛✶ ✲ ❙✐♠♣❧✐✜❝❛çã♦ ❡ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✹✳✷✳✷ ❊t❛♣❛ ✷ ✲ ❉✐str✐❜✉✐çã♦ ❡ Pr♦❝❡ss❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✹✳✷✳✸ ❊t❛♣❛ ✸ ✲ ❘❡❝♦♥str✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✹✳✸ ❘❡❞✉çã♦ ❞❡ ❊❢❡✐t♦s ❞❡ ❇❧♦❝❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✹✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺ ❘❡s✉❧t❛❞♦s ❞❛s ❙✐♠✉❧❛çõ❡s ✽✼
✺✳✶ ❘❡s✉❧t❛❞♦s ❖❜t✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽
✺✳✶✳✶ ❆♥á❧✐s❡ ❞♦ ❉❡s❡♠♣❡♥❤♦ ❞❛ ❙✐♠♣❧✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
✺✳✶✳✷ ❆♥á❧✐s❡ ❞❛ ◗✉❛❧✐❞❛❞❡ ❱✐s✉❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ✺✳✶✳✸ ❆♥á❧✐s❡ ❞♦ ❉❡s❡♠♣❡♥❤♦ ❞♦ ❋r❛♠❡✇♦r❦ P❛r❛❧❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✷ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺
✻ ❈♦♥❝❧✉sõ❡s ✶✶✼
❘❡❢❡rê♥❝✐❛s ✶✷✶
❆PP❊◆❉■❈❊❙ ✶✷✾
❆ ❚r❛❜❛❧❤♦s P✉❜❧✐❝❛❞♦s ✶✷✾
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❊①❡♠♣❧♦s ❞❡ ✉s♦ ❞❡ ❞✐✈❡rs❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✿ ✭❛✮ ♦r✐❣✐♥❛❧✱ ✭❜✮ ✈✐③✲ ✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✱ ✭❝✮ ❜✐❧✐♥❡❛r ❡ ✭❞✮ ❜✐❝ú❜✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ✭❛✮ ■♠❛❣❡♠ ❛♠♣❧✐❛❞❛ ✉t✐❧✐③❛♥❞♦ ✐♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r ❡ ✭❜✮ ✐♠❛❣❡♠ ♦❜t✐❞❛
❞❛ ✜❧tr❛❣❡♠ ❞❛ ♦r✐❣✐♥❛❧ ❝♦♠ ❣❛✉ss✐❛♥♦ ♣❛ss❛✲❜❛✐①❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✸ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❡ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❞❡ ♠❡♠ór✐❛ ❝♦♠♣❛rt✐❧❤❛❞❛✳ ✳ ✳ ✶✸
✷✳✹ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❡ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❞❡ ♠❡♠ór✐❛ ❞✐str✐❜✉í❞❛✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✺ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❡ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❤í❜r✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✷✳✻ ❍✐❡r❛rq✉✐❛ ❞❛s ♦♣❡r❛çõ❡s ❡♠ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✈í❞❡♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷✳✼ P❛r❛❧❡❧✐s♠♦ ❡♠ ♥í✈❡❧ ❞❡ ♣✐①❡❧✿ ✭❛✮ ♣♦♥t♦✲❛✲♣♦♥t♦✱ ✭❜✮ ✈✐③✐♥❤❛♥ç❛ ❡ ✭❝✮ ❞❡✲ ♣❡♥❞ê♥❝✐❛ ❣❧♦❜❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✶ ❊s♣❛❧❤❛♠❡♥t♦ ❞♦s ♣✐①❡❧s ♥♦ ❛✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦✳ ✭❛✮ ❯♠ ❝♦♥❥✉♥t♦ ❞❡
♣✐①❡❧s s❡❧❡❝✐♦♥❛❞♦✱ ✭❜✮ ❊s♣❛❧❤❛♠❡♥t♦ ❞♦s ♣✐①❡❧s ❆✱ ❇✱ ❈ ❡ ❉ ♥❛ ✐♠❛❣❡♠ ❛♠♣❧✐❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷ P❛ss♦s ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦ ❞♦ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✳ ✭❛✮ ✐♠❛❣❡♠
4×4 ❛ s❡r ❛♠♣❧✐❛❞❛✱ ✭❜✮ ♣✐①❡❧s ❡s♣❛❧❤❛❞♦s ❡♠ ✉♠❛ ♠❛tr✐③ 8×8 ✭❢❛t♦r ❞❡
❛♠♣❧✐❛çã♦ ✷✮✱ ❡ ✭❝✮ ✏❡s♣❛ç♦s ❡♠ ❜r❛♥❝♦✑ ♣r❡❡♥❝❤✐❞♦s ❝♦♠ ✈❛❧♦r❡s ❞♦ ♣✐①❡❧ ♠❛✐s ♣ró①✐♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✸ ❊❢❡✐t♦s ❞♦s ♠ét♦❞♦s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ❢❛t♦r ❞❡ r❡❞✉çã♦ ❡ ❛♠✲
♣❧✐❛çã♦ ❞❡ ✹✳ ✭❛✮ ❖r✐❣✐♥❛❧✱ ✭❜✮ ❱✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✱ ✭❝✮ ❇✐❧✐♥❡❛r ❡ ✭❞✮ ❇✐❝ú❜✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✹ ●rá✜❝♦ ❞❛s ❝✉r✈❛s ❞❡ ✈❛❧♦r❡s ❞❛s ✐♥t❡♥s✐❞❛❞❡s ❞♦s ♣✐①❡❧s ✉t✐❧✐③❛♥❞♦ ♦s ♠ét♦✲
❞♦s ❞❡ ✐♥t❡r♣♦❧❛çã♦✳ ✭❛✮ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✱ ✭❜✮ ❜✐❧✐♥❡❛r ❡ ✭❝✮ ❜✐❝ú❜✐❝♦✳ ✳ ✹✵ ✸✳✺ ●r❛❞✐❡♥t❡ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❡ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ r❡s✉❧t❛❞♦ ♣♦r ✐♥t❡r♣♦❧❛çã♦
❡ ❛ ♦r✐❣✐♥❛❧ ♥♦ t❛♠❛♥❤♦ ❞❛ ❛♠♣❧✐❛çã♦✳ ✭❛✮ ●r❛❞✐❡♥t❡ ❣❛✉ss✐❛♥♦ ❞❛ ✐♠❛❣❡♠✱ ✭❜✮ ❱✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✱ ✭❝✮ ❇✐❧✐♥❡❛r ❡ ✭❞✮ ❇✐❝ú❜✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✻ ❘❡s✉❧t❛❞♦ ❞♦s ♦♣❡r❛❞♦r❡s ❞❡ r❡❞✉çã♦ ❞❛ r❡s♦❧✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✸✳✼ ❘❡s✉❧t❛❞♦ ❞♦ ♦♣❡r❛❞♦r ❞❡ ✐♥t❡r♣♦❧❛çã♦ ✭◗✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✸✳✽ ❘❡s✉❧t❛❞♦s ❞❛s ♦♣❡r❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✾ ❘❡s✉❧t❛❞♦s ❞❛s ♦♣❡r❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✶✵ ❖❜t❡♥çã♦ ❞♦ r❡t❛❧❤♦ ph
k ❛ ♣❛rt✐r ❞♦ ✈❡t♦r ❡s♣❛rs♦ qk✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✶✶ ❘❡s✉❧t❛❞♦s ❞❛s ♦♣❡r❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✶✷ ●❡r❛çã♦ ❞❡ ✉♠ r❡t❛❧❤♦ plk✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✸✳✶✸ ●❡r❛çã♦ ❞❡ ✉♠ r❡t❛❧❤♦ pˆh
k✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✶ ❙❡❧❡çã♦ ❞❡ r❡❣✐õ❡s ❞❡ ✐♥t❡r❡ss❡ ♣❛r❛ ♣r♦❝❡ss❛♠❡♥t♦ s❡❧❡t✐✈♦✳ ✭❛✮ ♦r✐❣✐♥❛❧✱ ✭❜✮
s❡❣♠❡♥t❛çã♦ ❝♦♠ ❛❧❣♦r✐t♠♦ ❞❡ ❈❛♥♥②✱ ✭❝✮ ♣❛rt✐çã♦ ❝♦♠ ❜❧♦❝♦s ❞❡ t❛♠❛♥❤♦
4×4 ❡ ✭❞✮ ♣❛rt✐çã♦ ❝♦♠ ❜❧♦❝♦s ❞❡ t❛♠❛♥❤♦ 8×8✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✹✳✷ ❉✐❛❣r❛♠❛ ❣❡r❛❧ ❞♦ ❢r❛♠❡✇♦r❦ ♣r♦♣♦st♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹✳✸ ❈♦❞✐✜❝❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞♦s q✉❛❞r♦s✿ ✭❛✮ ♣r✐♠❡✐r♦ q✉❛❞r♦ ❞❡ r❡❢❡rê♥❝✐❛✱ ✭❜✮
s❡❣✉♥❞♦ q✉❛❞r♦✱ ✭❝✮ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ♣r✐♠❡✐r♦ ❡ ♦ s❡❣✉♥❞♦ q✉❛❞r♦✳ ✳ ✳ ✳ ✳ ✻✾
✹✳✹ ❍✐st♦❣r❛♠❛s ❞♦s ♣✐①❡❧s ❡♥tr❡ ♦s q✉❛❞r♦s ❡ ❞❡ s❡✉s r❡s♣❡❝t✐✈♦s ❞✐❢❡r❡♥❝✐❛✐s✿
✭❛✮ s❡❣✉♥❞♦ q✉❛❞r♦✱ ✭❜✮ ❞✐❢❡r❡♥❝✐❛❧ ❡♥tr❡ ♦ s❡❣✉♥❞♦ ❡ ♦ ♣r✐♠❡✐r♦ q✉❛❞r♦✳ ✳ ✳ ✼✵
✹✳✺ ❇❧♦❝♦s s❡❧❡❝✐♦♥❛❞♦s ❝♦♠♦ ❞❡ ✐♥t❡r❡ss❡ ✭❡♠ ❜r❛♥❝♦✮✿ ✭❛✮ s❡❣✉♥❞♦ q✉❛❞r♦✱ ✭❜✮ ❞✐❢❡r❡♥❝✐❛❧ ❡♥tr❡ ♦ s❡❣✉♥❞♦ ❡ ♦ ♣r✐♠❡✐r♦ q✉❛❞r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✻ ❘❡s✉❧t❛❞♦ ❞♦s q✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s ❛♠♣❧✐❛❞♦s✿ ✭❛✮ ❛♠♣❧✐❛❞♦ ♣♦r ✐♥t❡r♣♦✲
❧❛çã♦✱ ✭❜✮ ❛♠♣❧✐❛❞♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✱ ✭❝✮ ❡rr♦ ❡♥tr❡ ♦ q✉❛❞r♦ ❞✐❢❡r❡♥❝✐❛❧ ♦r✐❣✐♥❛❧ ❡ ♦ ✐♥t❡r♣♦❧❛❞♦✱ ✭❞✮ ❡rr♦ ❡♥tr❡ ♦ q✉❛❞r♦ ❞✐❢❡r❡♥❝✐❛❧ ♦r✐❣✐♥❛❧ ❡ ♦ ❛✉♠❡♥t❛❞♦ ♣♦r ❙❘✱ ✭❡✮ q✉❛❞r♦ ❝♦♠♣❡♥s❛❞♦ ❝♦♠ ♦ ❞✐❢❡r❡♥❝✐❛❧ ✐♥t❡r♣♦❧❛❞♦ ❡ ✭❢✮ q✉❛❞r♦ ❝♦♠♣❡♥s❛❞♦ ❝♦♠ ♦ ❞✐❢❡r❡♥❝✐❛❧ ❛♠♣❧✐❛❞♦ ♣♦r ❙❘✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✹✳✼ ❊t❛♣❛s ❞❡ s✐♠♣❧✐✜❝❛çã♦ ❡ ❝❧❛ss✐✜❝❛çã♦ ♣r♦❝❡ss❛❞❛s ❡♠ ♣❛r❛❧❡❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✹✳✽ ❊str✉t✉r❛ ❞❡ ❡♥❞❡r❡ç❛♠❡♥t♦ ❞♦ ❜❧♦❝♦ ❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✹✳✾ ❉✐str✐❜✉✐çã♦ ❞♦s ❞❛❞♦s ❛♦ ❧♦♥❣♦ ❞♦s ♣r♦❝❡ss♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✹✳✶✵ ❊str✉t✉r❛ ❞❡ ❡♥❞❡r❡ç❛♠❡♥t♦ ❞♦ ❜❧♦❝♦ ❞❡ s❛í❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✹✳✶✶ ❉✐str✐❜✉✐çã♦ ❞♦s ❞❛❞♦s ❛♦ ❧♦♥❣♦ ❞♦s ♣r♦❝❡ss♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✹✳✶✷ ❘❡♦r❞❡♥❛♠❡♥t♦ ❞♦s ❜❧♦❝♦s ♥♦s q✉❛❞r♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
✹✳✶✸ ❘❡❝♦♥str✉çã♦ ❞♦s q✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✹✳✶✹ ❘❡❝♦♥str✉çã♦ ❞♦s q✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s ❡♠ ♣❛r❛❧❡❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✹✳✶✺ ❊①❡♠♣❧♦s ❞♦ ❡❢❡✐t♦ ❞❡ ❜❧♦❝❛❣❡♠ ❡♠ q✉❛❞r♦s ❞❡ ✈í❞❡♦✿ ✭❛✮ ❛♠♣❧✐❛❞❛ ✉t✐✲ ❧✐③❛♥❞♦ s✉♣❡r✲r❡s♦❧✉çã♦✱ ✭❜✮ ❡rr♦ ❞❛ ✐♠❛❣❡♠ ❛ ❝♦♠ r❡❧❛çã♦ ❛♦ q✉❛❞r♦ ♦r✐❣✲ ✐♥❛❧✱ ✭❝✮ ❛♠♣❧✐❛❞❛ ✉t✐❧✐③❛♥❞♦ ✐♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r ❡ ✭❞✮ ❡rr♦ ❞❛ ✐♠❛❣❡♠ ❝ ❝♦♠ r❡❧❛çã♦ ❛♦ q✉❛❞r♦ ♦r✐❣✐♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✶ ◗✉❛❞r♦s ❞♦s ✈í❞❡♦s ✉t✐❧✐③❛❞♦s✿ ❇❛s❦❡t❜❛❧❧ ✭❇❆❙✮✱ ❇✐r❞s ✭❇■❘✮✱ ❉❛♥❝✐♥❣
✭❉❆◆✮✱ ❋❧❛♠✐♥❣♦ ✭❋▲❆✮✱ ❋♦♦t❜❛❧❧ ✭❋❖❖✮✱ ❑✐ss ✭❑■❙✮ ❡ ❘✉♥♥✐♥❣ ✭❘❯◆✮✳ ✳ ✽✾
✺✳✷ ❘❡❧❛çã♦ ❞♦s ❜❧♦❝♦s s❡❧❡❝✐♦♥❛❞♦s ♣❛r❛ s❡r❡♠ ♣r♦❝❡ss❛❞♦s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ♠❛✐s ❝✉st♦s♦ ✈❡rs✉s ♦s ❜❧♦❝♦s ♥ã♦✲s❡❧❡❝✐♦♥❛❞♦s ✭s✐♠♣❧✐✜❝❛❞♦s✮✱ q✉❡ s❡rã♦ ♣r♦❝❡s✲ s❛❞♦s ♣❡❧♦ ❛❧❣♦r✐t♠♦ ♠❛✐s s✐♠♣❧❡s✳ ✭❛✮ ❈❧❛ss✐✜❝❛çã♦ ❢❡✐t❛ q✉❛❞r♦✲❛✲q✉❛❞r♦ ❡ ✭❜✮ ❝❧❛ss✐✜❝❛çã♦ ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦ q✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s ✭r❡❢❡r❡♥❝✐❛❧ é ♠❛♥t✐❞♦ ❛ ❝❛❞❛ ✺ q✉❛❞r♦s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✸ P❡r❝❡♥t❛❣❡♠ ❞♦s ❜❧♦❝♦s ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ✏♥ã♦✲s❡❧❡❝✐♦♥❛❞♦s✑✿ ✭❛✮ ❝❧❛ss✐✜✲
❝❛çã♦ ❢❡✐t❛ q✉❛❞r♦✲❛✲q✉❛❞r♦ ❡ ✭❜✮ ❝❧❛ss✐✜❝❛çã♦ ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦ q✉❛❞r♦s ❞✐❢❡r✲ ❡♥❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✺✳✹ ❇❧♦❝♦s ♣♦r q✉❛❞r♦s ❡♠ ❢✉♥çã♦ ❞♦ t❛♠❛♥❤♦ ❞♦s ❜❧♦❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✺✳✺ ❚❡♠♣♦ ❞❡ s♦❧✉çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t❛♠❛♥❤♦ ❞♦s q✉❛❞r♦s ♣r♦❝❡ss❛❞♦s q✉❛❞r♦✲
❛✲q✉❛❞r♦✿ ✭❛✮ s❡♠ s✐♠♣❧✐✜❝❛çã♦ ❡ ✭❜✮ ❝♦♠ s✐♠♣❧✐✜❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✺✳✻ ❚❡♠♣♦ ❞❡ s♦❧✉çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t❛♠❛♥❤♦ ❞♦s q✉❛❞r♦s ♣r♦❝❡ss❛❞♦s ✉t✐✲
❧✐③❛♥❞♦ q✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s✿ ✭❛✮ s❡♠ s✐♠♣❧✐✜❝❛çã♦ ❡ ✭❜✮ ❝♦♠ s✐♠♣❧✐✜❝❛çã♦✳ ✾✼
✺✳✼ ❚❡♠♣♦ ♠é❞✐♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ♣♦r ❜❧♦❝♦✿ ✭❛✮ s❡♠ s✐♠♣❧✐✜❝❛çã♦ ✭❜✮ ❝♦♠ s✐♠♣❧✐✜❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✺✳✽ ❙♣❡❡❞✉♣s ❞❛ s✐♠♣❧✐✜❝❛çã♦✳ ✭❛✮ ◗✉❛❞r♦✲❛✲q✉❛❞r♦ ✭❜✮ ◗✉❛❞r♦s ❞✐❢❡r❡♥❝✐❛✐s✳ ✳ ✾✾
✺✳✾ ❇❧♦❝♦s ❞❡ 128×128 ❛✉♠❡♥t❛❞♦s ✉t✐❧✐③❛♥❞♦ ❞✐❢❡r❡♥t❡s ❛❧❣♦r✐t♠♦s✿ ✭❛✮ ♦r✐❣✐✲
♥❛❧✱ ✭❜✮ ✐♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r✱ ✭❝✮ ❙❆❘❚❱✱ ✭❞✮ ❙❆❘▲✶ ❡ ✭❡✮ ❙❘✈❙❘✳ ✳ ✳ ✳ ✳ ✶✵✹ ✺✳✶✵ ▼étr✐❝❛s ❞♦s ❜❧♦❝♦s ❤♦♠♦❣ê♥❡♦s ❡ ❤❡t❡r♦❣ê♥❡♦s✿ ✭❛✮ P❙◆❘ ❡ ✭❜✮ ❙❙■▼✳ ✳ ✳ ✶✵✹ ✺✳✶✶ ▼étr✐❝❛s ❞♦s ✈í❞❡♦s ❛✉♠❡♥t❛❞♦s ✉t✐❧✐③❛♥❞♦ ✐♥t❡r♣♦❧❛çã♦✱ ❙❆❘❚❱✱ ❙❆❘▲✶ ❡
❙❘✈❙❘ s❡♠ s✐♠♣❧✐✜❝❛çã♦✳ ✭❛✮ P❙◆❘ ✭❜✮ ❙❙■▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✶✷ ◗✉❛❧✐❞❛❞❡ ❞♦s ✈í❞❡♦ ✉t✐❧✐③❛♥❞♦ s✐♠♣❧✐✜❝❛çã♦ ❡♠ ❢✉♥çã♦ ❞♦ t❛♠❛♥❤♦ ❞♦
❜❧♦❝♦✿ ✭❛✮ P❙◆❘ ❡ ✭❜✮ ❙❙■▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✶✸ ❱❛❧♦r❡s r❡❧❛t✐✈♦s às ♠étr✐❝❛s s❡♠ s✐♠♣❧✐✜❝❛çã♦ ❝♦♠ ✉s♦ ❞❛ s✐♠♣❧✐✜❝❛çã♦✿ ✭❛✮
P❙◆❘ ❡ ✭❜✮ ❙❙■▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✶✹ ❘❡s✉❧t❛❞♦ ✈✐s✉❛❧ ❞♦ ❛✉♠❡♥t♦ ❝♦♠ s✐♠♣❧✐✜❝❛çã♦✿ ✭❛✮ ♦r✐❣✐♥❛❧ ✭r❡❢❡rê♥❝✐❛✮✱
✭❜✮ q✉❛❞r♦ ❛✉♠❡♥t❛❞❛ ♣♦r ✐♥t❡r♣♦❧❛çã♦✱ ✭❝✮ q✉❛❞r♦ ❛✉♠❡♥t❛❞♦ ❝♦♠ s✉♣❡r✲ r❡s♦❧✉çã♦ ❡ ✭❞✮ q✉❛❞r♦ ❛✉♠❡♥t❛❞♦ ❝♦♠ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❜❧♦❝♦s ✐♥t❡r♣♦❧❛❞♦s ❡ s✉♣❡r✲r❡s♦❧✉çã♦ ✭❜❧♦❝♦s 16×16✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽
✺✳✶✺ ❘❡s✉❧t❛❞♦ ✈✐s✉❛❧ ❞♦ ❛✉♠❡♥t♦ s✐♠♣❧✐✜❝❛❞♦ ❝♦♠ ❜❧♦❝♦s ❞❡ t❛♠❛♥❤♦ ✭❛✮ 8×8✱
✭❜✮ 16×16✱ ✭❝✮ 32×32❡ ✭❞✮ 64×64✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
✺✳✶✻ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❞♦s ❛❧❣♦r✐t♠♦s ❡♠ ♣❛r❛❧❡❧♦ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♣r♦❝❡ss♦s ♣❛r❛❧❡❧♦s✿ ✭❛✮ ❙❘✈❙❘✱ ✭❜✮ ❙❆❘❚❱ ❡ ✭❝✮ ❙❆❘▲✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✶✼ ❙♣❡❡❞✉♣ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♣r♦❝❡ss♦s ♣❛r❛❧❡❧♦s✿ ✭❛✮ ❙❘✈❙❘✱ ✭❜✮ ❙❆❘❚❱
❡ ✭❝✮ ❙❆❘▲✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✶✽ ❊✜❝✐ê♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♣r♦❝❡ss♦s ♣❛r❛❧❡❧♦s✿ ✭❛✮ ❙❘✈❙❘✱ ✭❜✮
❙❆❘❚❱ ❡ ✭❝✮ ❙❆❘▲✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
❉❡❞✐❝♦ ♠❡✉ ♠❡str❛❞♦ à ♠❡♠ór✐❛ ❞♦ ♠❡str❡ ▲✉✐③ ❈❛r❧♦s ❆❧❜♦r❣❤❡tt✐✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ❝❡rt❛♠❡♥t❡ ❞❡✈♦ ❛❣r❛❞❡❝❡r às ♠✐♥❤❛s ♣r♦❢❡ss♦r❛s ❡ ♦r✐❡♥t❛❞♦r❛s✱ ❆❧❡té✐❛ P❛trí❝✐❛ ❋❛✈❛❝❤♦ ❞❡ ❆r❛ú❥♦ ❡ ▼②❧❡♥❡ ❈❤r✐st✐♥❡ ◗✉❡✐r♦③ ❞❡ ❋❛r✐❛s✱ q✉❡ s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❛♠ ❞✉r❛♥t❡ ♦ t♦❞♦ ♦ ♣❡rí♦❞♦ ❞❡ss❡ ♠❡str❛❞♦✳ ❙❡♠ ❛s ❝✉✐❞❛❞♦s❛s ❧❡✐t✉r❛s✱ ❝rít✐❝❛s ❡ s✉❣❡stõ❡s ❢❡✐t❛s ♣♦r ❡❧❛s✱ ❡✉ ❥❛♠❛✐s ❝♦♥s❡❣✉✐r✐❛ ❝♦♥❝❧✉✐r ❡st❡ tr❛❜❛❧❤♦✳ P♦✉❝❛s ❧✐♥❤❛s ❞❡ t❡①t♦ ❥❛♠❛✐s r❡✢❡t✐r✐❛♠ ❛ ❡♥♦r♠❡ ✈❛❧♦r ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ t❡♥❤♦ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❛♣♦✐♦ r❡❝❡❜✐❞♦ ❞❡❧❛s✳ ❊❧❛s s❡rã♦ ✐♥❞✉❜✐t❛✈❡❧♠❡♥t❡ ❛s ♠❛✐♦r❡s r❡❢❡rê♥❝✐❛s ♥❛ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛✳
❚❛♠❜é♠ ♥ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡❞✐❝❛r ❡♥♦r♠❡s ❛❣r❛❞❡❝✐♠❡♥t♦s ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❞❛ ❣r❛❞✉❛çã♦ ❡ ❛t✉❛❧ ❝❤❡❢❡✱ ♦ Pr♦❢✳ ❏♦sé ❋❡❧✐♣♣❡ ❇❡❛❦❧✐♥✐✳ ❙❡♠ ♦ s❡✉ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❛♠✐③❛❞❡✱ ♣r♦✈❛✈❡❧♠❡♥t❡ s❡r✐❛ ✐♥✈✐á✈❡❧ ♣❛r❛ ♠✐♠ ❝♦♥❝✐❧✐❛r ♠❡✉ ❡♠♣r❡❣♦ ❝♦♠ ♠✐♥❤❛s ❛t✐✈✐✲ ❞❛❞❡s ♥♦ ♠❡✐♦ ❛❝❛❞ê♠✐❝♦✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ■♥st✐t✉t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ❚❡❧❡❝♦♠✉♥✐❝❛çõ❡s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ●r❛♥❛❞❛✱ ❘❛❢❛❡❧ ▼♦❧✐♥❛ ❡ ❙❛❧✈❛❞♦r ❱✐❧❧❡♥❛ ▼♦r❛❧❡s✱ ♣♦r t❡r❡♠ ♠❡ ❝❡❞✐❞♦ ♦ ❝ó❞✐❣♦✲❢♦♥t❡ ❞♦s ♠ét♦❞♦s q✉❡ ✉s❡✐✱ ❡♠ ♣❛rt❡s✱ ♥❛s s✐♠✉❧❛çõ❡s ❛♣r❡s❡♥t❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❈á❧❝✉❧♦ ❈✐❡♥tí✜❝♦ ✭▲❈❈✮✱ q✉❡ s❡♠♣r❡ ♠❡ ❛✉①✐❧✐❛r❛♠ ♥♦s ♣r♦❜❧❡♠❛s ♣r♦✜ss✐♦♥❛✐s✱ ♦ q✉❡ ❝♦♥tr✐❜✉✐✉ ♠✉✐t♦ ❝♦♠ ❛ ❡❧❛❜♦r❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦ ór❣ã♦ ❞❡ ❈♦♦r❞❡♥❛çã♦ ❞❡ ❆♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ P❡ss♦❛❧ ❞❡ ◆í✈❡❧ ❙✉♣❡r✐♦r ✭❈❆P❊❙✮ ❡ ❛♦ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❈✐❡♥tí✜❝♦ ❡ ❚❡❝♥♦❧ó❣✐❝♦ ✭❈◆Pq✮ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❞✐r❡t♦ ❡ ✐♥❞✐r❡t♦✳
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❛✉♠❡♥t♦ ❞✐♠❡♥s✐♦♥❛❧ ❞❡ s✐♥❛✐s ✈✐s✉❛✐s ❝♦♥s✐st❡ ♥❛ ❛❧t❡r❛çã♦ ❞♦ t❛♠❛♥❤♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ♦✉ ❞❡ ✉♠ ✈í❞❡♦ ♣❛r❛ ❞✐♠❡♥sõ❡s ❡s♣❛❝✐❛✐s ♠❛✐♦r❡s✱ ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❞❡ ♣r♦❝❡ss❛✲ ♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ s✐♥❛✐s ❬✾✵❪✳ ●❡r❛❧♠❡♥t❡✱ ❡ss❡ ❛✉♠❡♥t♦ é ❢❡✐t♦ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✳ ❈♦♥t✉❞♦✱ ❡ss❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣r♦❞✉③❡♠ ❞✐st♦rçõ❡s ♥❛s ✐♠❛✲ ❣❡♥s ❛✉♠❡♥t❛❞❛s✳ ❚❛✐s ❞✐st♦rçõ❡s ♦❝♦rr❡♠ ♣♦rq✉❡ ❛ ✐♠❛❣❡♠ ❛✉♠❡♥t❛❞❛ ♣♦ss✉✐ ❛♣❡♥❛s ❛s ❛♠♦str❛s ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧✱ ❞❡ ❞✐♠❡♥sõ❡s ♠❡♥♦r❡s✱ q✉❡ sã♦ ✐♥s✉✜❝✐❡♥t❡s ♣❛r❛ r❡❝♦♥✲ str✉çã♦ ❡①❛t❛ ❞♦ s✐♥❛❧✱ ♦ q✉❡ ❣❡r❛ ❡❢❡✐t♦s ❞❡ ❛❧✐❛s✐♥❣ ❬✸✽❪✳ ❆ss✐♠ s❡♥❞♦✱ ❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ❛♣❡♥❛s ❡st✐♠❛♠ ♦s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s ❞♦ s✐♥❛❧✱ ♦ q✉❡ ♠✉✐t❛s ✈❡③❡s ♣r♦❞✉③ r❡s✉❧t❛❞♦s ✐♥s❛t✐s❢❛tór✐♦s ♣❛r❛ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s✱ ♥❡❝❡ss✐t❛♥❞♦ ❞❡ ♦✉tr❛s té❝♥✐❝❛s ♣❛r❛ r❡❝♦♥st✐t✉✐r ♦s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s ❝♦♠ ♠❛✐♦r ♣r❡❝✐sã♦✳
◆♦ ❝♦♥t❡①t♦ ❞♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ✐♠❛❣❡♥s✱ ✉♠❛ ❞❛s té❝♥✐❝❛s ♣❛r❛ r❡❝♦♥st✐t✉✐r ❡ss❡s ❝♦❡✜❝✐❡♥t❡s ♥ã♦✲❛♠♦str❛❞♦s sã♦ ❛s té❝♥✐❝❛s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✳ ❊ss❛s té❝♥✐❝❛s ❝♦♥s✐st❡♠ ❡♠ ❛✉♠❡♥t❛r ❛ r❡s♦❧✉çã♦ ✉t✐❧✐③❛♥❞♦✱ ❣❡r❛❧♠❡♥t❡✱ ✐♥❢♦r♠❛çõ❡s ❞❡ ♦✉tr❛s ✐♠❛❣❡♥s ❡♠ ❜❛✐①❛ ♦✉ ❛❧t❛✲r❡s♦❧✉çã♦✳ ❖ ♣r✐♠❡✐r♦ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛❞♦ ♥❡st❡ tó♣✐❝♦ ❢♦✐ ♣✉❜❧✐❝❛❞♦ ❡♠ ✶✾✽✹ ♥♦ ❛rt✐❣♦ ▼✉❧t✐❢r❛♠❡ ✐♠❛❣❡ r❡st♦r❛t✐♦♥ ❛♥❞ r❡❣✐str❛t✐♦♥ ❬✽✷❪✱ ♠❛s ♦ t❡r♠♦ ✏s✉♣❡r✲r❡s♦❧✉çã♦✑ só ❢♦✐ ✐♥❝♦r♣♦r❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛ ❡♠ ✶✾✾✵ ♣♦r ■r❛♥✐ ❡ P❡❧❡❣ ❬✹✸❪✳ ❉❡ss❛ ❢♦r♠❛✱ ❞❡✈✐❞♦ ❛♦
✐♥t❡r❡ss❡ ♥❛ ✐♥❞ústr✐❛✱ ❛♣ós ♦ ❛rt✐❣♦ ❞❡ ■r❛♥✐ ❡ P❡❧❡❣✱ ❞✐✈❡rs❛s ♦✉tr❛s ❛❜♦r❞❛❣❡♥s ❞❡ s✉♣❡r✲ r❡s♦❧✉çã♦ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞❛s✳
P❛r❛ ♦❜t❡r ✐♠❛❣❡♥s ❡♠ ❛❧t❛✲r❡s♦❧✉çã♦✱ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲ r❡s♦❧✉çã♦ sã♦ ❢♦r♠✉❧❛❞♦s ✉t✐❧✐③❛♥❞♦ ♦ ❡s♣❛ç♦ ❞❡ ❢r❡q✉ê♥❝✐❛s✳ ❊ss❡s ♠ét♦❞♦s ❜❛s❡✐❛♠✲s❡ ♥❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ tr❛♥s❢♦r♠❛❞❛ ❞❡ ❋♦✉r✐❡r ❡ ♥❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ❝♦❡✜❝✐❡♥t❡s tr❛♥s❢♦r♠❛❞♦s ❞❛s ✐♠❛❣❡♥s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❡st✐♠❛r ❛ ✐♠❛❣❡♠ ❛ s❡r ❛♠♣❧✐❛❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡q✉❛çõ❡s✳ ❆ss✐♠✱ ❞✐✈❡rs♦s ♠ét♦❞♦s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ ❡st✐♠❛r ♦s ❝♦✲ ❡✜❝✐❡♥t❡s ♥♦ ❡s♣❛ç♦ tr❛♥s❢♦r♠❛❞♦✳ ❚❡❦❛❧♣ ❡t ❛❧✳ ❬✼✾❪ ✉t✐❧✐③❛♠ ❛♥á❧✐s❡ ❞❡ ❝♦rr❡s♣♦♥❞ê♥❝✐❛ ♣❛r❛ ♠✐t✐❣❛r ♦s ❡❢❡✐t♦s ❞♦ r✉í❞♦ ♣r♦❞✉③✐❞♦ ♣❡❧❛ r❡❝♦♥str✉çã♦ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ✐♥s✉✜❝✐❡♥t❡s✳ ❯♠❛ ❛❜♦r❞❛❣❡♠ q✉❡ ✉t✐❧✐③❛ ♠í♥✐♠♦s q✉❛❞r❛❞♦s r❡❝✉rs✐✈♦s é ♣r♦♣♦st❛ ♣♦r ❑✐♠ ❡t ❛❧✳ ❬✹✾❪✳ ❆❧é♠ ❞✐ss♦✱ té❝♥✐❝❛s ❜❛s❡❛❞❛s ♥♦ t❡♦r❡♠❛ ❞❛ ❛♠♦str❛❣❡♠ ♠✉❧t✐❝❛♥❛❧ é ✉s❛❞❛ ♣♦r ❯r ❡ ●r♦ss ❬✽✸❪✳
❆❧é♠ ❞♦s s✐st❡♠❛s q✉❡ tr❛❜❛❧❤❛♠ ♥♦ ❡s♣❛ç♦ ❞❡ ❢r❡q✉ê♥❝✐❛✱ ✉♠❛ ♦✉tr❛ ❝❧❛ss❡ ❞❡ ♠ét♦❞♦s ✉t✐❧✐③❛♠ ♦ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧ ♣❛r❛ ❡st✐♠❛r ❛ ✐♥❢♦r♠❛çã♦ ♥ã♦✲❛♠♦str❛❞❛✳ P❛r❛ ✐ss♦✱ ❞✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞❛s✱ t❛✐s ❝♦♠♦ ❛ r❡❝♦♥str✉çã♦ ❞❡ ❛♠♦str❛s ♥ã♦✲✉♥✐❢♦r♠❡♠❡♥t❡ ❡s♣❛ç❛❞❛s✱ ♣r♦❥❡çã♦ ✐♥✈❡rs❛ ✭❜❛❝❦♣r♦❥❡❝t✐♦♥✮ ❬✶✵✱ ✷✵✱ ✹✺❪✱ ♠♦❞❡❧♦s ❡st♦❝ást✐❝♦s ❬✶✼✱ ✽✺✱ ✽✻❪✱ r❡❣✉❧❛r✐③❛çã♦ ❞❡ ❚✐❦❤♦♥♦✈ ❬✻✺✱ ✽✶❪✱ ❡t❝✳
❆❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ ✈♦❧t❛❞♦s ♣❛r❛ ✐♠❛❣❡♥s sã♦✱ ❣❡r❛❧♠❡♥t❡✱ ❝♦♠♣✉t❛❝✐♦♥❛❧✲ ♠❡♥t❡ ❝✉st♦s♦s✱ ✉♠❛ ✈❡③ q✉❡ ❡♥✈♦❧✈❡♠ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ♦♣❡r❛çõ❡s ❡ tr❛❜❛❧❤❛♠ ❝♦♠ ❣r❛♥❞❡ ❝❛r❣❛ ❞❡ ❞❛❞♦s✳ ❆ss✐♠✱ q✉❛♥❞♦ ❡ss❡s ❛❧❣♦r✐t♠♦s sã♦ ❛❞❛♣t❛❞♦s ♣❛r❛ ♦ ❛✉♠❡♥t♦ ❞✐✲ ♠❡♥s✐♦♥❛❧ ❞♦s q✉❛❞r♦s ❞♦s ✈í❞❡♦s✱ t❡♠✲s❡ q✉❡ ♦ ❡s❢♦rç♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ s❡ ♣r♦❝❡ss❛r ✉♠❛ ú♥✐❝❛ ✐♠❛❣❡♠ é ♠✉❧t✐♣❧✐❝❛❞♦ ♣❡❧♦ ♥ú♠❡r♦ ❞❡ q✉❛❞r♦s t♦t❛❧ ❞♦ ✈í❞❡♦✳ ❆ss✐♠ s❡♥❞♦✱ ♣❛r❛ ✉t✐❧✐③❛çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ ♣❛r❛ ✈í❞❡♦s✱ é ❞❡s❡❥á✈❡❧ q✉❡ ❤❛❥❛♠ r❡❝✉rs♦s q✉❡ ♣❡r♠✐t❛♠ r❡❞✉③✐r ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳
◆❡ss❡ ❝❡♥ár✐♦✱ ❡st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ✉♠❛ ❡str❛té❣✐❛ ♣❛r❛ r❡❞✉③✐r ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛✲ ♠❡♥t♦ ❞♦ ❛✉♠❡♥t♦ ❞✐♠❡♥s✐♦♥❛❧ ❞♦s q✉❛❞r♦s ❞❡ ✈í❞❡♦s✱ ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦
s❡❧❡t✐✈♦ q✉❡ ♣❡r♠✐t❛♠ q✉❡ ♥❡♠ t♦❞♦s ♦s ❞❛❞♦s s❡❥❛♠ ♣r♦❝❡ss❛❞♦s ♣❛r❛ ❣❡r❛r ♦ ✈í❞❡♦ ❞❡ ❛❧t❛✲r❡s♦❧✉çã♦✳ ❈♦♠❜✐♥❛❞♦ ❝♦♠ ❡ss❛s té❝♥✐❝❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ s❡❧❡t✐✈♦✱ ✉♠ ❢r❛♠❡✇♦r❦ ♣❛r❛ ❞✐str✐❜✉✐r ❡ ♣r♦❝❡ss❛r ♣❛r❛❧❡❧❛♠❡♥t❡ ♦s ❞❛❞♦s é ♣r♦♣♦st♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛✉♠❡♥t❛r s✐❣♥✐✜❝❛♥t❡♠❡♥t❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ❛✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦✳
P❛r❛ ✐ss♦✱ ♦ ❈❛♣ít✉❧♦ ✷ r❡✈✐s❛ ♦s ❝♦♥❝❡✐t♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✱ ❝♦♠♣✉t❛çã♦ ♣❛r❛❧❡❧❛ ❡ ❛♣r❡s❡♥t❛ ❛ ♥♦çã♦ ❞❡ s✐♠♣❧✐✜❝❛çã♦✳ ❊♠ ❣❡r❛❧✱ ♥❡ss❡ ❝❛♣ít✉❧♦ é ❢❡✐t❛ ✉♠❛ ❛♠♣❧❛ ❡①♣♦s✐çã♦ ❞♦s ❝♦♥❝❡✐t♦s q✉❡ s❡rã♦ ✉t✐❧✐③❛❞♦s ♥♦s ❞❡♠❛✐s ❝❛♣ít✉❧♦s ❞❡st❛ ❞✐ss❡rt❛çã♦✳
❊♠ s❡❣✉✐❞❛✱ ♥♦ ❈❛♣ít✉❧♦ ✸✱ sã♦ ❞❡s❝r✐t♦s ♦s três ❛❧❣♦r✐t♠♦s ✉s❛❞♦s ♣❛r❛ t❡st❛r ❛ ❡s✲ tr❛té❣✐❛ ♣r♦♣♦st❛ ♣❛r❛ ❞❡❝♦♠♣♦s✐çã♦ ❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞♦s ❞❛❞♦s✳ ❚♦❞♦s ♦s ❛❧❣♦r✐t♠♦s ❡s❝♦❧❤✐❞♦s ❢✉♥❝✐♦♥❛♠ ♥♦ ❞♦♠í♥✐♦ ❡s♣❛❝✐❛❧✱ s❡♥❞♦ q✉❡ ♦s ❞♦✐s ❞❡❧❡s s❡ ✉t✐❧✐③❛♠ ♠♦❞❡❧♦s ❇❛②❡s✐❛♥♦s✱ ❡ ♦ t❡r❝❡✐r♦ ❜✉s❝❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❡s♣❛rs❛ ❞❛ ✐♠❛❣❡♠ ❞❡ ❜❛✐①❛✲r❡s♦❧✉çã♦ q✉❡ ❝♦rr❡s♣♦♥❞❛ à ✉♠❛ ♣r♦❥❡çã♦ ❞❛ ✐♠❛❣❡♠ ❞❡ ❛❧t❛✲r❡s♦❧✉çã♦✳
❖ ❈❛♣ít✉❧♦ ✹ ❛♣r❡s❡♥t❛ ❛ ❡str❛té❣✐❛ ❞❡ ❞❡❝♦♠♣♦s✐çã♦✱ ❛ r❡❞✉çã♦ ❞❛ ❝❛r❣❛ ❞❡ ❞❛❞♦s ❛ s❡r ♣r♦❝❡ss❛❞❛✱ ❛ ❞✐str✐❜✉✐çã♦ ❞♦s ❞❛❞♦s ❡ ♦ ♣r♦❝❡ss❛♠❡♥t♦✳ ❊ss❛ ❡str❛té❣✐❛ é ❞❡s❝r✐t❛ ❡♠ ❢♦r♠❛ ❞❡ ✉♠ ❢r❛♠❡✇♦r❦✱ ♣r♦❥❡t❛❞♦ ❞❡ ❢♦r♠❛ q✉❡ ♥ã♦ ❡st❡❥❛ ❛❝♦♣❧❛❞♦ ❛♦ ❛❧❣♦r✐t♠♦ ❞❡ ❛✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦✳ ❉❡ss❛ ❢♦r♠❛✱ ♣❡r♠✐t❡ q✉❡ ❡ss❛ ❡str❛té❣✐❛ ♣♦ss❛ s❡r ✉t✐❧✐③❛❞❛ ♣♦r ❞✐❢❡r❡♥t❡s ❛❧❣♦r✐t♠♦s ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦ s❡♠ q✉❡ ❤❛❥❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ r❡♣r♦❥❡t❛r ♦✉ ♠♦❞✐✜❝❛r ♦ ❛❧❣♦r✐t♠♦ ❡s❝♦❧❤✐❞♦✳
❖ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ❞❛s s✐♠✉❧❛çõ❡s ❢❡✐t❛s ♣❛r❛ t❡st❛r ♦ ❢r❛♠❡✇♦r❦ ♣r♦♣♦st♦✳ ◆❡ss❡ ❝❛♣ít✉❧♦ é ❢❡✐t❛ ✉♠❛ ❡①♣♦s✐çã♦ ❡ ✉♠❛ ❛♥á❧✐s❡ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❢r❛♠❡✇♦r❦ ❝♦♠ r❡❧❛çã♦ ❛♦ t❡♠♣♦ ❡ à q✉❛❧✐❞❛❞❡ ❞♦ s✐♥❛❧ ❛♠♣❧✐❛❞♦✳
P❛r❛ ✜♥❛❧✐③❛r✱ ♦ ❈❛♣ít✉❧♦ ✻ ❞✐s❝✉rs❛ s♦❜r❡ ❛s ❝♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ❞♦ tr❛❜❛❧❤♦✱ ❛♣r❡✲ s❡♥t❛♥❞♦ ✉♠❛ r❡✢❡①ã♦ s♦❜r❡ ♦s r❡s✉❧t❛❞♦s ❡ ❡①♣♦♥❞♦ ♥♦✈❛s ♣❡rs♣❡❝t✐✈❛s ❞❛ ♣r♦♣♦st❛ ♣❛r❛ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳
❈❛♣ít✉❧♦ ✷
❘❡❢❡r❡♥❝✐❛❧ ❚❡ór✐❝♦
❊st❡ ❝❛♣ít✉❧♦ tr❛③ ✉♠❛ ❜r❡✈❡ ❛♣r❡s❡♥t❛çã♦ ❞♦s ❝♦♥❝❡✐t♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❞❡s❡♥✈♦❧✈✐✲ ♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❖s ❝♦♥❝❡✐t♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ❡♠ s❡çõ❡s✱ ❛s q✉❛✐s ❢♦r❛♠ ❞✐✈✐❞✐❞❛s ❡♠ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ■♠❛❣❡♥s ❡ ❱í❞❡♦s ✭❙❡çã♦ ✷✳✶✮✱ ❙✐♠♣❧✐✜❝❛çã♦ ❞❡ ❆❧❣♦r✐t♠♦s ✭❙❡çã♦ ✷✳✷✮✱ ❈♦♠♣✉t❛çã♦ P❛r❛❧❡❧❛ ✭❙❡çã♦ ✷✳✸✮✱ P❛r❛❧❡❧✐s♠♦ ❡♠ Pr♦❝❡ss❛♠❡♥t♦ ❞❡ ❱í❞❡♦s ✭❙❡çã♦ ✷✳✹✮ ❡ ▼étr✐❝❛s ❞❡ ❆♥á❧✐s❡ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✭❙❡çã♦ ✷✳✺✮✳
✷✳✶ ❆✉♠❡♥t♦ ❞❡ ❘❡s♦❧✉çã♦ ❞❡ ■♠❛❣❡♥s ❡ ❱í❞❡♦s
❆✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ✐♠❛❣❡♥s ❡♥✈♦❧✈❡ ♦ ❡st✉❞♦ ❞❡ ♠ét♦❞♦s ❡ ❛❧❣♦r✐t♠♦s q✉❡ ♣r♦✲ ❞✉③❡♠ ✐♠❛❣❡♥s ❞❡ ❛❧t❛✲r❡s♦❧✉çã♦✱ ❛ ♣❛rt✐r ❞❡ ✐♠❛❣❡♥s ❞❡ r❡s♦❧✉çõ❡s ♠❡♥♦r❡s✳ ●❡r❛❧♠❡♥t❡✱ ❡ss❛ tr❛♥s❢♦r♠❛çã♦ ❜❛✐①❛✲♣❛r❛✲❛❧t❛ r❡s♦❧✉çã♦ ❝♦♥s✐❞❡r❛ ❛ tr❛♥s❢♦r♠❛çã♦ ❝♦♠ ❛ ♠❡❧❤♦r q✉❛❧✲ ✐❞❛❞❡ ♣♦ssí✈❡❧✳ ❆ss✐♠✱ ♦ ♥í✈❡❧ ❞❡ ❞❡t❛❧❤❡s ♠❛♥t✐❞♦ ♥✉♠ ♣r♦❝❡ss♦ ❞❡ ❝♦♠♣❛r❛çã♦ q✉❡ ✉t✐❧✐③❛ ✐♠❛❣❡♥s ❞❡ ❛❧t❛ r❡s♦❧✉çã♦✱ q✉❡ sã♦ r❡❞✉③✐❞❛s ♣❛r❛ ✐♠❛❣❡♥s ❞❡ r❡s♦❧✉çã♦ ♠❡♥♦r❡s✱ ❡ ♥♦✈❛✲ ♠❡♥t❡ tr❛♥s❢♦r♠❛❞❛s ❡♠ ✐♠❛❣❡♥s ❞❡ ❛❧t❛✲r❡s♦❧✉çã♦✱ ❞❡✜♥❡♠ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ q✉❛❧✐❞❛❞❡ ❞♦ ❛❧❣♦r✐t♠♦✳
❖s ♠ét♦❞♦s ♠❛✐s ❝♦♠✉♥s ❞❡ ❛✉♠❡♥t♦ ❞❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧ ✭r❡s♦❧✉çã♦✮ ❞❡ ✐♠❛❣❡♥s ❡ ✈í❞❡♦s ❝♦♥s✐st❡♠ ❞❡ té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✳ ▲♦❣♦✱ ❞✐❢❡r❡♥t❡s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣r♦❞✉③❡♠ ❞✐✈❡rs♦s ❡❢❡✐t♦s ♥❛s ✐♠❛❣❡♥s ❣❡r❛❞❛s✱ ❝♦♠♦ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✳
✭❛✮ ✭❜✮
✭❝✮ ✭❞✮
❋✐❣✉r❛ ✷✳✶✿ ❊①❡♠♣❧♦s ❞❡ ✉s♦ ❞❡ ❞✐✈❡rs❛s té❝♥✐❝❛s ❞❡ ✐♥t❡r♣♦❧❛çã♦✿ ✭❛✮ ♦r✐❣✐♥❛❧✱ ✭❜✮ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦✱ ✭❝✮ ❜✐❧✐♥❡❛r ❡ ✭❞✮ ❜✐❝ú❜✐❝❛✳
◆❛ ❋✐❣✉r❛ ✷✳✶✲✭❜✮✱ ♥♦t❛✲s❡ q✉❡ ♦ ♠ét♦❞♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦ ❞♦ ✈✐③✐♥❤♦ ♠❛✐s ♣ró①✐♠♦ ❞❡✐①❛ ❡✈✐❞❡♥t❡ ♦ ❡❢❡✐t♦ ❞❡ ❛❧✐❛s✐♥❣✳ ■ss♦ ♦❝♦rr❡ ♣♦rq✉❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❝♦♥t♦r♥♦s ❡ ❞❡t❛❧❤❡s r❡♣r❡s❡♥t❛♠ ❝♦♠♣♦♥❡♥t❡s ❞❡ ❛❧t❛✲❢r❡q✉ê♥❝✐❛✳ ◗✉❛♥❞♦ ❛♠♣❧✐❛✲s❡ ❛ ✐♠❛❣❡♠✱ é r❡❝♦♥str✉í❞❛ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ s✉❜✲❛♠♦str❛❣❡♠✳
❈♦♠♦ ♣♦❞❡ s❡r ✈✐st♦ ♥❛s ❋✐❣✉r❛s ✷✳✶✲✭❝✮ ❡ ✷✳✶✲✭❞✮✱ q✉❛♥❞♦ ✉t✐❧✐③❛♠✲s❡ té❝♥✐❝❛s ❞❡ ✐♥✲ t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r ❡ ❜✐❝ú❜✐❝❛ ♦ ❡❢❡✐t♦ ❞❡ ❛❧✐❛s✐♥❣ é ❛♠❡♥✐③❛❞♦✱ ♣♦✐s ❛ ✐♥❢♦r♠❛çã♦ ❞❛s ❛❧t❛s ❢r❡q✉ê♥❝✐❛s ♣❡r❞✐❞❛s é r❡❝♦♥str✉í❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❝♦♠♣♦s✐çã♦ s✉❛✈✐③❛❞❛✳ ❊st❡ ❡❢❡✐t♦ t❛♠❜é♠ ♣♦❞❡ s❡r ❛♠❡♥✐③❛❞♦ ♣♦r ♠❡✐♦ ❞❡ té❝♥✐❝❛s ❛♥t✐❛❧✐❛s✐♥❣✱ ♦♥❞❡ ✉t✐❧✐③❛♠✲s❡ ✜❧tr♦s q✉❡ ♣❡r♠✐t❡♠ ❛ ♣❛ss❛❣❡♠ ❞❡ ❢r❡q✉ê♥❝✐❛s ❜❛✐①❛s✳
✭❛✮ ✭❜✮
❋✐❣✉r❛ ✷✳✷✿ ✭❛✮ ■♠❛❣❡♠ ❛♠♣❧✐❛❞❛ ✉t✐❧✐③❛♥❞♦ ✐♥t❡r♣♦❧❛çã♦ ❜✐❧✐♥❡❛r ❡ ✭❜✮ ✐♠❛❣❡♠ ♦❜t✐❞❛ ❞❛ ✜❧tr❛❣❡♠ ❞❛ ♦r✐❣✐♥❛❧ ❝♦♠ ❣❛✉ss✐❛♥♦ ♣❛ss❛✲❜❛✐①❛✳
❈♦♠♣❛r❛♥❞♦ ❛s ❋✐❣✉r❛s ✷✳✷✲✭❛✮ ❡ ✷✳✷✲✭❜✮ é ♣♦ssí✈❡❧ ♥♦t❛r ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ❛ ♦♣❡r❛çã♦ ❞❡ ❛✉♠❡♥t♦ ❞✐♠❡♥s✐♦♥❛❧ ♣♦r ✐♥t❡r♣♦❧❛çã♦ ❡ ❛s ♦♣❡r❛çõ❡s ❞❡ ✜❧tr❛❣❡♠✳ ❉❡st❛s ✜❣✉r❛s✱ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡ ♦ r❡s✉❧t❛❞♦ ❛♠♣❧✐❛❞♦ ♣♦r ✐♥t❡r♣♦❧❛çã♦ ❡ ❛ ♦♣❡r❛çã♦ ❞❡ s✉❛✈✐③❛çã♦ ❞❛ ✐♠❛❣❡♠ ❞ã♦ r❡s✉❧t❛❞♦s s❡♠❡❧❤❛♥t❡s✳
❖ r❡❞✐♠❡♥s✐♦♥❛♠❡♥t♦ q✉❡ ♥ã♦ ✉t✐❧✐③❛ ✐♥t❡r♣♦❧❛çã♦ é ❝❤❛♠❛❞♦ ❞❡ s✉♣❡r✲r❡s♦❧✉çã♦✳ ❊st❡ t❡r♠♦ ♣♦❞❡ s❡r ❝♦♥❢✉s♦✱ ♣♦rt❛♥t♦ ♦ t❡r♠♦ ③♦♦♠ ❞✐❣✐t❛❧ é ❛❞♦t❛❞♦ ♣❛r❛ ❛ ♦♣❡r❛çã♦ ❞❡ ❛✉♠❡♥t♦ ♥❛s ❞✐♠❡♥sõ❡s ❞❛ ✐♠❛❣❡♠✱ ❡♥q✉❛♥t♦ s✉♣❡r✲r❡s♦❧✉çã♦ é ✉s❛❞♦ ♣❛r❛ ❛ ♦♣❡r❛çã♦ ❞❡ ❢✉sã♦ ❞❡ ❞✐✈❡rs❛s ✐♠❛❣❡♥s ❡♠ ❜❛✐①❛ r❡s♦❧✉çã♦ ❡♠ ♦✉tr❛ ❝♦♠ ❛❧t❛ r❡s♦❧✉çã♦ ❬✷✽❪✳ ❖ ♣r♦❜❧❡♠❛
❞❛ s✉♣❡r r❡s♦❧✉çã♦ é ❢♦r♠✉❧❛❞♦ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ s❡♥❞♦ yh ∈ RNh ❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧
❡♠ ❛❧t❛✲r❡s♦❧✉çã♦✱ r❡♣r❡s❡♥t❛❞❛ ❝♦♠♦ ✉♠ ✈❡t♦r ❞❡ Nh ♣✐①❡❧s ❞❡ ❧❛r❣✉r❛✳ ❙❡❥❛♠ t❛♠❜é♠
♦ ♦♣❡r❛❞♦r ❞❡ ❜♦rr❛♠❡♥t♦ ❡ ♦ ♦♣❡r❛❞♦r ❞❡ r❡❞✉çã♦✱ ❍ : RNh → RNh ❡ ❙ : RNh → RNl✱
r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖ ♦♣❡r❛❞♦r ❍ r❡❛❧✐③❛ ✉♠❛ ✜❧tr❛❣❡♠ ♣❛ss❛✲❜❛✐①❛ ♥❛ ✐♠❛❣❡♠✱ ❡♥q✉❛♥t♦
q✉❡ ♦ ♦♣❡r❛❞♦r ❙ r❡❛❧✐③❛ ✉♠❛ r❡❞✉çã♦ ♣♦r ✉♠ ❢❛t♦r ✐♥t❡✐r♦ s✱ ❞✐♠✐♥✉✐♥❞♦ ♦ t❛♠❛♥❤♦
❞❛ ✐♠❛❣❡♠✳ ❙❡♥❞♦ zl ∈ RNl ❛ ✈❡rsã♦ ❞❡ ❜❛✐①❛ r❡s♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧✱ ❞❛❞❛ ♣❡❧❛
❊q✉❛çã♦ ✷✳✶ ❛❜❛✐①♦✱
zl =SHyh+v, ✭✷✳✶✮
♦♥❞❡ v é ✉♠ r✉í❞♦ ❣❛✉ss✐❛♥♦✳
❉❛❞♦zl✱ ♦ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ❡♠ ❡♥❝♦♥tr❛ryˆ∈RNht❛❧ q✉❡argmax|yˆ−yh| ≤ǫ✱ ♦♥❞❡ǫé
✉♠ ❡rr♦ t♦❧❡r❛❞♦ ♣❛r❛ ❛ ❛♣r♦①✐♠❛çã♦✳ ❉❡✈✐❞♦ à ❝❛r❛❝t❡ríst✐❝❛ ❣❛✉ss✐❛♥❛ ❞❡v✱ ❛ ❡st✐♠❛çã♦
❞❛ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ é ♦❜t✐❞❛ ♣❡❧❛ ♠✐♥✐♠✐③❛çã♦ ❞❡kSHyˆ−zlk2✳ P♦rt❛♥t♦✱ é ♣♦ssí✈❡❧
♥♦t❛r q✉❡ ❛ r❡❞✉çã♦ ❞♦ r✉í❞♦ v é ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ✐♠♣♦rt❛♥t❡ ♥♦ ♣r♦❜❧❡♠❛ ❞♦ ❛✉♠❡♥t♦
❞❡ r❡s♦❧✉çã♦ ❞❡ ✐♠❛❣❡♥s✳ ❈♦♥t✉❞♦✱ ❝♦♠♦ ❛ ❝♦♠♣♦s✐çã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❙❍ é r❡t❛♥❣✉❧❛r✱ ❝♦♠ ♠❛✐s ❝♦❧✉♥❛s ❞♦ q✉❡ ❧✐♥❤❛s✱ ❡st❡ s✐st❡♠❛ ♥ã♦ ♣♦❞❡ s❡r ✐♥✈❡rt✐❞♦ ❞✐r❡t❛♠❡♥t❡✱ s❡♥❞♦ ✉♠ s✐st❡♠❛ ❧✐♥❡❛r♠❡♥t❡ ❞❡♣❡♥❞❡♥t❡ ❡✱ ♣♦rt❛♥t♦✱ t❡♥❞♦ ❞✐✈❡rs❛s s♦❧✉çõ❡s✳
❉✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ❞❡ tr❛❜❛❧❤♦ ❢♦r❛♠ tr❛t❛❞❛s ♣❛r❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❛✉✲ ♠❡♥t♦ ❞❡ ❡s❝❛❧❛✱ s❡♣❛r❛♥❞♦ ♦s ♦♣❡r❛❞♦r❡s ❙ ❡ ❍✳ ❆❧❣✉♥s tr❛❜❛❧❤♦s ❛ss✉♠❡♠ q✉❡ ♥ã♦ ❤á ❡❢❡✐t♦ ❞❡ ❜♦rr❛♠❡♥t♦ ❛ss♦❝✐❛❞♦✳ ❊ss❛s ❛❜♦r❞❛❣❡♥s ❝♦♥s✐st❡♠ ❞❡ ♠ét♦❞♦s ❞❡ ✐♥t❡r♣♦✲ ❧❛çã♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ s❡ ❤á ✉♠ ❡❢❡✐t♦ ❞❡ ❜♦rr❛♠❡♥t♦ ❡♥✈♦❧✈✐❞♦✱ ❡♥tã♦ ♦ ♣r♦❝❡ss♦ ❞❡ r❡❝✉♣❡r❛çã♦ ❞❛ ✐♠❛❣❡♠ ❛✉♠❡♥t❛❞❛ ❝♦♥s✐st❡ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ r❡♠♦çã♦ ❞❡ ❜♦rr❛♠❡♥t♦ ✭❞❡❜❧✉rr✐♥❣✮ ❬✺✼✱ ✾✹❪✳ ❙❡♥❞♦ ❛ss✐♠✱ ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ♣❛r❛ ❛✉♠❡♥t♦ ❞❡ r❡s♦❧✉çã♦ ❞❡ ✐♠✲ ❛❣❡♥s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❛ ✐♥✈❡rsã♦ ❞❡ ❢♦r♠❛ ❧✐♥❡❛r♠❡♥t❡ ❡stá✈❡❧ ❬✶✻✱ ✷✻✱ ✸✶✱ ✹✹✱ ✺✺✱ ✼✸✱ ✼✻✱ ✽✶❪✳
✷✳✷ Pr♦❝❡ss❛♠❡♥t♦ ❙✐♠♣❧✐✜❝❛❞♦
❆❧❣♦r✐t♠♦s sã♦ ❡str❛té❣✐❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ ❝♦♥✲ ❥✉♥t♦ ❞❡ r❡❣r❛s ❜❡♠✲❞❡✜♥✐❞❛s ❬✶✾❪✳ ❆ss✐♠✱ ❡♠❜♦r❛ ❡①✐st❛♠ ❞✐✈❡rs❛s ❢♦r♠❛s ♣❛r❛ s❡ s♦❧✉✲ ❝✐♦♥❛r ✉♠ ♣r♦❜❧❡♠❛✱ ❞✐st✐♥t♦s ❛❧❣♦r✐t♠♦s ♣♦❞❡♠ s❡r ❡✜❝❛③❡s ♣❛r❛ r❡s♦❧✉çã♦ ❝♦♠ ❞✐❢❡r❡♥t❡s ❣r❛✉s ❞❡ ❡✜❝✐ê♥❝✐❛✳
◆♦ ❝♦♥t❡①t♦ ❞❡ ❛♥á❧✐s❡ ❞❡ ❛❧❣♦r✐t♠♦s✱ ❡✜❝✐ê♥❝✐❛ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❜❛✐①❛ ❝♦♠♣❧❡①✐❞❛❞❡ ♥❛ ✉t✐❧✐③❛çã♦ ❞♦ ❡s♣❛ç♦ ✭♠❡♠ór✐❛ ❡ ❞❛❞♦s✮ ♦✉ ♥❛ ❞❡ ❡①❡❝✉çã♦ ✭❈P❯✮✳ ❉❡✈✐❞♦ à ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s q✉❡ ❝♦st✉♠❛♠ s❡r ♠❛♥✐♣✉❧❛❞❛s ❡♠ ❛♣❧✐❝❛çõ❡s ❞❡ ✈í❞❡♦ ❞✐❣✐t❛❧✱ ❛ ❡✜❝✐ê♥❝✐❛ ❞♦s ❛❧❣♦r✐t♠♦s ❛ss♦❝✐❛❞♦s ❛ ❡st❡ t✐♣♦ ❞❡ ❛♣❧✐❝❛çã♦ é ❞❡ ❡①tr❡♠❛ r❡❧❡✈â♥❝✐❛✳ P♦r✲ t❛♥t♦✱ ♣❛r❛ q✉❡ ✉♠ ❛❧❣♦r✐t♠♦ s❡❥❛ ❡✜❝✐❡♥t❡ ❡ ❝♦♠♣❛tí✈❡❧ ❝♦♠ ✉♠❛ ❛rq✉✐t❡t✉r❛ ❞❡ ❤❛r❞✇❛r❡✱ ❛❧❣✉♠❛s ❡str❛té❣✐❛s ❞❡✈❡♠ s❡r t♦♠❛❞❛s✳ ❆s ❡str❛té❣✐❛s ❞❡ s✐♠♣❧✐✜❝❛çã♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✉s❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ sã♦ ❞❡✜♥✐❞❛s ❡♠ ♥í✈❡❧ ❞❡ ❞❛❞♦s ❡ ❡♠ ♥í✈❡❧ ❞❡ ✐♥str✉çã♦✳
✷✳✷✳✶ ❙✐♠♣❧✐✜❝❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡♠ ◆í✈❡❧ ❞❡ ❉❛❞♦s
❆ s✐♠♣❧✐✜❝❛çã♦ ❞♦ ♣r♦❝❡ss❛♠❡♥t♦ ❡♠ ♥í✈❡❧ ❞❛❞♦s é ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉✐t♦ ❝♦♠✉♠ ❡♠ ❡♠ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ s✐♥❛✐s✱ ✐♠❛❣❡♥s ❡ ✈í❞❡♦s✳ ❉❡ss❛ ❢♦r♠❛✱ ❞❡✜♥❡✲s❡ ❡ss❛ s✐♠♣❧✐✜❝❛çã♦
