❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
▼❖❉❊▲❖ ❈❘■P❚❖●❘➪❋■❈❖ ❇❆❙❊❆❉❖ ❊▼ ❆❯❚Ô▼❆❚❖❙
❈❊▲❯▲❆❘❊❙ ❚❘■❉■▼❊◆❙■❖◆❆■❙ ❍❮❇❘■❉❖❙
❉❆◆■❊▲▲■ ❆❘❆Ú❏❖ ▲■▼❆
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❉❆◆■❊▲▲■ ❆❘❆Ú❏❖ ▲■▼❆
▼❖❉❊▲❖ ❈❘■P❚❖●❘➪❋■❈❖ ❇❆❙❊❆❉❖ ❊▼ ❆❯❚Ô▼❆❚❖❙
❈❊▲❯▲❆❘❊❙ ❚❘■❉■▼❊◆❙■❖◆❆■❙ ❍❮❇❘■❉❖❙
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❈♦♠✲ ♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ▼✐♥❛s ●❡✲ r❛✐s✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✳ ❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ●✐♥❛ ▼❛✐r❛ ❇❛r❜♦s❛ ❞❡ ❖❧✐✈❡✐r❛
Dados Internacionais de Catalogação na Publicação (CIP) Sistema de Bibliotecas da UFU
L732m Lima, Danielli Araújo, 1989-
Modelo criptográfico baseado em autômatos celulares tridimensio-nais híbridos / Danielli Araújo Lima. - 2012.
224 f. : il.
Orientadora: Gina Maira Barbosa de Oliveira.
Dissertação (mestrado) – Universidade Federal de Uberlândia, Progra- ma de Pós-Graduação em Ciência da Computação.
Inclui bibliografia.
1. Computação - Teses. 2. Inteligência artificial - Teses. 2. Criptografia - Teses. I. Oliveira, Gina Maira Barbosa de. II. Universidade Federal de Uberlândia. Programa de Pós-Graduação em Ciência da Computação. III. Título.
CDU: 681.3
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛✲ ❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏▼♦❞❡❧♦ ❝r✐♣t♦❣rá✜❝♦ ❜❛s❡❛❞♦ ❡♠ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s tr✐❞✐♠❡♥s✐♦♥❛✐s ❤í❜r✐❞♦s✑ ♣♦r ❉❛♥✐❡❧❧✐ ❆r❛ú❥♦ ▲✐♠❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐✲ ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❯❜❡r❧â♥❞✐❛✱ ✸ ❞❡ ❏✉❧❤♦ ❞❡ ✷✵✶✷
❖r✐❡♥t❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ●✐♥❛ ▼❛✐r❛ ❇❛r❜♦s❛ ❞❡ ❖❧✐✈❡✐r❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❇r✉♥♦ ❆✉❣✉st♦ ◆❛ss✐❢ ❚r❛✈❡♥ç♦❧♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❉❛t❛✿ ❏✉❧❤♦ ❞❡ ✷✵✶✷
❆✉t♦r✿ ❉❛♥✐❡❧❧✐ ❆r❛ú❥♦ ▲✐♠❛
❚ít✉❧♦✿ ▼♦❞❡❧♦ ❝r✐♣t♦❣rá✜❝♦ ❜❛s❡❛❞♦ ❡♠ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s tr✐❞✐♠❡♥✲ s✐♦♥❛✐s ❤í❜r✐❞♦s
❋❛❝✉❧❞❛❞❡✿ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉t❛çã♦
●r❛✉✿ ▼❡str❛❞♦
❋✐❝❛ ❣❛r❛♥t✐❞♦ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛ ♦ ❞✐r❡✐t♦ ❞❡ ❝✐r❝✉❧❛çã♦ ❡ ✐♠♣r❡ssã♦ ❞❡ ❝ó♣✐❛s ❞❡st❡ ❞♦❝✉♠❡♥t♦ ♣❛r❛ ♣r♦♣ós✐t♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ❛❝❛❞ê♠✐❝♦s✱ ❞❡s❞❡ q✉❡ ♦ ❛✉t♦r s❡❥❛ ❞❡✈✐❞❛♠❡♥t❡ ✐♥❢♦r♠❛❞♦✳
❆✉t♦r
❖ ❆❯❚❖❘ ❘❊❙❊❘❱❆ P❆❘❆ ❙■ ◗❯❆▲◗❯❊❘ ❖❯❚❘❖ ❉■❘❊■❚❖ ❉❊ P❯❇▲■❈❆➬➹❖ ❉❊❙❚❊ ❉❖❈❯▼❊◆❚❖✱ ◆➹❖ P❖❉❊◆❉❖ ❖ ▼❊❙▼❖ ❙❊❘ ■▼P❘❊❙❙❖ ❖❯ ❘❊P❘❖✲ ❉❯❩■❉❖✱ ❙❊❏❆ ◆❆ ❚❖❚❆▲■❉❆❉❊ ❖❯ ❊▼ P❆❘❚❊❙✱ ❙❊▼ ❆ P❊❘▼■❙❙➹❖ ❊❙❈❘■❚❆ ❉❖ ❆❯❚❖❘✳
❝
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦✳✳✳
❆ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛ ❡ ♣r♦❢❡ss♦r❛ ●✐♥❛✱ ♣❡❧❛ ❛♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ t❡♠❛ tã♦ ✐♥t❡r❡ss❛♥t❡ q✉❡ sã♦ ♦s ❆❈s✱ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ❞❡s❞❡ ❛ ■♥✐❝✐❛çã♦ ❈✐❡♥tí✜❝❛ ❡ t❛♠❜é♠ ♣♦r s✉❛ ✈❛❧✐♦s❛ ❝♦♥tr✐❜✉✐çã♦ ❛♦ ❧♦♥❣♦ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ r❡✈✐sã♦ t❡ór✐❝❛ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦ PP●❈❈✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ q✉❡ ♠❡ ❢♦✐ ❝♦♥❝❡❞✐❞❛ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ ▼❡str❛❞♦✱ ❞✐s♣♦♥✐❜✐❧✐③❛♥❞♦ t♦❞♦s ♦s ♠❡✐♦s ♠❛t❡r✐❛✐s ❡ ❤✉♠❛♥♦s ♣❛r❛ ❛ s✉❛ ❝♦♥❝r❡t✐③❛çã♦✳
❙❡♠ ❝✐t❛r ♥♦♠❡s ♣❛r❛ ♥ã♦ ❝♦rr❡r ♦ r✐s❝♦ ❞❡ ❛❧❣✉♠ ❡sq✉❡❝✐♠❡♥t♦✱ q✉❡r♦ t❛♠❜é♠ ❛❣r❛✲ ❞❡❝❡r ❛ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞❛ ❋❆❈❖▼ q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❞❡s❞❡ ❛ ❣r❛❞✉❛çã♦✳
❆♦ ❢✉♥❝✐♦♥ár✐♦ ❊r✐s✈❛❧❞♦✱ ♣❡❧❛ ♣r♦♥t✐❞ã♦ q✉❡ s❡♠♣r❡ ♠♦str♦✉ ♣❛r❛ r❡s♦❧✈❡r ❛ss✉♥t♦s ✐♠♣♦rt❛♥t❡s ❞♦ ♠❡✉ ♠❡str❛❞♦✳
❆ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s✱ ♣❡❧❛ tr♦❝❛ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦s ❞✉r❛♥t❡ ♦s ❡st✉❞♦s ❡ ❡①❡❝✉çã♦ ❞❡ tr❛❜❛❧❤♦s✱ ♣❡❧❛ ❝♦♥✈✐✈ê♥❝✐❛ ❡ t❛♠❜é♠ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦✳
❆ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣❡❧♦ ❝♦♥st❛♥t❡ ❛♣♦✐♦✱ ❛♠♦r ❡ ❞❡❞✐❝❛çã♦ ❛♦ ❧♦♥❣♦ ❞❡ ♠✐♥❤❛ ❢♦r♠❛çã♦ ♣❡ss♦❛❧ ❡ ♣r♦✜ss✐♦♥❛❧✱ q✉❡ ❢♦r❛♠ ❡ss❡♥❝✐❛✐s ♣❛r❛ s✉♣❡r❛r ❝❛❞❛ ✉♠❛ ❞❛s ❡t❛♣❛s ❞❡ ♠✐♥❤❛ ✈✐❞❛✳ ❊♠ ❡s♣❡❝✐❛❧✱ ❛ ♠✐♥❤❛ ♠ã❡ q✉❡ ♠❡ ❛✉①✐❧✐♦✉ ❡♠ ❡t❛♣❛s ✐♠♣♦rt❛♥t❡s ❞❡ss❡ tr❛❜❛❧❤♦✳
❆♦s ✐♥t❡❣r❛♥t❡s ❞❛ ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✱ ♣❡❧♦s ❝♦♠❡♥tár✐♦s ❡ s✉❣❡stõ❡s ❛♣r❡s❡♥t❛❞❛s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ✈❛❧♦r✐③❛r ♦ tr❛❜❛❧❤♦✳
❆ t♦❞♦s q✉❡✱ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛✱ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ s❡ r❡❛❧✐③❛ss❡✳
❘❡s✉♠♦
❆ ♣♦♣✉❧❛r✐③❛çã♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❡❧❡trô♥✐❝♦s q✉❡ ❝❛♣t✉r❛♠ ✐♠❛❣❡♥s ❞✐❣✐t❛✐s✱ ❜❡♠ ❝♦♠♦ ❛ ❝r✐❛çã♦ ❞❡ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s q✉❡ ♣♦ss✐❜✐❧✐t❛♠ ❛ tr♦❝❛ ❡ ❝♦♠♣❛rt✐❧❤❛♠❡♥t♦ ❞❛s ♠❡s♠❛s ❛tr❛✈és ❞❡ ❝❛♥❛✐s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♣r♦✈♦❝❛r❛♠ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ✐♥❡r❡♥t❡s✳ ❉❡♥tr❡ ❡ss❡s ♣r♦❜❧❡♠❛s ❡stã♦ ❛ q✉❡❜r❛ ❞❡ s❡❣✉r❛♥ç❛ ❡ ♣r✐✈❛❝✐❞❛❞❡ ❡♠ s✐st❡✲ ♠❛s ❞❡ ✐♥❢♦r♠❛çã♦✳ P❛r❛ q✉❡ ❡ss❛s q✉❡stõ❡s s❡❥❛♠ r❡s♦❧✈✐❞❛s✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ s✐st❡♠❛s ❝r✐♣t♦❣rá✜❝♦s ♥❛ tr❛♥s♠✐ssã♦ ❞❡ss❛s ✐♥❢♦r♠❛çõ❡s s❡ ❢❛③ ♥❡❝❡ssár✐❛✳ ❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❛ ❝r✐♣t♦❣r❛✜❛ é ❛ ❣❛r❛♥t✐❛ ❞❡ q✉❡ ❛s ✐♥❢♦r♠❛çõ❡s tr❛♥s♠✐t✐❞❛s ♥ã♦ s❡rã♦ ❝♦♣✐❛❞❛s✱ ♠♦✲ ❞✐✜❝❛❞❛s ♦✉ ❢❛❧s✐✜❝❛❞❛s✳ ▼✉✐t♦s ❛❧❣♦r✐t♠♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝❧áss✐❝❛ ❡ ♠♦❞❡r♥❛ ❥á ❢♦r❛♠ ✐♥✈❡st✐❣❛❞♦s ♣❛r❛ ❣❛r❛♥t✐r ❛ tr♦❝❛ s❡❣✉r❛ ❞❡ ✐♥❢♦r♠❛çõ❡s✳ ❊♥tr❡t❛♥t♦✱ q✉❛♥❞♦ ❛ ♠❡♥s❛❣❡♠ q✉❡ ❡st✐✈❡r s❡♥❞♦ ❡♥✈✐❛❞❛ ❢♦r ✉♠❛ ✐♠❛❣❡♠✱ ♦s ❛❧❣♦r✐t♠♦s ❝♦♥✈❡♥❝✐♦♥❛✐s ♥ã♦ ❢❛✈♦r❡❝❡♠ ♦ ❛rr❛♥❥♦ ♥❡♠ ❛ q✉❛♥t✐❞❛❞❡ ♠❛ss✐✈❛ ❞❡ ✐♥❢♦r♠❛çõ❡s q✉❡ sã♦ ❝❛r❛❝t❡ríst✐❝❛s ❡str✉t✉r❛✐s ❞❛s ♠❡s♠❛s✳ ❆ss✐♠✱ ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❡st❡ t❡♠❛ sã♦ ♦s ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ✭❆❈s✮✱ q✉❡ ❡stã♦ s❡♥❞♦ ❡st✉❞❛❞♦s ♣❡❧❛ s✐♠♣❧✐❝✐❞❛❞❡ ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ t❛♠❜é♠ ♣♦r s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛r ❞❛❞♦s ❡♠ ♣❛r❛❧❡❧♦✳ ◆❡ss❡ tr❛❜❛❧❤♦ ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ❝r✐♣t♦❣rá✜❝♦ tr✐❞✐♠❡♥s✐♦♥❛❧ ❜❛s❡❛❞♦ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ❤í❜r✐❞♦s ❢♦✐ ❡❧❛❜♦r❛❞♦ ❡ ❝❤❛♠❛❞♦ ❞❡ ✸❉❍❈❆✳ ❊ss❡ ♠ét♦❞♦ ✉t✐❧✐③❛ ♦ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♥s✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ à ❡✈♦❧✉çã♦ ❞♦ ❆❈ ♣❛r❛ trás✱ ❡ ❞✉❛s r❡❣r❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝✐❢r❛❣❡♠✳ ❯♠❛ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❝❛ót✐❝❛ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ❝✐❢r❛❣❡♠ ❡❢❡t✐✈❛ ❞❛ ♠❡♥s❛❣❡♠ ❡ ✉♠❛ r❡❣r❛ ❞❡ ❝♦♥t♦r♥♦✱ q✉❡ ❣❛r❛♥t❡ ❛ ❡①✐stê♥❝✐❛ ❞❛ ♣ré✲✐♠❛❣❡♠ ♣❛r❛ q✉❛❧q✉❡r r❡t✐❝✉❧❛❞♦ ♣♦ssí✈❡❧✳ ❊ss❡ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ ❜❛s❡✐❛✲s❡ ❡♠ ✉♠ ♣r❡❝✉rs♦r ❝❤❛♠❛❞♦ ❍❈❆ q✉❡ ✉t✐❧✐③❛ ❆❈s ✉♥✐❞✐♠❡♥s✐♦♥❛✐s✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉♠❛ ❛♥á✲ ❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ ❞♦ ♠♦❞❡❧♦ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ❢♦✐ r❡❛❧✐③❛❞❛ ❛tr❛✈és ❞❛ ❚❡♦r✐❛ ❞♦s ●r❛❢♦s✳ ❆ ❞❡✜♥✐çã♦ ❞♦ ♥♦✈♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ tr✐❞✐♠❡♥s✐♦♥❛❧✱ ❜❡♠ ❝♦♠♦ ♦s ❡①♣❡r✐♠❡♥t♦s r❡❛❧✐③❛❞♦s ♣❛r❛ s✉❛ ✈❛❧✐❞❛çã♦ ❡ r❡✜♥❛♠❡♥t♦✱ sã♦ ❞✐s❝✉t✐❞♦s ♥❡ss❛ ❞✐ss❡rt❛çã♦✳ ❖ ♠ét♦❞♦ r❡s✉❧t❛♥t❡ s❡ ♠♦str♦✉ s❡❣✉r♦ ❡ ♣❛ssí✈❡❧ ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❝♦♠ ❛❧t♦ ♥í✈❡❧ ❞❡ ♣❛r❛❧❡❧✐s♠♦✳ ❆ss✐♠✱ s❡ t♦r♥❛ ✉♠❛ ♦♣çã♦ ❡①tr❡♠❛♠❡♥t❡ ✐♥t❡r❡ss❛♥t❡ ♣❛r❛ ❛ ❝✐❢r❛❣❡♠ ❞❡ ❣r❛♥❞❡s ✈♦❧✉♠❡s ❞❡ ❞❛❞♦s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛s ✐♠❛❣❡♥s ❞✐❣✐t❛✐s ❝♦❧♦r✐❞❛s✳
❆❜str❛❝t
❚❤❡ ♣♦♣✉❧❛r✐③❛t✐♦♥ ♦❢ ❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s t♦ ❝❛♣t✉r❡ ❞✐❣✐t❛❧ ✐♠❛❣❡s✱ ❛s ✇❡❧❧ ❛s t❤❡ ❝r❡❛✲ t✐♦♥ ♦❢ s❡✈❡r❛❧ ❛♣♣❧✐❝❛t✐♦♥s ❡♥❛❜❧✐♥❣ ❡①❝❤❛♥❣❡ ❛♥❞ s❤❛r✐♥❣ t❤❡s❡ ✐♠❛❣❡s ❜② ❝♦♠♠✉♥✐❝❛t✐♦♥ ❝❤❛♥♥❡❧s ❤❛s ❜r♦✉❣❤t s♦♠❡ ✐♥❤❡r❡♥t ♣r♦❜❧❡♠s✳ ❆♠♦♥❣ t❤❡s❡ ♣r♦❜❧❡♠s ✐t ❝❛♥ ❜❡ ❝✐t❡❞ t❤❡ s❡❝✉r✐t② ✈✐♦❧❛t✐♦♥ ❛♥❞ ♣r✐✈❛❝② ✐♥ ✐♥❢♦r♠❛t✐♦♥ s②st❡♠s✳ ❚❤❡ ✉s❡ ♦❢ ❝r②♣t♦❣r❛♣❤✐❝ s②st❡♠s ✐♥ s✉❝❤ ✐♥❢♦r♠❛t✐♦♥ tr❛♥s♠✐ss✐♦♥ ✐s r❡q✉✐r❡❞ t♦ s♦❧✈❡ t❤❡s❡ ✐ss✉❡s✳ ❚❤❡ ♠❛✐♥ ❣♦❛❧ ♦❢ ❝r②♣✲ t♦❣r❛♣❤② ✐s t♦ ❣✉❛r❛♥t❡❡ t❤❛t t❤❡ ✐♥❢♦r♠❛t✐♦♥ ✇✐❧❧ ♥♦t ❜❡ ❝♦♣✐❡❞✱ ♠♦❞✐✜❡❞ ♦r ❢❛❧s✐✜❡❞✳ ▼❛♥② ❝❧❛ss✐❝ ❛♥❞ ♠♦❞❡r♥ ❡♥❝r②♣t✐♦♥ ❛❧❣♦r✐t❤♠s ❤❛✈❡ ❜❡❡♥ ✐♥✈❡st✐❣❛t❡❞ t♦ ❡♥s✉r❡ s❡❝✉r❡ ❡①❝❤❛♥❣❡ ♦❢ ✐♥❢♦r♠❛t✐♦♥✳ ❍♦✇❡✈❡r✱ ✇❤❡♥ t❤❡ ♠❡ss❛❣❡ t♦ ❜❡ s❡♥t ✐s ❛♥ ✐♠❛❣❡✱ t❤❡ ❝♦♥✲ ✈❡♥t✐♦♥❛❧ ❛❧❣♦r✐t❤♠s ❞♦ ♥♦t ❢❛✈♦r ✐♠❛❣❡ str✉❝t✉r❛❧ ❢❡❛t✉r❡s✿ t❤❡ s♣❛t✐❛❧ ❛rr❛♥❣❡♠❡♥t ❛♥❞ t❤❡ ♠❛ss✐✈❡ ❛♠♦✉♥t ♦❢ ✐♥❢♦r♠❛t✐♦♥✳ ❚❤✉s✱ ❛ ♥❡✇ ❛♣♣r♦❛❝❤ ❢♦r t❤✐s t♦♣✐❝ ✐s t❤❡ ✉s❛❣❡ ♦❢ ❝❡❧❧✉❧❛r ❛✉t♦♠❛t❛ ✭❈❆✮ ✐♥ ✐♠❛❣❡ ❡♥❝r②♣t✐♦♥✳ ❈❆ ❛r❡ ❜❡✐♥❣ st✉❞✐❡❞ ❞✉❡ t♦ t❤❡✐r ✐♠✲ ♣❧❡♠❡♥t❛t✐♦♥ s✐♠♣❧✐❝✐t② ❛♥❞ ❛❧s♦ ❞✉❡ t♦ t❤❡✐r ❝❛♣❛❝✐t② t♦ ♣r♦❝❡ss ❞❛t❛ ✐♥ ❛ ❢❛st ♣❛r❛❧❧❡❧ ✇❛②✳ ■♥ t❤✐s ✇♦r❦ ❛ ♥♦✈❡❧ ❝r②♣t♦❣r❛♣❤✐❝ ♠♦❞❡❧ ❜❛s❡❞ ♦♥ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ❤②❜r✐❞ ❝❡❧❧✉❧❛r ❛✉t♦♠❛t❛ ✇❛s ❡❧❛❜♦r❛t❡❞ ❛♥❞ ♥❛♠❡❞ ✸❉❍❈❆✳ ❚❤✐s ♠❡t❤♦❞ ❡♠♣❧♦②s ♣r❡✲✐♠❛❣❡ ❝❛❧❝✉❧✉s ✇❤✐❝❤ r❡♣r❡s❡♥ts ❈❆ ❜❛❝❦✇❛r❞ ❡✈♦❧✉t✐♦♥ ❛♥❞ t✇♦ r✉❧❡s ❛r❡ ✉s❡❞ ✐♥ t❤❡ ❡♥❝r②♣t✐♦♥ ♣r♦❝❡ss✳ ❚❤❡ ✜rst ♦♥❡ ✐s ❝❛❧❧❡❞ ♠❛❥♦r r✉❧❡✱ ❛♥❞ ✐t ✐s r❡s♣♦♥s✐❜❧❡ ❢♦r t❤❡ ❡✛❡❝t✐✈❡ ❡♥❝r②♣t✐♦♥ ♦❢ t❤❡ ♠❡ss❛❣❡✳ ❚❤❡ s❡❝♦♥❞ ♦♥❡ ✐s ✉s❡❞ ♦♥❧② ✐♥ ❜♦✉♥❞❛r② ❧❛tt✐❝❡ ❝❡❧❧s t♦ ❡♥s✉r❡ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ♣r❡✲✐♠❛❣❡ ❢♦r ❛♥② ❧❛tt✐❝❡✳ ❚❤✐s t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ♠♦❞❡❧ ✐s ❜❛s❡❞ ♦♥ ❛ ♣r❡❝✉rs♦r ♠♦❞❡❧ ❝❛❧✲ ❧❡❞ ❍❈❆✱ ✇❤✐❝❤ ✉s❡s ♦♥❡✲❞✐♠❡♥s✐♦♥❛❧ ❈❆✳ ■♥✐t✐❛❧❧②✱ ❛♥ ❛♥❛❧②s✐s ♦❢ ♦♥❡✲❞✐♠❡♥s✐♦♥❛❧ ♠♦❞❡❧ s❛❢❡t② ✇❛s ♣❡r❢♦r♠❡❞ ✉s✐♥❣ ●r❛♣❤ ❚❤❡♦r②✳ ❚❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ t❤❡ ♥❡✇ t❤r❡❡✲❞✐♠❡♥s✐♦♥❛❧ ❝r②♣t♦❣r❛♣❤✐❝ ♠♦❞❡❧✱ ❛s ✇❡❧❧ ❛s ❡①♣❡r✐♠❡♥ts ❢♦r ✐ts ✈❛❧✐❞❛t✐♦♥ ❛♥❞ r❡✜♥❡♠❡♥t ❛r❡ ❞✐s❝✉s✲ s❡❞ ✐♥ t❤✐s ❞✐ss❡rt❛t✐♦♥✳ ❚❤❡ r❡s✉❧t✐♥❣ ♠❡t❤♦❞ ❤❛s ♣r♦✈❡❞ t♦ ❜❡ s❛❢❡ ❛♥❞ ❛♣♣r♦♣r✐❛t❡❞ ❢♦r ❛♥ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✇✐t❤ ❛ ❤✐❣❤✲❧❡✈❡❧ ♦❢ ♣❛r❛❧❧❡❧✐s♠✳ ❚❤✉s✱ ✐t ❜❡❝♦♠❡s ❛ ✈❡r② ✐♥t❡r❡st✐♥❣ ♦♣t✐♦♥ ❢♦r ❡♥❝r②♣t✐♦♥ ✉s✐♥❣ ❧❛r❣❡ ✈♦❧✉♠❡s ♦❢ ❞❛t❛✱ ❡s♣❡❝✐❛❧❧② ❞✐❣✐t❛❧ ❝♦❧♦r ✐♠❛❣❡s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①①✈✐✐
✶ ■♥tr♦❞✉çã♦ ✷✾
✶✳✶ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✶✳✷ ❊str✉t✉r❛ ❞♦ t❡①t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✷ ❆✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ✸✸
✷✳✶ ❆✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ✉♥✐❞✐♠❡♥s✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✶✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ❛✉tô♠❛t♦ ❝❡❧✉❧❛r ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✷ ❆✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ❜✐❞✐♠❡♥s✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✸ ❆✉tô♠❛t♦s ❝❡❧✉❧❛r❡s tr✐❞✐♠❡♥s✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✹ ❈❧❛ss✐✜❝❛çã♦ ❞✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✺ Pr♦♣r✐❡❞❛❞❡ ❞❡ s❡♥s✐t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✻ P❛râ♠❡tr♦s ❞❡ ♣r❡✈✐sã♦ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❞✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✼ ❈á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✽ ❱❛r✐❛çõ❡s ❞♦ ❛✉tô♠❛t♦ ❝❡❧✉❧❛r ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✾ ❈♦♥s✐❞❡r❛çõ❡s ❡♠ r❡❧❛çã♦ ❛♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✸ ❈r✐♣t♦❣r❛✜❛ ❡ s❡❣✉r❛♥ç❛ ✹✼
✸✳✶ ❍✐stór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷ ❚❡r♠✐♥♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✸ ▼ét♦❞♦s ❝❧áss✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹ ❈r✐♣t♦❣r❛✜❛ ♠♦❞❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹✳✶ ❈r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✹✳✷ ❈r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✺ ❚❡♦r✐❛ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❡ s❡❣✉r❛♥ç❛ ❞❡ ♠ét♦❞♦s ❝r✐♣t♦❣rá✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✻ ❈r✐♣t♦❛♥á❧✐s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✻✳✶ ❈r✐♣t♦❛♥á❧✐s❡ ❞✐❢❡r❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✻✳✷ ❈r✐♣t♦❛♥á❧✐s❡ ❧✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✼ ❈r✐♣t♦❣r❛✜❛ ♣❛r❛ ✐♠❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
①✈✐✐✐ ❙✉♠ár✐♦
✸✳✽ ❈♦♥s✐❞❡r❛çõ❡s ❡♠ r❡❧❛çã♦ ❛♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹ ❈r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞❛ ❡♠ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ✺✼
✹✳✶ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ●✉t♦✇✐t③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ●✉t♦✇✐t③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✳✷ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞❡ ●✉t♦✇✐t③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ ❜✐❞✐r❡❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✹✳✷✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ ❜✐❞✐✲ r❡❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✷✳✷ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞❡ s❡♥s✐t✐✈✐❞❛❞❡ ❜✐❞✐r❡❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✸ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦r✐t♠♦ r❡✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✹✳✸✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦r✐t♠♦ r❡✈❡rs♦ ❡♠ ❬❖❧✐✈❡✐r❛ ❡t ❛❧✳✱ ✷✵✵✽❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸✳✷ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝á❧❝✉❧♦ ❞❡ ♣ré✲
✐♠❛❣❡♥s ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦r✐t♠♦ r❡✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✹ ▼♦❞❡❧♦ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❝♦♠ t❡①t♦ ❝✐❢r❛❞♦ ❞❡ t❛♠❛♥❤♦ ✈❛r✐á✈❡❧ ✭❱▲❊✮ ✳ ✳ ✳ ✻✼
✹✳✹✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝♦♠ t❡①t♦ ❞❡ t❛♠❛♥❤♦ ✈❛r✐á✈❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✹✳✷ ❈♦♥s✐❞❡r❛çõ❡s ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝♦♠ t❡①t♦ ❞❡ t❛♠❛♥❤♦
✈❛r✐á✈❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ❡♠ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s ✉♥✐❞✐♠❡♥s✐♦♥❛✐s
✭❍❈❆✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺✳✶ ❱❡rsã♦ ✜♥❛❧ ❞♦ ♠♦❞❡❧♦ ❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✺✳✷ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✺✳✸ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✻ ▼♦❞❡❧♦ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ❡♠ ❆✉tô♠❛t♦s ❈❡❧✉❧❛r❡s ❜✐❞✐♠❡♥s✐♦♥❛✐s
✭❚❍❈❆✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✻✳✶ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❚❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✻✳✷ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❚❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✼ ❖✉tr♦s ♠♦❞❡❧♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ♣❛r❛ ✐♠❛❣❡♥s ❜❛s❡❛❞♦s ❡♠ ❆❈s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✽ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❜❛s❡❛❞♦ ❡♠ ❛✉tô♠❛t♦s ❝❡❧✉❧❛r❡s tr✐❞✐♠❡♥s✐♦♥❛✐s
❙✉♠ár✐♦ ①✐①
✻ ▼♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ✸❉❍❈❆ ✾✺
✻✳✶ ■♠❛❣❡♥s ❞✐❣✐t❛✐s ❡ ♣❛❞rã♦ ❘●❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✻✳✷ ❇❛s❡ ❞♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✻✳✸ ▼♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ três ❜❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✻✳✸✳✶ ❈á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ três ❜❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✻✳✸✳✷ Pr♦❝❡ss♦ ❞❡ ❞❡❝✐❢r❛❣❡♠ ♥♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ três ❜❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✻✳✸✳✸ ❆♥á❧✐s❡ ❞♦ ♣❛r❛❧❡❧✐s♠♦ ♥♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ três ❜❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✻✳✸✳✹ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ três ❜❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✻✳✹ ▼♦❞❡❧♦ ❝♦♠ ❜❧♦❝♦ ú♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✻✳✹✳✶ ❈á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ♥♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ ❜❧♦❝♦ ú♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✻✳✹✳✷ ❆♥á❧✐s❡ ❞♦ ♣❛r❛❧❡❧✐s♠♦ ♥♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ ❜❧♦❝♦ ú♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✻✳✹✳✸ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ ❜❧♦❝♦ ú♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✻✳✺ ▼♦❞❡❧♦ ❝♦♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ❜♦r❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✻✳✻ ▼♦❞❡❧♦ ❝♦♠ r♦t❛çã♦ ❞♦ ♥ú❝❧❡♦ ❞❛ r❡❣r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✻✳✻✳✶ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❝♦♠ ✐♥t❡r❝❛❧❛çã♦✱ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛s ❜♦r❞❛s ❡ r♦t❛çã♦ ❞♦ ♥ú❝❧❡♦ ❞❛ r❡❣r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✻✳✼ ▼♦❞❡❧♦ ✜♥❛❧ ✸❉❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶
✼ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✶✷✸
✼✳✶ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦s ❡①♣❡r✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✼✳✶✳✶ ❚❡st❡ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✼✳✶✳✷ ❊♥tr♦♣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✼✳✷ ❊s♣❡❝✐✜❝❛çã♦ ❞♦ t❛♠❛♥❤♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ❜♦r❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✼✳✷✳✶ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ❜♦r❞❛ ♥♦ ❡✐①♦ ❞❛ s❡♥s✐t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ✼✳✷✳✷ ❉❡s❧♦❝❛♠❡♥t♦ ❡s♣❛❝✐❛❧ ❞❛s ❜♦r❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ✼✳✸ ❊①♣❡r✐♠❡♥t♦s ♣❛r❛ ❞❡✜♥✐çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♣❛ss♦s ❞❡ ❞❡ ♣ré✲✐♠❛❣❡♠ ♥❛
❝✐❢r❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✼✳✸✳✶ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ r❡t✐❝✉❧❛❞♦s ❝ú❜✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✼✳✸✳✷ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ r❡t✐❝✉❧❛❞♦s ✐rr❡❣✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✼✳✸✳✸ P❡rt✉r❜❛çã♦ ❞❡ ✶ ❜✐t ❞♦ ♥ú❝❧❡♦ ❞❛ r❡❣r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✽ ✼✳✹ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ ✐♠❛❣❡♥s r❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✼✳✹✳✶ ❆♥á❧✐s❡ ❞❡ ❤✐st♦❣r❛♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✼✳✹✳✷ ❊①♣❡r✐♠❡♥t♦s ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡❣r❛s ❞❡ ❛❧t❛ ❝❛r❞✐♥❛❧✐❞❛❞❡ ✳ ✳ ✶✹✸ ✼✳✹✳✸ ❚❡st❡ ❝♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s tr✐❞✐♠❡♥s✐♦♥❛❧ ❡ ❜✐❞✐♠❡♥s✐♦♥❛❧ ✶✺✷
✽ ❈♦♥❝❧✉sã♦ ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✶✺✺
✽✳✶ ❊s♣❡❝✐✜❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ✸❉❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼ ✽✳✶✳✶ ❊s♣❡❝✐✜❝❛çã♦ ♣❛❞rã♦ ♣❛r❛ ♦ ✸❉❍❈❆ ♥❛ ❝✐❢r❛❣❡♠ ❞❡ ✐♠❛❣❡♥s ❝♦❧♦r✐❞❛s✶✺✽ ✽✳✶✳✷ ❊s♣❡❝✐✜❝❛çã♦ ♣❛❞rã♦ ♣❛r❛ ♦ ✸❉❍❈❆ ♥❛ ❝✐❢r❛❣❡♠ ❞❡ ✐♠❛❣❡♥s ♥❛
①① ❙✉♠ár✐♦
✽✳✶✳✸ ❊s♣❡❝✐✜❝❛çã♦ ♣❛❞rã♦ ♣❛r❛ ♦ ✸❉❍❈❆ ♥❛ ❝✐❢r❛❣❡♠ ❞❡ ✐♠❛❣❡♥s ❜✐♥ár✐❛s✶✺✾ ✽✳✶✳✹ ❊s♣❡❝✐✜❝❛çã♦ ♣❛❞rã♦ ♣❛r❛ ♦ ✸❉❍❈❆ ♥❛ ❝✐❢r❛❣❡♠ ❞❡ t❡①t♦s ❧✐♥❡❛r❡s ✶✻✵ ✽✳✷ ❉❡✜♥✐çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ✸❉❍❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵ ✽✳✸ ❚r❛❜❛❧❤♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✻✺
❆ P❛râ♠❡tr♦ Z ✶✼✶
❇ ❈r✐♣t♦❣r❛✜❛ ❝❧áss✐❝❛ ✶✼✸
❇✳✶ ▼ét♦❞♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✭❙❤✐❢t✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸ ❇✳✷ ▼ét♦❞♦ ❞❡ s✉❜st✐t✉✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✺ ❇✳✸ ▼ét♦❞♦ ❞❡ tr❛♥s♣♦s✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻
❈ ❈r✐♣t♦❣r❛✜❛ ♠♦❞❡r♥❛ ✶✼✾
❈✳✶ ❈r✐♣t♦❣r❛✜❛ s✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾ ❈✳✶✳✶ ❊str✉t✉r❛ ❞❡ ❋❡✐st❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾ ❈✳✶✳✷ ❙✐st❡♠❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❉❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾ ❈✳✶✳✸ ❙✐st❡♠❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❆❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷ ❈✳✷ ❈r✐♣t♦❣r❛✜❛ ❛ss✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷ ❈✳✷✳✶ ❖ ❈r✐♣t♦s✐st❡♠❛ ❘❙❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷ ❈✳✷✳✷ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ❝r✐♣t♦s✐st❡♠❛s ❞❡ ❝❤❛✈❡ ♣ú❜❧✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✹
❉ ▼áq✉✐♥❛ ❞❡ ▼♦♦r❡ ✶✽✺
❊ ❊♥tr♦♣✐❛ ✶✽✼
❋ ❇❛♥❝♦ ❞❡ ✐♠❛❣❡♥s ✶✾✶
● ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛ ♣❛rt✐r ❞♦ ❜❛♥❝♦ ❞❡ ✐♠❛❣❡♥s ✶✾✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ✭❛✮ ❘❡❣r❛ ❞❡ tr❛♥s✐çã♦ ❞❡ r❛✐♦ ✶✳ ✭❜✮ ❘❡t✐❝✉❧❛❞♦ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ s❡♥❞♦ ❡✈♦❧✉í❞♦ ♣♦r T = 2 ♣❛ss♦s ❞❡ t❡♠♣♦ ✭❡✈♦❧✉çã♦ ❢♦r✇❛r❞✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✷✳✷ ❉✐❛❣r❛♠❛ ❡s♣❛ç♦✲t❡♠♣♦r❛❧ r❡♣r❡s❡♥t❛♥❞♦ ❛ ❡✈♦❧✉çã♦ ❞❡ ✉♠ ❆❈✳ ✭❛✮ r❡♣r❡✲ s❡♥t❛çã♦ ❜✐♥ár✐❛ ✭❜✮ r❡♣r❡s❡♥t❛çã♦ ♣♦r ♣✐①❡❧s ♣r❡t♦ ❡ ❜r❛♥❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✸ ✭❛✮ ❱✐③✐♥❤❛♥ç❛ ❞❡ ❱♦♥ ◆❡✉♠❛♥♥ ✷❉✳ ✭❜✮ ❱✐③✐♥❤❛♥ç❛ ❞❡ ▼♦♦r❡ ✷❉✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✹ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦ ❆❈ ❜✐❞✐♠❡♥s✐♦♥❛❧ ♣♦r ✽ ♣❛ss♦s ❞❡ t❡♠♣♦ ✉s❛♥❞♦ ❛
r❡❣r❛ ❞♦ ▲✐❢❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✺ ✭❛✮ ❱✐③✐♥❤❛♥ç❛ ❞❡ ❱♦♥ ◆❡✉♠❛♥♥ ✸❉✳ ✭❜✮ ❱✐③✐♥❤❛♥ç❛ ❞❡ ▼♦♦r❡ ✸❉✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✻ ❈♦♠♣♦rt❛♠❡♥t♦ ❞✐♥â♠✐❝♦ ❡♠ ❆❈s ❊❧❡♠❡♥t❛r❡s s❡❣✉♥❞♦ ❬▲✐✱ ✶✾✾✶❪ ✭❛✮ ❘❡✲
❣r❛ ✷✺✶✿ ♥✉❧❛✳ ✭❜✮ ❘❡❣r❛ ✸✻✿ ♣♦♥t♦ ✜①♦✳ ✭❝✮ ❘❡❣r❛ ✸✹✿ ♣♦♥t♦ ✜①♦✳ ✭❞✮ ❘❡❣r❛ ✸✼✿ ❝✐❝❧♦ ❞✉♣❧♦✳ ✭❡✮ ❘❡❣r❛ ✸✺✿ ❝✐❝❧♦ ❞✉♣❧♦✳ ✭❢✮ ❘❡❣r❛ ✹✶✿ r❡❣r❛ ♣❡r✐ó❞✐❝♦✳ ✭❣✮ ❘❡❣r❛ ✸✵✿ ❝❛ót✐❝❛✳ ✭❤✮ ❘❡❣r❛ ✶✶✵✿ ❝♦♠♣❧❡①❛ ❬❖❧✐✈❡✐r❛✱ ✷✵✵✸❪✳ ✹✵ ✷✳✼ ✭❛✮ ❘❡❣r❛ ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ à ❡sq✉❡r❞❛✳ ✭❜✮ ❘❡❣r❛ ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ à
❞✐r❡✐t❛✳ ✭❝✮ ❘❡❣r❛ ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ ❜✐❞✐r❡❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✽ ❊①❡♠♣❧♦ ❞❡ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ❝♦♠ ✈✐③✐♥❤❛♥ç❛ ❞❡t❡r♠✐♥íst✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✾ ❊①❡♠♣❧♦ ❞❡ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ❝♦♠ ✈✐③✐♥❤❛♥ç❛ ❛♠❜í❣✉❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✶✵ ❊①❡♠♣❧♦ ❞❡ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ❝♦♠ ✈✐③✐♥❤❛♥ç❛ ✐♠♣♦ssí✈❡❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✶✶ ✭❛✮ ■♥✐❝✐❛❧✐③❛çã♦ ✭❜✮ ❱❛❧✐❞❛çã♦ ✭❝✮ ❉❡s❝❛rt❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✶ ❈❛♥❛❧ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✶ ❊✈♦❧✉çã♦ ❞❡ ✉♠ r❡t✐❝✉❧❛❞♦ ♣♦r ✶✺ ♣❛ss♦s ❞❡ t❡♠♣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷ ✭❛✮ ■♥✐❝✐❛❧✐③❛çã♦ ❞♦s m−1 ❜✐ts✳ ✭❜✮ ❈á❧❝✉❧♦ ❞❛ ♣ré✲✐♠❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✸ ❊♥❝r✐♣t❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❘❡❣r❛ ✸✵ ✭❡✈♦❧✉çã♦ ❜❛❝❦✇❛r❞✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✹ ❉❡s❡♥❝r✐♣t❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❘❡❣r❛ ✸✵ ✭❡✈♦❧✉çã♦ ❢♦r✇❛r❞✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✺ ❆♥á❧✐s❡ ❞❛ ♣❡rt✉r❜❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✻ ✭❛✮ ■♥✐❝✐❛❧✐③❛çã♦ ❛❧❡❛tór✐❛✳ ✭❜✮ ❈á❧❝✉❧♦ ❞❛ ♣ré✲✐♠❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✼ ❊♥❝r✐♣t❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❘❡❣r❛ ✾✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✽ ❉❡s❡♥❝r✐♣t❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❘❡❣r❛ ✾✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✾ Pr♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ♣❛r❛ r❡❣r❛s ❝♦♠ s❡♥s✐t✐✈✐❞❛❞❡ ❜✐❞✐r❡❝✐♦♥❛❧✳ ✳ ✳ ✻✺
①①✐✐ ▲✐st❛ ❞❡ ❋✐❣✉r❛s
✹✳✶✵ ❘❡❣r❛s ❝❛♣❛③❡s ❞❡ r❡s♦❧✈❡r ❛ ❝♦♥❞✐çã♦ ✐♠♣♦st❛ ♣❡❧❛ r❡❣✐ã♦ ❞❡ ❝♦♥t♦r♥♦ ❞♦ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ♣r♦♣♦st♦ ♣♦r ❲✉❡♥s❝❤❡ ❡ ▲❡ss❡r✳ ✭❛✮ ❘❡❣r❛s s❡♥sí✈❡✐s à ❞✐r❡✐t❛✳ ✭❜✮ ❘❡❣r❛s s❡♥sí✈❡✐s à ❡sq✉❡r❞❛ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✶✶ ❈á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠ ♣❛ss♦ ❛ ♣❛ss♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❍❈❆✳ ✭❛✮
❘❡t✐❝✉❧❛❞♦ ✐♥✐❝✐❛❧✳ ✭❜✮ ❈á❧❝✉❧♦ ❞❛s ❝é❧✉❧❛s ❞❡ ❜♦r❞❛ ❛ ♣❛rt✐r ❞❛ r❡❣r❛ ❞❡ ❝♦♥t♦r♥♦✳ ✭❝ ✲ ❣✮ ❈á❧❝✉❧♦ ❞❛s ❞❡♠❛✐s ❝é❧✉❧❛s ❞❛ ♣ré✲✐♠❛❣❡♠ ❛ ♣❛rt✐r ❞❛ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✶✷ ❈á❧❝✉❧♦ ♣❛r❛❧❡❧♦ ❞❡ três ♣ré✲✐♠❛❣❡♥s ❞♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❍❈❆✳ ✭❛✮
❘❡t✐❝✉❧❛❞♦ ✐♥✐❝✐❛❧✳ ✭❜ ✲ ❦✮ ❈á❧❝✉❧♦ ♣❛ss♦ ❛ ♣❛ss♦ ❞❛s ❝é❧✉❧❛s ❞♦ r❡t✐❝✉❧❛❞♦ ❞❛ ♣ré✲✐♠❛❣❡♠ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✸ ❘❡❣r❛s ❞❡ tr❛♥s✐çã♦ ❜✐❞✐♠❡♥s✐♦♥❛✐s ✉t✐❧✐③❛❞❛s ♥♦ ❝á❧❝✉❧♦ ❞❡ ✉♠❛ ♣ré✲✐♠❛❣❡♠✳ ✼✼ ✹✳✶✹ ✭❛✮ ❘❡t✐❝✉❧❛❞♦ ✐♥✐❝✐❛❧ ✉t✐❧✐③❛❞♦ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝✐❢r❛❣❡♠✳ ✭❜✮ ■♥í❝✐♦ ❞♦ ❝á❧✲
❝✉❧♦ ♣ré✲✐♠❛❣❡♠ ❛ ♣❛rt✐r ❞❛s ❝é❧✉❧❛s ❞❛ ❜♦r❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✶✺ ❈á❧❝✉❧♦ ❞❛ ♣ré✲✐♠❛❣❡♠ ♥♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✶✻ ✭❛✮ ▼❛tr✐③ ❜✐♥ár✐❛ ❞❡16×16♣✐①❡❧s✳ ✭❜✮ ■♠❛❣❡♠ ❞♦ ❞✐sq✉❡t❡ ❝♦rr❡s♣♦♥❞❡♥t❡
à ♠❛tr✐③✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✶ ▼áq✉✐♥❛ ▼♦♦r❡ ❣❡♥ér✐❝❛ ♣❛r❛ ❆❈ ❞❡ r❛✐♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✷ ▼áq✉✐♥❛ ▼♦♦r❡ r❡❧❛t✐✈❛ à ❡①❡❝✉çã♦ f orward ❞❛ ❘❡❣r❛ ✸✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺✳✸ ▼áq✉✐♥❛ ▼♦♦r❡ r❡❧❛t✐✈❛ à ❡①❡❝✉çã♦ f orward ❞❡ ✉♠ ❆❈ ❤í❜r✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
✺✳✹ ❘❡❣r❛ ❞❡ tr❛♥s✐çã♦ s❡♥sí✈❡❧ à ❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✺ ❈á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✻ ❘❡❣r❛ ✐♥✈❡rs❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✼ ❘❡❣r❛ ✐♥❞✐r❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✽ ❘❡❣r❛ ✽✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✾ ▼áq✉✐♥❛ ❞❡ ▼♦♦r❡ ❣❡♥ér✐❝❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ♣ré✲✐♠❛❣❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✶✵ ✭❛✮ ▼áq✉✐♥❛ ❞❡ ▼♦♦r❡ r❡❧❛t✐✈❛ à ❡①❡❝✉çã♦ ❜❛❝❦✇❛r❞ ❞❛ ❘❡❣r❛ ✸✵✳ ✭❜✮
▼áq✉✐♥❛ ❞❡ ▼♦♦r❡ r❡❧❛t✐✈❛ à ❡①❡❝✉çã♦backward ❞❛ ❘❡❣r❛ ✽✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
✺✳✶✶ ▼áq✉✐♥❛ ❞❡ ▼♦♦r❡ ❞❛ ❡✈♦❧✉çã♦ ❜❛❝❦✇❛r❞ ♣❛r❛ ♦ ❆❈ ❤í❜r✐❞♦ ❞♦ ♠♦❞❡❧♦ ❍❈❆✳ ✾✶ ✻✳✶ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧✳ ✭❜✮ ■♠❛❣❡♠ ❝✐❢r❛❞❛ ♣♦r ❜❧♦❝♦s r❡s✉❧t❛♥❞♦ ❡♠ ③♦♥❛s
❞❡ t❡①t✉r❛s ❬❲✉ ❡t ❛❧✳✱ ✷✵✶✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✻✳✷ ❊①❡♠♣❧♦ ❞❡ ✐♠❛❣❡♠ ❘●❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✻✳✸ ✭❛✮ ❉♦♠í♥✐♦ ❡ ❈♦♥tr❛❞♦♠í♥✐♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ r❛✐♦ ✶✳ ✭❜✮
❚r❛♥s❢♦r♠❛çã♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ♣❛r❛ ✉♠❛ ✈✐③✐♥❤❛♥ç❛ ✉♥✐❞✐✲ ♠❡♥s✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✻✳✹ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❘●❇ ❞❡ t❛♠❛♥❤♦ 5×5 ♣✐①❡❧s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✻✳✺ ❊①❡♠♣❧♦ ❞❛ ✐♠❛❣❡♠ ❢r❛❣♠❡♥t❛❞❛ ❡♠ três ♠❛tr✐③❡s ❘✱ ● ❡ ❇ ❞❡ ♦r❞❡♠ ✺✳ ✳ ✶✵✵ ✻✳✻ ❊①❡♠♣❧♦ ❞❡ ✐♠❛❣❡♠ ❜✐❞✐♠❡♥s✐♦♥❛❧ tr❛♥s❢♦r♠❛❞❛ ❡♠ ✉♠ r❡t✐❝✉❧❛❞♦ tr✐❞✐✲
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①①✐✐✐
✻✳✼ ✭❛✮ ◗✉❛♥t✐❞❛❞❡ ❞❡ ❝é❧✉❧❛s ❞❛ ❜♦r❞❛ ❞♦ ♠♦❞❡❧♦ ✉♥✐❞✐♠❡♥s✐♦♥❛❧✳ ✭❜✮ ◗✉❛♥✲ t✐❞❛❞❡ ❞❡ ❝é❧✉❧❛s ❞❛ ❜♦r❞❛ ❞♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✳ ✭❝✮ ◗✉❛♥t✐❞❛❞❡ ❞❡ ❝é❧✉❧❛s ❞❛ ❜♦r❞❛ ❞♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✻✳✽ ❊①❡♠♣❧♦ ❞❡ ❝á❧❝✉❧♦ ❞❛ ♣ré✲✐♠❛❣❡♠ ♣❛r❛ r❛✐♦ ✶ ❡ s❡♥s✐t✐✈✐❞❛❞❡ ❛♦ ♥♦rt❡ ✳ ✳ ✶✵✺ ✻✳✾ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ ❞♦ ❜✐t ✐❞❡♥t✐✜❝❛❞♦ ♣♦r ✏❄✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✻✳✶✵ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ✐♠❛❣❡♠ ❝✐❢r❛❞❛ ♣♦r r❡❣r❛ ❞❡ r❛✐♦ ✶ ❡ s❡♥s✐t✐✈✐❞❛❞❡ ❛♦ ♥♦rt❡✳✶✵✽ ✻✳✶✶ ❊①❡♠♣❧♦ ❞❡ ❞❡❝✐❢r❛❣❡♠ ✭❡①❡❝✉çã♦ ❢♦r✇❛r❞✮ ♣❛r❛ r❛✐♦ ✶ ❡ s❡♥s✐t✐✈✐❞❛❞❡ ❛♦
♥♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✻✳✶✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✈✐③✐♥❤❛♥ç❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✻✳✶✸ ❊①❡♠♣❧♦ ❞❡ ✐♠❛❣❡♥s ❝✐❢r❛❞❛s ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ✸❉ s✐♠♣❧❡s✳ ✭❛✮ ■♠❛❣❡♠
❝♦♠ t♦❞♦s ♣✐①❡❧s ❜r❛♥❝♦s✳ ✭❜✮ ■♠❛❣❡♠ ✏❛✑ ❝✐❢r❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✭❝✮ ■♠❛❣❡♠ ♠❡✐♦ ❝✐r❝✉❧♦ ♣r❡t♦ ❡ ❜r❛♥❝♦✳ ✭❞✮ ■♠❛❣❡♠ ✏❝✑ ❝✐❢r❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✻✳✶✹ ❊①❡♠♣❧♦ ❞❡ ✐♠❛❣❡♥s ❝✐❢r❛❞❛s ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❜ás✐❝♦ ❝♦♠ ✐♥t❡r❝❛❧❛✲
çã♦✳✭❛✮ ■♠❛❣❡♠ ❝♦♠ t♦❞♦s ♣✐①❡❧s ❜r❛♥❝♦s✳ ✭❜✮ ■♠❛❣❡♠ ✏❛✑ ❝✐❢r❛❞❛ ✉t✐❧✐✲ ③❛♥❞♦ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✭❝✮ ■♠❛❣❡♠ ♠❡✐♦ ❝✐r❝✉❧♦ ♣r❡t♦ ❡ ❜r❛♥❝♦✳ ✭❞✮ ■♠❛❣❡♠ ✏❝✑ ❝✐❢r❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❣r❛ ♣r✐♥✲ ❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✻✳✶✺ ❉❡s❧♦❝❛♠❡♥t♦ ❞❡ ✉♠❛ ♣♦s✐çã♦ ❞❛ ❜♦r❞❛ ♥♦ ♠❡s♠♦ ❡✐①♦ ❞❛ s❡♥s✐t✐✈✐❞❛❞❡✳ ✳ ✶✶✽ ✻✳✶✻ ❉❡s❧♦❝❛♠❡♥t♦ ❡s♣❛❝✐❛❧ ❞❛s ❜♦r❞❛s ♥♦s três ❡✐①♦s ❝♦♠ ❛tr❛s♦ ❞❡ ✉♠ ❝✐❝❧♦ ❞❡
❝❧♦❝❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✻✳✶✼ ❉❡s❧♦❝❛♠❡♥t♦ ❡s♣❛❝✐❛❧ ❞❛s ❜♦r❞❛s ♥♦s três ❡✐①♦s ❝♦♠ ❛tr❛s♦ ❞❡ ❞♦✐s ❝✐❝❧♦s
❞❡ ❝❧♦❝❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✻✳✶✽ ❉❡s❧♦❝❛♠❡♥t♦ ❡s♣❛❝✐❛❧ ❞❛s ❜♦r❞❛s ❝♦♠ ❛tr❛s♦ ❞❡ q✉❛tr♦ ❝✐❝❧♦s ❞❡ ❝❧♦❝❦✳ ✳ ✳ ✶✷✵ ✻✳✶✾ ❊①❡♠♣❧♦ ❞❡ ✐♠❛❣❡♥s ❝✐❢r❛❞❛s ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❜❧♦❝♦ ú♥✐❝♦ ❝♦♠ ❞❡s✲
❧♦❝❛♠❡♥t♦✳✭❛✮ ■♠❛❣❡♠ ❝♦♠ t♦❞♦s ♣✐①❡❧s ❜r❛♥❝♦s✳ ✭❜✮ ■♠❛❣❡♠ ✏❛✑ ❝✐❢r❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✭❝✮ ■♠❛✲ ❣❡♠ ♠❡✐♦ ❝✐r❝✉❧♦ ♣r❡t♦ ❡ ❜r❛♥❝♦✳ ✭❞✮ ■♠❛❣❡♠ ✏❝✑ ❝✐❢r❛❞❛ ✉t✐❧✐③❛♥❞♦ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ❡ ❞❡ ❝♦♥t♦r♥♦ ✐♥❞✐❝❛❞❛s ♥❛ ❚❛❜❡❧❛ ✻✳✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✼✳✶ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ A✳ ✭❜✮ ■♠❛❣❡♠ ♣❡rt✉r❜❛❞❛ A′✳ ✭❝✮ ■♠❛❣❡♠ ❞♦ ❳❖❘
❡♥tr❡ A⊕A′✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹
✼✳✷ ✭❛✮ ■♠❛❣❡♠ ♣❧❛♥❛A❝✐❢r❛❞❛ ♣♦rT = 25✳ ✭❜✮ ■♠❛❣❡♠ ♣❡rt✉r❜❛❞❛A′
❝✐❢r❛❞❛ ♣♦r T = 25✳ ✭❝✮ ■♠❛❣❡♠ ❞♦ ❳❖❘ ❡♥tr❡ A⊕A′
①①✐✈ ▲✐st❛ ❞❡ ❋✐❣✉r❛s
✼✳✹ ✭❛✮ ❊①❡♠♣❧♦ ✶ ❞❡ r❡t✐❝✉❧❛❞♦ ❳❖❘ q✉❡ ♣r❡s❡r✈❛ ♣❛❞rã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ ✉t✐❧✐③❛♥❞♦ ♠♦❞❡❧♦ s❡♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❜♦r❞❛s✳ ✭❜✮ ❊①❡♠♣❧♦ ✷ ❞❡ r❡t✐❝✉✲ ❧❛❞♦ ❳❖❘ q✉❡ ♣r❡s❡r✈❛ ♣❛❞rã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ ✉t✐❧✐③❛♥❞♦ ♠♦❞❡❧♦ ❝♦♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❜♦r❞❛s✳ ✭❝✮ ❊①❡♠♣❧♦ ❞❡ r❡t✐❝✉❧❛❞♦ ❳❖❘ q✉❡ ♥ã♦ ❛♣r❡✲ s❡♥t❛ ♣❛❞rã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ ✉t✐❧✐③❛♥❞♦ ♠♦❞❡❧♦ ❝♦♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❜♦r❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ✼✳✺ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❞❡ 64×64 ♣✐①❡❧s ♥♦ ♣❛❞rã♦ ❘●❇✳ ✭❜✮ ❍✐st♦❣r❛♠❛ ❞♦
❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵ ✼✳✻ ✭❛✮ ■♠❛❣❡♠ ❝✐❢r❛❞❛ ❛ ♣❛rt✐r ❞❛ ✐♠❛❣❡♠ ❞❛ ❋✐❣✉r❛ ✼✳✺ ♣❛❞rã♦ ❘●❇✳ ✭❜✮
❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ✼✳✼ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❞❡ 64×64 ♣✐①❡❧s ♥♦ ♣❛❞rã♦ ❘●❇✳ ✭❜✮ ❍✐st♦❣r❛♠❛ ❞♦
❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶ ✼✳✽ ✭❛✮ ■♠❛❣❡♠ ❝✐❢r❛❞❛ ❛ ♣❛rt✐r ❞❛ ✐♠❛❣❡♠ ❞❛ ❋✐❣✉r❛ ✼✳✼ ♣❛❞rã♦ ❘●❇✳ ✭❜✮
❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷ ✼✳✾ ✭❛✮ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ ❞❡ 64×64 ♣✐①❡❧s ♥♦ ♣❛❞rã♦ ❘●❇✳ ✭❜✮ ❍✐st♦❣r❛♠❛ ❞♦
❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷ ✼✳✶✵ ✭❛✮ ■♠❛❣❡♠ ❝✐❢r❛❞❛ ❛ ♣❛rt✐r ❞❛ ✐♠❛❣❡♠ ❞❛ ❋✐❣✉r❛ ✼✳✾ ♥♦ ♣❛❞rã♦ ❘●❇✳ ✭❜✮
❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❘✳ ✭❝✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ●✳ ✭❞✮ ❍✐st♦❣r❛♠❛ ❞♦ ❝❛♥❛❧ ❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸ ✼✳✶✶ ❈♦♥❥✉♥t♦ ❞❛s ✶✵ ♣✐♦r❡s ✐♠❛❣❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺ ✼✳✶✷ ●rá✜❝♦s ❞♦s ❞❡s✈✐♦s ❞♦ ♣❡r❝❡♥t✉❛❧ ❞❡ ③❡r♦s ❡♠ r❡❧❛çã♦ ❛ ✺✵✪ ✉t✐❧✐③❛♥❞♦✲
s❡ ✷✺ ♣❛ss♦s ♥❛ ❝✐❢r❛❣❡♠✳ ✭❛✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✶✳ ✭❜✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✷✳ ✭❝✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✸✳ ✭❞✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽ ✼✳✶✸ ●rá✜❝♦s ❞♦s ❞❡s✈✐♦s ❞♦ ♣❡r❝❡♥t✉❛❧ ❞❡ ③❡r♦s ❡♠ r❡❧❛çã♦ ❛ ✺✵✪ ✉t✐❧✐③❛♥❞♦✲
s❡ ✸✵ ♣❛ss♦s ♥❛ ❝✐❢r❛❣❡♠✳ ✭❛✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✶✳ ✭❜✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✷✳ ✭❝✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✸✳ ✭❞✮ ❈♦♥❥✉♥t♦ ❞❡ ♥ú❝❧❡♦s ❢♦r♠❛❞♦s ❛ ♣❛rt✐r ❞❛ ♠ás❝❛r❛ ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵ ✼✳✶✹ ✭❛✮ ■♠❛❣❡♥s Pr❡t♦ ❡ ❇r❛♥❝♦ ♥♦ ♣❛❞rã♦ ❘●❇✳ ✭❜✮ ■♠❛❣❡♥s ❇✐♥ár✐❛s✳ ✳ ✳ ✳ ✳ ✶✺✸ ✼✳✶✺ ✭❛✮ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ❞♦ ♠♦❞❡❧♦ ✸❉ ❝♦♠ ✐♠❛❣❡♠ ♥♦ ♣❛❞rã♦ ❘●❇ ✭N =
64×64×24✮✳ ✭❜✮ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ❞♦ ♠♦❞❡❧♦ ✷❉ ❝♦♠ ✐♠❛❣❡♠ ♥♦ ♣❛❞rã♦
❘●❇ ✭N = (64×8)×(64×3)✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸
✼✳✶✻ ✭❛✮ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ❞♦ ♠♦❞❡❧♦ ✸❉ ❝♦♠ ✐♠❛❣❡♠ ❜✐♥ár✐❛ ✭N = 16×16×16✮✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①①✈
✽✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ✈✐③✐♥❤❛♥ç❛ ❞❛ r❡❣r❛ ❞❡ r❛✐♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼ ❆✳✶ ❈á❧❝✉❧♦ ❞♦ ♣❛râ♠❡tr♦ Z ❞❛ r❡❣r❛ ✶✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷
❇✳✶ ❆❧❢❛❜❡t♦ ♣♦rt✉❣✉ês ❬❙t✐♥s♦♥✱ ✷✵✵✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✹ ❇✳✷ ✭❛✮ ◆✉♠❡r❛çã♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ t❡①t♦ ♣❧❛♥♦✳ ✭❜✮ ◆✉♠❡r❛çã♦ ❝♦rr❡s♣♦♥✲
❞❡♥t❡ ❛♦ t❡①t♦ ❝✐❢r❛❞♦ ❬❙t✐♥s♦♥✱ ✷✵✵✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✹ ❇✳✸ ❋✉♥çã♦ ❞❡ ❡♥❝r✐♣t❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ s✉❜st✐t✉✐çã♦ ❬❙t✐♥s♦♥✱ ✷✵✵✻❪✳ ✳ ✳ ✳ ✳ ✳ ✶✼✺ ❇✳✹ ❋r❡q✉ê♥❝✐❛ ❞♦ ✉s♦ ❞❡ ❧❡tr❛s ♥❛ ❧í♥❣✉❛ ♣♦rt✉❣✉❡s❛ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻ ❇✳✺ ❊①❡♠♣❧♦ ❞♦ ♠ét♦❞♦ ❞❡ tr❛♥s♣♦s✐çã♦ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻ ❈✳✶ ❊str✉t✉r❛ ❞❡ ❋❡✐st❡❧ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✵ ❈✳✷ ❱❛❧♦r❡s ❞❡✜♥✐❞♦s ♣❡❧❛ ❙✲❜♦① ✻ ✭S6✮ ♥♦ ❉❊❙ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✶
❈✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❡t❛♣❛ ♥♦ ❉❊❙ ❬▼❛❝❡❞♦✱ ✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✶ ❊✳✶ ❏❛♥❡❧❛s ❞❛ s❡q✉ê♥❝✐❛ ❜✐♥ár✐❛ {0100101110011101}✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✽
❊✳✷ ❏❛♥❡❧❛s 2×4♣♦ssí✈❡✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾
❊✳✸ ❈♦♥str✉çã♦ ❞❛s ❥❛♥❡❧❛s ❞❡ ✉♠ r❡t✐❝✉❧❛❞♦ ❞❡ ♦r❞❡♠ 16×16✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾
●✳✶ ■♠❛❣❡♠ ♦r✐❣✐♥❛❧ ✉t✐❧✐③❛❞❛ ♥❛ ❝✐❢r❛❣❡♠ ✭✺✸✳♣♣♠✮ ❞❡64×64♣✐①❡❧s ♥♦ ♣❛❞rã♦
❘●❇ ❡ ♥♦ ❢♦r♠❛t♦ ❞❡ ✏P♦rt❛❜❧❡ P✐①❡❧ ▼❛♣✑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶ ●✳✷ ❊✈♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ s❡♥❞♦ ❝✐❢r❛❞❛ ♣♦r t ❂ ✶✱ ✷✱ ✳✳✳✱ ✷✺ ♣❛ss♦s ❞❡
t❡♠♣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✹ ●✳✸ ❊✈♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ♣❡rt✉r❜❛❞❛ s❡♥❞♦ ❝✐❢r❛❞❛ ♣♦r t ❂ ✶✱ ✷✱ ✳✳✳✱ ✷✺ ♣❛ss♦s
❞❡ t❡♠♣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✹ ●✳✹ ❊✈♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ❳❖❘ ❛♦ ❧♦♥❣♦ ❞❡ t ❂ ✶✱ ✷✱ ✳✳✳✱ ✷✺ ♣❛ss♦s ❞❡ t❡♠♣♦✳ ✳ ✳ ✷✵✺ ●✳✺ ❊✈♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ♦r✐❣✐♥❛❧ s❡♥❞♦ ❝✐❢r❛❞❛ ♣♦r t ❂ ✶✱ ✷✱ ✳✳✳✱ ✷✺ ♣❛ss♦s ❞❡
t❡♠♣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✼ ●✳✻ ❊✈♦❧✉çã♦ ❞❛ ✐♠❛❣❡♠ ♣❡rt✉r❜❛❞❛ s❡♥❞♦ ❝✐❢r❛❞❛ ♣♦r t ❂ ✶✱ ✷✱ ✳✳✳✱ ✷✺ ♣❛ss♦s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ Pr✐♥❝✐♣❛✐s t✐♣♦s ❞❡ ❛t❛q✉❡s ❛ s✐st❡♠❛s ❝r✐♣t♦❣rá✜❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✻✳✶ Pr✐♥❝✐♣❛✐s ❝♦r❡s ❡ r❡s♣❡❝t✐✈❛s r❡♣r❡s❡♥t❛çõ❡s ♣❛❞rã♦ ❘●❇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✻✳✷ ◆ú❝❧❡♦s ❞❛s r❡❣r❛s ✉t✐❧✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✻✳✸ ✭❳✮ ❇✐t ❞❡ s❛í❞❛ ❞❛ r❡❣r❛ ♣r✐♥❝✐♣❛❧ ✭❨✮ ❇✐t ❞❡ s❛í❞❛ ❞❛ r❡❣r❛ ❞❡ ❝♦♥t♦r♥♦✳ ✳ ✶✵✹ ✼✳✶ ❉❡s❧♦❝❛♠❡♥t♦ ❞❡ ✶ ❝é❧✉❧❛ ❞❛ ❜♦r❞❛ ♥♦ ❡✐①♦ ❞❛ s❡♥s✐t✐✈✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ✼✳✷ ❉❡s❧♦❝❛♠❡♥t♦ ❞❡ ✷ ❝é❧✉❧❛s ❞❛ ❜♦r❞❛ ♥♦ ❡✐①♦ ❞❛ s❡♥s✐t✐✈✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ✼✳✸ ❉❡s❧♦❝❛♠❡♥t♦ ❞❡ ✹ ❝é❧✉❧❛s ❞❛ ❜♦r❞❛ ♥♦ ❡✐①♦ ❞❛ s❡♥s✐t✐✈✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ✼✳✹ ❱❡r✐✜❝❛çã♦ ❞❛ ✐♥t❡r❢❡rê♥❝✐❛ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛s ❞❡♠❛✐s ❜♦r❞❛s ❞♦ r❡t✐❝✉❧❛❞♦✳✶✸✶ ✼✳✺ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦
❡♠ r❡t✐❝✉❧❛❞♦s 16×16×16✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷
✼✳✻ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❡♠ r❡t✐❝✉❧❛❞♦s 32×32×32✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸
✼✳✼ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❡♠ r❡t✐❝✉❧❛❞♦s 64×64×64✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸
✼✳✽ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❡♠ r❡t✐❝✉❧❛❞♦s 128×128×128✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹
✼✳✾ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❡♠ r❡t✐❝✉❧❛❞♦s 256×256×256✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹
✼✳✶✵ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣ré✲✐♠❛❣❡♥s ♥❡❝❡ssár✐❛s ♣❛r❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❡♠ r❡t✐❝✉❧❛❞♦s 512×512×512✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺
✼✳✶✶ ❊s♣❡❝✐✜❝❛çã♦ ❞❡t❛❧❤❛❞❛ ❞❛s ❝♦❧✉♥❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✼✳✶✷ ❊①♣❡r✐♠❡♥t♦ q✉❡ ❛✈❛❧✐❛ q✉❛❧ é ❛ ♠❡❧❤♦r ❞✐♠❡♥sã♦ ❞❡ ❝✐❢r❛❣❡♠ ♣❛r❛ ✉♠
r❡t✐❝✉❧❛❞♦ ❝♦♠ ❞✐♠❡♥sõ❡s ✐rr❡❣✉❧❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ✼✳✶✸ Pr♦♣❛❣❛çã♦ ❞❛ ♣❡rt✉r❜❛çã♦ ❞❡ ✉♠ ❜✐t ❞♦ ♥ú❝❧❡♦ ❞❛ r❡❣r❛✴❝❤❛✈❡ ❝r✐♣t♦❣rá✜❝❛✳✶✸✾ ✼✳✶✹ ❘❡s✉❧t❛❞♦ ❣❡r❛❧ ❞♦s ✹✵✵✵✵ ❡①♣❡r✐♠❡♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ✼✳✶✺ ❘❡s✉❧t❛❞♦ ❣❡r❛❧ ❞♦s ✹✵✵✵✵ ❡①♣❡r✐♠❡♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ✼✳✶✻ ❈♦♥❥✉♥t♦ ❞❛s q✉❛tr♦ ♠ás❝❛r❛s ❝♦♠ ❡♥tr♦♣✐❛s ♠❛✐s ❛❧t❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻ ✼✳✶✼ ❉✐str✐❜✉✐çã♦ ❞❡ ❢r❡q✉ê♥❝✐❛s ♣❛r❛ ❛s r❡❣r❛s ❣❡r❛❞❛s ❛ ♣❛rt✐r ❞❛s q✉❛tr♦ ♠ás✲
❝❛r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻
