❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❘❆❙❚❘❖❙ ❉❊ ❊❳❊❈❯➬➹❖ ❉❊
P❘❖●❘❆▼❆❙ P❆❘❆ ❈❖▼P❘❊❊◆❙➹❖ ❉❊ P❖◆❚❖❙ ❉❊
❱❆❘■❆➬➹❖ ❊▼ ❈Ó❉■●❖✲❋❖◆❚❊
❑▲➱❘■❙❙❖◆ ❱■◆❮❈■❯❙ ❘■❇❊■❘❖ ❉❆ P❆■❳➹❖
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❑▲➱❘■❙❙❖◆ ❱■◆❮❈■❯❙ ❘■❇❊■❘❖ ❉❆ P❆■❳➹❖
❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❘❆❙❚❘❖❙ ❉❊ ❊❳❊❈❯➬➹❖ ❉❊
P❘❖●❘❆▼❆❙ P❆❘❆ ❈❖▼P❘❊❊◆❙➹❖ ❉❊ P❖◆❚❖❙ ❉❊
❱❆❘■❆➬➹❖ ❊▼ ❈Ó❉■●❖✲❋❖◆❚❊
❉✐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♦✿ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❙♦❢t✇❛r❡✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ▼❛r❝❡❧♦ ❞❡ ❆❧♠❡✐❞❛ ▼❛✐❛
Dados Internacionais de Catalogação na Publicação (CIP) P149a Paixão, Klérisson Vinícius Ribeiro da, 1983-
Alinhamento de rastros de execução de programas para compreensão de pontos de variação em código-fonte / Klérisson Vinícius Ribeiro da Paixão. - 2009.
125 f. : il.
Orientador: Marcelo de Almeida Maia.
Dissertação (mestrado) – Universidade Federal de Uberlândia, Pro- grama de Pós-Graduação em Ciência da Computação.
Inclui bibliografia.
1. Engenharia de software - Teses. I. Maia, Marcelo de Almeida. II. Universidade Federal de Uberlândia. Programa de Pós-Graduação em Ciência da Computação. III. Título.
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛✲ ❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏❆❧✐♥❤❛♠❡♥t♦ ❞❡ r❛str♦s ❞❡ ❡①❡❝✉çã♦ ❞❡ ♣r♦❣r❛♠❛s ♣❛r❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ♣♦♥t♦s ❞❡ ✈❛r✐❛çã♦ ❡♠ ❝ó❞✐❣♦✲ ❢♦♥t❡✑ ♣♦r ❑❧ér✐ss♦♥ ❱✐♥í❝✐✉s ❘✐❜❡✐r♦ ❞❛ P❛✐①ã♦ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❯❜❡r❧â♥❞✐❛✱ ✶✸ ❞❡ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✵✾
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ▼❛r❝❡❧♦ ❞❡ ❆❧♠❡✐❞❛ ▼❛✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❙té♣❤❛♥❡ ❏✉❧✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s ❡ ❛ ◆♦ss❛ ❙❡♥❤♦r❛ ♣♦r t❡r❡♠ ♠❡ ❛❝♦♠♣❛♥❤❛❞♦ ❞✉r❛♥t❡ ♠❛✐s ❡ss❛ ❥♦r♥❛❞❛✳ ❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ▼❛r❝❡❧♦ ▼❛✐❛✱ ❝♦♠ q✉❡♠ ❡✉ t❛♥t♦ ❛♣r❡♥❞✐ s♦❜r❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❙♦❢t✇❛r❡ ❡ ♣❡sq✉✐s❛✳ ▼✐♥❤❛ ❛❞♠✐r❛çã♦ ♣❡❧❛ s✉❛ s❡r✐❡❞❛❞❡ ❡ ❞❡❞✐❝❛çã♦ ❛♦ s❡✉ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ ❡♠ ❡s♣❡❝✐❛❧ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡♠ ✈ár✐♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s✱ ♣❛❧❛✈r❛s ❞❡ ✐♥❝❡♥t✐✈♦ ❡ ❞❡ ❝rít✐❝❛✳
❆♦s ♠❡✉s ♣❛✐s✱ ❆❞✐❧s♦♥ ❡ ❱❛♥❥❛✱ ✐r♠ã♦s ❆♥❞r❡② ❡ ▼❛r❝❡❧♦✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ ♣❛❧❛✈r❛s ❞❡ s❛❜❡❞♦r✐❛✱ ❛♠♦r ❡ ❛♣♦✐♦ ❝♦♥st❛♥t❡s✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛✱ ❈rí❝✐❛✱ ♣♦r ❝♦♠♣r❡❡♥❞❡r ♣r♦❢✉♥❞❛♠❡♥t❡ ❛ ❞✐❢í❝✐❧ t❛r❡❢❛ ❞❡ tr✐❧❤❛r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ tr❛❜❛❧❤♦ ❞❡ ♠❡str❛❞♦✱ ♠❡ ❛♣♦✐❛♥❞♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧♠❡♥t❡ ❝♦♠ s❡✉ ❝❛r✐♥❤♦✱ ❛ q✉❛❧q✉❡r ♠♦♠❡♥t♦ ❡♠ q✉❡ ❡✉ ♥❡❝❡ss✐t❛ss❡✳
❆♦s ❛♠✐❣♦s ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❡str❛❞♦ ❯❋❯✴❋❆❈❖▼✱ ❝✉❥♦ ❛♣♦✐♦ ❡ ❛♠✐③❛❞❡ ♠❡ ❛❥✉✲ ❞❛r❛♠ ♠✉✐t♦ ♥❡ss❛ ❝❛♠✐♥❤❛❞❛✳ ❊♠ ❡s♣❡❝✐❛❧ ❛♦s ♣❛r❝❡✐r♦s ❞✐r❡t♦s ❞❡st❛ ♣❡sq✉✐s❛✱ ❋❡❧✐♣❡ ❈é③❛r✱ ❱✐❝t♦r ❙♦❜r❡✐r❛ ❡ ❘♦❞r✐❣♦ ❘❡✐s ♣❡❧❛ ❛♠✐③❛❞❡✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♠❡str❛❞♦ ❯❋❯✴❋❆❈❖▼✳
❆♦s ♣r♦❢❡ss♦r❡s ▼❛r❝♦ ❚ú❧✐♦ ❱❛❧❡♥t❡ ❡ ❙té♣❤❛♥❡ ❏✉❧✐❛ ♣♦r t❡r❡♠ ❛❝❡✐t❛❞♦ ♣❛rt✐❝✐♣❛r ❞❛ ♠✐♥❤❛ ❜❛♥❝❛ ❞❡ ♠❡str❛❞♦✳
❘❡s✉♠♦
➱ ❢❛t♦ ❝♦♥❤❡❝✐❞♦✱ q✉❡ ♠✉❞❛♥ç❛s sã♦ ✐♥❡r❡♥t❡s ❛ s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❚♦❞♦ s♦❢t✲ ✇❛r❡ ❞❡ s✉❝❡ss♦ ♣❛ss❛ ♣♦r ❝♦♥tí♥✉❛s ❡✈♦❧✉çõ❡s s❡❥❛ ♣❛r❛ ❛t❡♥❞❡r ❛s ♥♦✈❛s ❡①♣❡❝t❛t✐✈❛s ❞♦s ✉sú❛r✐♦s✱ ♠✉❞❛♥ç❛s ❞❡ ❤❛r❞✇❛r❡ ❡ ♠✉❞❛♥ç❛s ♥♦ ❛♠❜✐❡♥t❡ ♦♣❡r❛❝✐♦♥❛❧✳ ❈♦♥t✉❞♦✱ ✉♠ ❞♦s ♣r♦❜❧❡♠❛s ♠❛✐s s✐❣♥✐✜❝❛t✐✈♦s ♥❛s ❛t✉❛✐s ♣rát✐❝❛s ❞❡ ❡✈♦❧✉çã♦ ❞❡ s♦❢t✇❛r❡ é ❛ ❞✐✜❝✉❧❞❛❞❡ ❞♦s ♠❛♥t❡♥❡❞♦r❡s ❡♠ ❡♥❝♦♥tr❛r s❡çõ❡s ♥♦s ❝ó❞✐❣♦s ❢♦♥t❡s q✉❡ ♣r❡❝✐s❛♠ s❡r ❛❧t❡r❛❞❛s ♦✉ ♦♥❞❡ ♥♦✈❛s ❝❛r❛❝t❡ríst✐❝❛s ♣r❡❝✐s❛♠ s❡r ✐♥s❡r✐❞❛s✳ ❖✉tr♦ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ♥❛s r❡❢❛t♦✲ r❛çõ❡s ♣r♦❞✉③✐❞❛s ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ♠✉❞❛♥ç❛ q✉❡ t❛♠❜é♠ ♣♦❞❡♠ r❡♣r❡s❡♥t❛r ✉♠ ❞❡s❛✜♦ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❡♥tr❡ ❞✐❢❡r❡♥t❡s ✈❡rsõ❡s✳ ◆❡st❡ tr❛❜❛❧❤♦ é ♣r♦✲ ♣♦st♦ ✉♠ ♠❡❝❛♥✐s♠♦ ♣❛r❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝ó❞✐❣♦✲❢♦♥t❡ q✉❡ s❡r✈✐rã♦ ❞❡ ❜❛s❡ ♣❛r❛ ✐♥s❡rçã♦ ❞❡ ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❡♠ ✉♠ s✐st❡♠❛ ❡ ♣❛r❛ ❝♦♠♣❛r❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝ó❞✐❣♦ ❞❡ ✈❡rsõ❡s ❞✐❢❡r❡♥t❡s s♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞♦ ❝♦♥❝❡✐t♦ q✉❡ ❡❧❡s ✐♠♣❧❡♠❡♥t❛♠✳ ❊s♣❡❝✐✜❝❛♠❡♥t❡✱ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❜❛s❡✐❛✲s❡ ♥♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ ❞✉❛s s❡q✉ê♥❝✐❛s ❞❡ ❝❤❛♠❛❞❛s ❞❡ ♠ét♦❞♦s ♦❜t✐❞❛s ❞❛ ❡①❡❝✉çã♦ ❞❡ ❞❡t❡r♠✐♥❛❞❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❞♦ s✐st❡♠❛✳ ❖s ♣♦♥t♦s ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦ ♠♦str❛♠ ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ❞✉❛s ❢✉♥❝✐✲ ♦♥❛❧✐❞❛❞❡s s✐♠✐❧❛r❡s ♦✉ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❡♥tr❡ ❞✉❛s ✈❡rsõ❡s ❞✐❢❡r❡♥t❡s ❞♦ s✐st❡♠✳ ❖ ♠ét♦❞♦ é ✈❛❧✐❞❛❞♦ ❝♦♠ ❛ ❛♥á❧✐s❡ ❞❡ r❡s✉❧t❛❞♦s ♥❛ ❢❡r✲ r❛♠❡♥t❛ ❈❆❙❊ ❆r❣♦❯▼▲✳ ❊st❛ ❛❜♦r❞❛❣❡♠ ♠♦str♦✉✲s❡ út✐❧ ♣❛r❛ ♣r♦✈❡r ❧♦❝❛❧✐③❛çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❛rt❡❢❛t♦s ❞♦ ❝ó❞✐❣♦✲❢♦♥t❡ q✉❡ ❛❥✉❞❡♠ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ s✐st❡♠❛ ❞✐♠✐♥✉✐♥❞♦ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s q✉❡ ♦s ❞❡s❡♥✈♦❧✈❡❞♦r❡s ❞❡✈❡rã♦ ❛♥❛❧✐s❛r✳
❆❜str❛❝t
❚❤❡ ❢❛❝t t❤❛t r❡q✉✐r❡♠❡♥t ❝❤❛♥❣❡s ❛r❡ ✐♥❤❡r❡♥t ✐♥ s♦❢t✇❛r❡ ♣r♦❥❡❝ts ✐s ✇❡❧❧ ❦♥♦✇♥✳ ❆❧❧ s✉❝❝❡ss❢✉❧ s♦❢t✇❛r❡ ♠✉st ❝♦♥t✐♥✉❛❧❧② ❡✈♦❧✈❡ t♦ s✉♣♣♦rt ✉s❡r r❡q✉❡sts✱ ❤❛r❞✇❛r❡ ❝❤❛♥❣❡s ❛♥❞ ❡♥✈✐r♦♥♠❡♥t ❝❤❛♥❣❡s✳ ❍♦✇❡✈❡r✱ ❞✐s❝♦✈❡r✐♥❣ ✇❤❛t ❛r❡ t❤❡ s♦❢t✇❛r❡ ❛rt✐❢❛❝ts t❤❛t ♥❡❡❞ t♦ ❡✈♦❧✈❡ ♦r ✇❤❡r❡ ❛ ♥❡✇ ❢❡❛t✉r❡ ❤❛✈❡ t♦ ❜❡ ✐♥s❡rt❡❞ ✐s ❛ ♠❛❥♦r ❝❤❛❧❧❡♥❣❡ t♦ ❙♦❢t✇❛r❡ ▼❛✐♥t❡♥❛♥❝❡✳ ■♥ ❛❞❞✐t✐♦♥✱ ❞✐s❝♦✈❡r✐♥❣ ✇❤❡r❡ t❤❡ s♦✉r❝❡ ❝♦❞❡ ✇❛s r❡❢❛❝t♦r❡❞ ✐s ❛♥♦t❤❡r ♣r♦❜❧❡♠ t❤❛t ❤✐♥❞❡rs t❤❡ ❧♦❝❛t✐♦♥ ♦❢ ❝♦♥❝❡♣ts ✐♥ s♦✉r❝❡ ❝♦❞❡✳ ❚❤✐s ✇♦r❦ ♣r♦♣♦s❡s ❛ ♠❡t❤♦❞ t♦ ❧♦❝❛t❡ s♦✉r❝❡ ❝♦❞❡ ❛rt✐❢❛❝ts t❤❛t ✇✐❧❧ ❞r✐✈❡ t❤❡ ❡✈♦❧✉t✐♦♥ ♣r♦❝❡ss ✐♥ ♦r❞❡r t♦ ❛❞❞ ♥❡✇ ❢❡❛t✉r❡s ✐♥ t❤❡ s②st❡♠ ♦r t♦ ❝♦♠♣❛r❡ s♦✉r❝❡ ❝♦❞❡ ❛rt✐❢❛❝ts ❡①tr❛❝t❡❞ ❢r♦♠ ❞✐✛❡r❡♥t ✈❡rs✐♦♥s ♦❢ t❤❡ s❛♠❡ s②st❡♠ ✐♥ ♦r❞❡r t♦ ❛♥❛❧②s❡ ✇❤❡r❡ r❡❢❛❝t♦r✐♥❣s ❤❛✈❡ t❛❦❡♥ ♣❧❛❝❡✳ ❚❤❡ ❛♣♣r♦❛❝❤ ✐s ❜❛s❡❞ ♦♥ t❤❡ ♣❛✐r✇✐s❡ ❛❧✐❣♥♠❡♥t ♦❢ ♠❡t❤♦❞ ❝❛❧❧ s❡q✉❡♥❝❡s ♦❜t❛✐♥❡❞ ❢r♦♠ t❤❡ ❡①❡❝✉t✐♦♥ ♦❢ ♣r❡❞❡✜♥❡❞ ❢✉♥❝t✐♦♥❛❧✐t✐❡s✳ ❚❤❡ ♠✐s❛❧✐❣♥❡❞ ♣♦✐♥ts s❤♦✇ t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ t✇♦ s✐♠✐❧❛r ❢✉♥❝t✐♦♥❛❧✐t✐❡s ♦r t❤❡ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ s♦♠❡ ❢✉♥❝t✐♦♥❛❧✐t② ✐♥ t✇♦ ❞✐✛❡r❡♥t ✈❡rs✐♦♥s ♦❢ t❤❡ s②st❡♠✳❚❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞ ✐s ✈❛❧✐❞❛t❡❞ ✇✐t❤ t❤❡ ❛♥❛❧②s✐s ♦❢ t❤❡ ❆r❣♦❯▼▲ ❈❆❙❊ t♦♦❧✳ ❙♣❡❝✐✜❝❛❧❧②✱ t❤❡ ♠❡t❤♦❞ ❤❛✈❡ ♣r♦✈❡♥ t♦ ❜❡ ✉s❡❢✉❧ t♦ ❧♦❝❛t❡ ♣♦t❡♥t✐❛❧ s♦✉r❝❡ ❝♦❞❡ ❛rt✐❢❛❝t t❤❛t ❤❡❧♣s t❤❡ s②st❡♠ ❝♦♠♣r❡❤❡♥s✐♦♥ ✇✐t❤ t❤❡ r❡❞✉❝t✐♦♥ ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ❡❧❡♠❡♥ts t❤❛t t❤❡ ❞❡✈❡❧♦♣❡r s❤♦✉❧❞ ❛♥❧②s❡✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐
✶ ■♥tr♦❞✉çã♦ ✶✷
✶✳✶ ❊①♣♦s✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✷ ❍✐♣ót❡s❡s ❡ Pr♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✸ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✹ ❏✉st✐✜❝❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✺ ❱✐sã♦ ●❡r❛❧ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✷ ❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛ ❡ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❙❡qüê♥❝✐❛s ✶✻
✷✳✶ ❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✶✳✶ ❆♥á❧✐s❡ ❊stát✐❝❛ ❡ ❆♥á❧✐s❡ ❉✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❙❡qüê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷✳✶ ❉❡✜♥✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✷✳✷ ❆❧❢❛❜❡t♦s✱ ❙í♠❜♦❧♦s ❡ ❙❡qüê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✷✳✸ ❆❧✐♥❤❛♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✷✳✹ ❆❧✐♥❤❛♠❡♥t♦s ❞❡ P❛r❡s ❞❡ ❙❡qüê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✷✳✺ P♦♥t✉❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✷✳✻ ❋♦r♠❛❧✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷✳✼ ❆❧❣♦r✐t♠♦s ❞❡ Pr♦❣r❛♠❛çã♦ ❉✐♥â♠✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷✳✽ ❆❧❣♦r✐t♠♦ ◆❡❡❞❧❡♠❛♥ ❡ ❲✉♥s❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✸ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❘❛str♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✸✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❘❛str♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✸✳✷ ❆❧✐♥❤❛♠❡♥t♦ ▲♦❝❛❧ ✈s✳ ❆❧✐♥❤❛♠❡♥t♦ ●❧♦❜❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✸✳✸ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ P❛r❡s ❞❡ ❙❡qüê♥❝✐❛ ✈s✳ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ▼ú❧t✐♣❧❛s
❙❡qüê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✸✳✹ ❆❧✐♥❤❛♠❡♥t♦s ◆ã♦ ■❞ê♥t✐❝♦s ❡ ❈♦♠ ❊s♣❛ç♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✹ ❈♦♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
❙❯▼➪❘■❖ ✐①
✸ ❆❜♦r❞❛❣❡♠ Pr♦♣♦st❛ ♣❛r❛ ❈♦♠♣r❡❡♥sã♦ ❞❡ P♦♥t♦s ❞❡ ❱❛r✐❛çã♦ ✷✽ ✸✳✶ ❉❡✜♥✐çã♦ ❞❡ ❘♦t❡✐r♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✷ ▼ó❞✉❧♦ ❞❡ ❊①tr❛çã♦ ❞❡ ❘❛str♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✷✳✶ ▼❛r❝❛çã♦ ❞♦ ❘❛str♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❘❛str♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✹ ❊①❡♠♣❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✹✳✶ ❉❡✜♥✐çã♦ ❞❡ ❘♦t❡✐r♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✹✳✷ ❊①tr❛çã♦ ❞❡ ❘❛str♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✹✳✸ ❆❧✐♥❤❛♠❡♥t♦ ❞♦s ❘❛str♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✺ ❈♦♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹ ❊st✉❞♦ ❞❡ ❈❛s♦✿ ❆r❣♦❯▼▲ ✸✾
✹✳✶ ●♦❛❧ ◗✉❡st✐♦♥ ▼❡tr✐❝ ✭●◗▼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛ ❱✐❛❜✐❧✐❞❛❞❡ ❞❛ ❆❜♦r❞❛❣❡♠ Pr♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷✳✶ P❧❛♥❡❥❛♠❡♥t♦ ❞♦ ❊st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷✳✷ ❈♦♥t❡①t♦ ✶✿ ▼❡s♠❛ ❱❡rsã♦✱ ❋✉♥çõ❡s ■❣✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✷✳✸ ❈♦♥t❡①t♦ ✷✿ ▼❡s♠❛ ❱❡rsã♦✱ ❋✉♥çõ❡s ❙✐♠✐❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✷✳✹ ❈♦♥t❡①t♦ ✸✿ ❱❡rsõ❡s ❉✐❢❡r❡♥t❡s✱ ❋✉♥çõ❡s ■❣✉❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷✳✺ ❈♦♥t❡①t♦ ✹✿ ❱❡rsõ❡s ❉✐❢❡r❡♥t❡s✱ ❋✉♥çõ❡s ❙✐♠✐❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸ ❆✈❛❧✐❛çã♦ ❞❛ ❆❜♦r❞❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✺ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✺✼
✻ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✻✵
✻✳✶ ❈♦♥tr✐❜✉✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✻✳✷ ▲✐♠✐t❛çõ❡s ■❞❡♥t✐✜❝❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✻✳✸ ❚r❛❜❛❧❤♦ ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✻✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ P♦ssí✈❡❧ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❚❆●●❚❈❆ ❡ ❚❆●❈❚❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✷ ❖✉tr♦ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❚❆●●❚❈❆ ❡ ❚❆●❈❚❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✸ P♦❧ít✐❝❛ ❞❡ ♣♦♥t✉❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ ▼❛tr✐③ ❞❡ ♣♦♥t✉❛çã♦ ❡ ❛❧✐♥❤❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✺ ■♥✐❝✐❛❧✐③❛çã♦ ❞❛s ▼❛tr✐③❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✻ ❈á❧❝✉❧♦ ❞❡ ✉♠❛ ❝é❧✉❧❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✼ ▼❛tr✐③ ❞❡ s✉❜st✐t✉✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✽ ❈é❧✉❧❛ C(2,2) ♣r❡❡♥❝❤✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✾ ❋✐♥❛❧ ❞❛ s❡❣✉♥❞❛ ❡t❛♣❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✶✵ ■♥í❝✐♦ ❞❛ ❞❡❞✉çã♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✶ ❆❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❛❞❛♣t❛❞♦ ❞❡ ❬❞❆▼❙P+✵✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✷ ▼❛r❝❛çã♦ ❞❡ ✉♠ r❛str♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✸ ❘❡s✉❧t❛❞♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✹ ❆♣❧✐❝❛çã♦ ❛❧✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✶ ❊str✉t✉r❛ ❍✐❡rárq✉✐❝❛ ❞♦ ●◗▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷ ❊①❡♠♣❧♦ ♠♦❞❡❧♦ ●◗▼ ❬❉❞❙❑✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✸ ❊sq✉❡♠❛ ❞♦s ❡st✉❞♦s r❡❛❧✐③❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❊①❡♠♣❧♦ ❞❡ ❛❧✐♥❤❛♠❡♥t♦s ❡♥tr❡ ✸ s❡qüê♥❝✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✶ ❊①❡♠♣❧♦s ❞❡ r❛str♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✷ ▼ét♦❞♦s ❞❛ t❤r❡❛❞ ✶ ❞♦ r♦t❡✐r♦ ❞❡ ❡①❡❝✉çã♦ ❉❡s❡♥❤❛r ❘❡t❛ ❝♦♠ s❡✉s t✐✲
♠❡st❛♠♣s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✸ ▼ét♦❞♦s ❞❛ t❤r❡❛❞ ✶ ❞♦ r♦t❡✐r♦ ❞❡ ❡①❡❝✉çã♦ ❉❡s❡♥❤❛r ❈ír❝✉❧♦ ❝♦♠ s❡✉s
t✐♠❡st❛♠♣s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✹ ▼ét♦❞♦s ❡ ✐❞❡♥t✐✜❝❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✺ ❙❡❣♠❡♥t♦s ❡♥tr❡ ♦s r❛str♦s ❞♦s ❘♦t❡✐r♦ ❞❡ ❡①❡❝✉çã♦ ✶ ❡ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✻ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦s ✶ ❡ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✼ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦s ✶✵ ❡ ✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✽ ▼ét♦❞♦s s✉❣❡r✐❞♦s ♣❛r❛ ✐♠♣❧❡♠❡♥t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✶ ❙✉♠ár✐♦ ❞♦ ▼♦❞❡❧♦ ●◗▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷ ❙✉♠ár✐♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✸ ❙✉♠ár✐♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✹ ❈❤❛♠❛❞❛ ❞❡ ♠ét♦❞♦s ❞♦ s❡❣♠❡♥t♦ ✶✱ r♦t❡✐r♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✺ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦ ✷✽✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✻ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦ ✻✽✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✼ ▼ét♦❞♦s ❞❡s❛❧✐♥❤❛❞♦s ❞♦ r♦t❡✐r♦ ✶ ♥♦ s❡❣♠❡♥t♦ ✻✽✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✽ ▼ét♦❞♦ ❞❡s❛❧✐♥❤❛❞♦ ❞♦ r♦t❡✐r♦ ✷ ♥♦ s❡❣♠❡♥t♦ ✻✽✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✾ ❙✉♠ár✐♦ ❞♦s ❛rt❡❢❛t♦s ❞❡ ❝ó❞✐❣♦ ❛ s❡r❡♠ ❡st✉❞❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✶✵ ❙✉♠ár✐♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✶✶ ❙❡❣♠❡♥t♦ ✶✱ ❉✐❛❣r❛♠❛ ❞❡ ❈❧❛ss❡✱ ✈❡rsã♦ ✵✳✷✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✶✷ ❙❡❣♠❡♥t♦ ✶✱ ❉✐❛❣r❛♠❛ ❞❡ ❈❧❛ss❡✱ ✈❡rsã♦ ✵✳✷✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✶✸ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦ ✶✽✼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✹ ❆♥á❧✐s❡ ❞❡ ❞❡s❛❧✐♥❤❛♠❡♥t♦✿ ❙❡❣♠❡♥t♦ ✽✹✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✺ ❙✉♠ár✐♦ ❞♦s ❛rt❡❢❛t♦s ❞❡ ❝ó❞✐❣♦ ❛ s❡r❡♠ ❡st✉❞❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✻ ❙✉♠ár✐♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❞♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
➱ ❢❛t♦ q✉❡ ♠✉❞❛♥ç❛s sã♦ ✐♥❡r❡♥t❡s ❛ s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❬❇❘✵✵❪✳ ❚♦❞♦ s♦❢t✇❛r❡ ❞❡ s✉❝❡ss♦ ♣❛ss❛ ♣♦r ❝♦♥tí♥✉❛s ❡✈♦❧✉çõ❡s s❡❥❛ ♣❛r❛ ❛t❡♥❞❡r às ♥♦✈❛s ❡①♣❡❝t❛t✐✈❛s ❞♦s ✉s✉ár✐♦s✱ ♠✉❞❛♥ç❛s ❞❡ ❤❛r❞✇❛r❡✱ ♠✉❞❛♥ç❛s ♥♦ ❛♠❜✐❡♥t❡ ♦♣❡r❛❝✐♦♥❛❧✱ ❡t❝✳
❈♦♥t✉❞♦✱ ♣r♦✈❡r ❡✈♦❧✉çõ❡s ❝♦♠ ❢❛❝✐❧✐❞❛❞❡✱ r❛♣✐❞❡③ ❡ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❛✐♥❞❛ é ✉♠ ❣r❛♥❞❡ ❞❡s❛✜♦ ♣❛r❛ ❛ ❡♥❣❡♥❤❛r✐❛ ❞❡ s♦❢t✇❛r❡✱ ♣♦rq✉❡ ❛s ❛♣❧✐❝❛çõ❡s ❡stã♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠♣❧❡①❛s✳ ❊ss❛ ❝♦♠♣❧❡①✐❞❛❞❡ é ❝♦♥s❡qüê♥❝✐❛ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❛t❡♥❞❡r ❛ r❡q✉✐s✐t♦s s♦✜st✐❝❛❞♦s✱ ♦ q✉❡ ❞❡♠❛♥❞❛ ❛❜r❛♥❣❡♥t❡s ♠❡t♦❞♦❧♦❣✐❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ♥♦✈❛s ♥♦t❛çõ❡s ❞❡ ♠♦❞❡❧❛❣❡♠✱ ❧✐♥❣✉❛❣❡♥s ❞❡ ♣r♦❣r❛♠❛çã♦ ♠♦❞❡r♥❛s✱ t❡❝♥♦❧♦❣✐❛s ❞✐str✐❜✉í❞❛s✱ ❝♦♠♣♦♥❡♥t❡s r❡✉sá✈❡✐s✱ ❝❛✉s❛♥❞♦ ✐♠♣❛❝t♦ ❞✐r❡t♦ ♥❛s t❛r❡❢❛s ❞❡ ♠❛♥✉t❡♥çã♦ ❞❡ s♦❢t✇❛r❡ q✉❡ ♣♦r s✉❛ ✈❡③ ❝♦♥s✐st❡♠ ♥❛ ♠❛✐♦r ♣❛rt❡ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡✈♦❧✉çã♦✳
◆❛ ❧✐t❡r❛t✉r❛ ❬❇❘✵✵❪✱ ♠❛♥✉t❡♥çã♦ ❞❡ s♦❢t✇❛r❡ é✱ ❝♦♠✉♠❡♥t❡✱ ❝❧❛ss✐✜❝❛❞❛ ❡♠ ❝❛t❡❣♦r✐❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ r❛③ã♦ ❞❛s ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s✳ ❆❜❛✐①♦✱ s❡❣✉❡ t❛❧ ❝❧❛ss✐✜❝❛çã♦✿
P❡r❢❡❝t✐✈❛ ❆t❡♥❞❡r ♣❡❞✐❞♦s ❞♦ ✉s✉ár✐♦ ♣❛r❛ ♠♦❞✐✜❝❛r ❢✉♥çõ❡s ❡①✐st❡♥t❡s✱ ✐♥❝❧✉✐r ♥♦✈❛s ❢✉♥çõ❡s ❡ ❡❢❡t✉❛r ♠❡❧❤♦r❛♠❡♥t♦s ❣❡r❛✐s❀
❆❞❛♣t❛t✐✈❛ ❆❞❛♣t❛r ♦ s♦❢t✇❛r❡ ❛♦ ❛♠❜✐❡♥t❡❀ ❈♦rr❡t✐✈❛ ■❞❡♥t✐✜❝❛r ❡ ❝♦rr✐❣✐r ❡rr♦s❀
Pr❡✈❡♥t✐✈❛ ▼❡❧❤♦r❛r ❛ ♠❛♥✉t❡♥❛❜✐❧✐❞❛❞❡ ♦✉ ❝♦♥✜❛❜✐❧✐❞❛❞❡✳
■♠♣♦rt❛ r❡ss❛❧t❛r q✉❡ ❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞❛s t❛r❡❢❛s ❞❡ ♠❛♥✉t❡♥çã♦ tê♠ s✉❛ ♦r✐❣❡♠ ❡♠ ♥♦✈❛s r❡q✉✐s✐çõ❡s ❞♦ ✉s✉ár✐♦✱ ♦✉ s❡❥❛✱ tr❛t❛♠✲s❡ ❞❡ t❛r❡❢❛s ❞❡ ♠❛♥✉t❡♥çã♦ ♣❡r❢❡❝t✐✈❛ ❬❇❡♥✾✻✱❇❘✵✵❪✳
❖ ♣r♦❝❡ss♦ ❞❡ ❛❞✐❝✐♦♥❛r ♥♦✈❛s ❢✉♥çõ❡s ❛ ✉♠ s✐st❡♠❛ ❥á ❡①✐st❡♥t❡ é ❞❡♥♦♠✐♥❛❞♦ ❞❡ ♠✉❞❛♥ç❛ ✐♥❝r❡♠❡♥t❛❧✶✳ ❆s ❛t✐✈✐❞❛❞❡s ❞❛ ♠✉❞❛♥ç❛ ✐♥❝r❡♠❡♥t❛❧ sã♦ ❛s s❡❣✉✐♥t❡s ❬❋❘✵✼❪✿
✶❉♦ ✐♥❣❧ês ■♥❝r❡♠❡♥t❛❧ ❈❤❛♥❣❡✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ✶✸
✶✳ ■♥✐❝✐❛çã♦✿ ❆♥á❧✐s❡ ❞❛ ♠✉❞❛♥ç❛ r❡q✉❡r✐❞❛ ❡ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s r❡❧❡✈❛♥t❡s❀ ✷✳ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s✿ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ♥♦ ❝ó❞✐❣♦ ❢♦♥t❡✳
✸✳ ❆♥á❧✐s❡ ❞❡ ✐♠♣❛❝t♦✿ ■❞❡♥t✐✜❝❛çã♦ ❞♦ ❝♦♥❥✉♥t♦ ❝♦♠♣❧❡t♦ ❞❡ ❝❧❛ss❡s q✉❡ s❡rã♦ ❛❢❡t❛❞❛s ♣❡❧❛ ♠✉❞❛♥ç❛❀
✹✳ Pr❡❢❛❝t♦r✐♥❣✿ ❘❡❢❛t♦r❛çã♦ ❞♦ ♣r♦❣r❛♠❛ ♣❛r❛ ❢❛❝✐❧✐t❛r ❛ ♠✉❞❛♥ç❛❀
✺✳ ❆t✉❛❧✐③❛çã♦✿ ■♠♣❧❡♠❡♥t❛çã♦ ❞♦s ❝♦♥❝❡✐t♦s ❡ ✐♥❝♦r♣♦r❛çã♦ ❞♦ ♥♦✈♦ ❝ó❞✐❣♦ ♥♦ s✐st❡♠❛ ❥á ❡①✐st❡♥t❡❀
✻✳ Pr♦♣❛❣❛çã♦ ❞❛ ♠✉❞❛♥ç❛✿ ❈♦rr❡çã♦ ❞❛s ✐♥❝♦♥s✐stê♥❝✐❛s ❝❛✉s❛❞❛s ♣❡❧❛ ♣r♦♣❛❣❛çã♦ ❞❛ ♠✉❞❛♥ç❛❀
✼✳ P♦st❢❛❝t♦r✐♥❣✿ ❘❡❢❛t♦r❛çã♦ ♣❛r❛ ♠❡❧❤♦r❛r ❛ ❡str✉t✉r❛ ❞♦ s✐st❡♠❛❀
✽✳ ◆♦✈❛ ❜❛s❡✿ ❊♥tr❡❣❛ ♥♦ ♥♦✈♦ ❝ó❞✐❣♦✱ ❛t✉❛❧✐③❛çã♦ ❞❛ ❞♦❝✉♠❡♥tãçã♦ ❡ ❡♥tr❡❣❛ ❞❛ ♥♦✈❛ ✈❡rsã♦ ❛♦s ❝❧✐❡♥t❡s✳
▲♦❣♦ ♥❛ ❢❛s❡ ❞❡ ▲♦❝❛❧✐③❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❡♥❝♦♥tr❛✲s❡ ✉♠ ❞♦s ♣r♦❜❧❡♠❛s ♠❛✐s s✐❣♥✐✜✲ ❝❛t✐✈♦s ♥❛s ❛t✉❛✐s ♣rát✐❝❛s ❞❡ ❡✈♦❧✉çã♦ ❞❡ s♦❢t✇❛r❡ q✉❡ é ❛ ❞✐✜❝✉❧❞❛❞❡ ❞♦s ♠❛♥t❡♥❡❞♦r❡s ❡♠ ❡♥❝♦♥tr❛r s❡çõ❡s ♥♦s ❝ó❞✐❣♦s ❢♦♥t❡s q✉❡ ♣r❡❝✐s❛♠ s❡r ❛❧t❡r❛❞❛s ♦✉ ♦♥❞❡ ♥♦✈❛s ❝❛✲ r❛❝t❡ríst✐❝❛s ♣r❡❝✐s❛♠ s❡r ✐♥s❡r✐❞❛s ❬▲❨❈✵✵❪✳ ❱ár✐❛s ❛❜♦r❞❛❣❡♥s ❥á ❢♦r❛♠ ❛♣r❡♥s❡♥t❛❞❛s ♣❛r❛ ♠✐t✐❣❛r t❛❧ ♣r♦❜❧❡♠❛✳ ❚é❝♥✐❝❛s ❡stát✐❝❛s✱ ✐♥❝❧✉✐♥❞♦ ❝❛s❛♠❡♥t♦ ❞❡ ♣❛❞rã♦✱ ❛♥á❧✐s❡ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❝❧❛ss❡s ❡ r❡❝✉♣❡r❛çã♦ ❞❡ ✐♥❢♦r♠çã♦ sã♦ ❞❡t❛❧❤❛❞❛s ❡♠ ❬▼❘❇+✵✺❪✳
❚é❝♥✐❝❛s ❞✐♥â♠✐❝❛s ❢♦r❛♠ ❡①♣❧♦r❛❞❛s ❡♠ ❬❲❙✾✺✱❙❞❆▼✵✽❪✳ ❈♦♥t✉❞♦✱ ❝♦♠♦ ❡♥❝♦♥tr❛r ❛r✲ t❡❢❛t♦s ❡①❛t♦s ♣❛r❛ ❡❢❡t✉❛r ❛ ♠✉❞❛♥ç❛✱ ♦✉ ♠❡s♠♦ ♣♦♥t♦s q✉❡ ❞✐r❡❝✐♦♥❛rã♦ ❛s ♠✉❞❛♥ç❛s✱ sã♦ q✉❡stõ❡s ❛✐♥❞❛ ❛❜❡rt❛s✳
❆s r❡❢❛t♦r❛çõ❡s ♣r♦❞✉③✐❞❛s ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ♠✉❞❛♥ç❛ t❛♠❜é♠ ♣♦❞❡♠ r❡♣r❡s❡♥t❛r ✉♠ ❞❡s❛✜♦ ♣❛r❛ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❡♥tr❡ ❞✐❢❡r❡♥t❡s ✈❡rsõ❡s✱ ♣♦rq✉❡ ♦ ❝ó❞✐❣♦✲ ❢♦♥t❡ q✉❡ ✐♠♣❧❡♠❡♥t❛ ✉♠ ❝♦♥❝❡✐t♦ ❡♠ ✉♠❛ ✈❡rsã♦ ♣♦❞❡ t❡r s✐❞♦ ❛❧t❡r❛❞♦ ❡♠ ✉♠❛ ✈❡rsã♦ s❡❣✉✐♥t❡✱ ♠❡s♠♦ q✉❡ ♥ã♦ ❤❛❥❛ ♠✉❞❛♥ç❛ ❞❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✳
❖✉tr♦ ❢❛t♦ q✉❡ s❡ ♦❜s❡r✈❛ ♥❛ ♣rát✐❝❛ ❞❛ ❡♥❣❡♥❤❛r✐❛ ❞❡ s♦❢t✇❛r❡ é ♦ ✉s♦ r❡❝♦rr❡♥t❡ ❞❡ ❝ó♣✐❛s ❞❡ ❛rt❡❢❛t♦s ✭✏❝❧♦♥❡s✑✮ ♣❡❧♦s ♣r♦❣r❛♠❛❞♦r❡s ❞✉r❛♥t❡ ❛s t❛r❡❢❛s ❞❡ ♠❛♥✉t❡♥çã♦ ❬❑❇▲◆✵✹❪✳ ◗✉❛♥❞♦ s❡ t❡♠ ♥♦✈❛s ❞❡♠❛♥❞❛s ♣❛r❛ s❡r❡♠ ❛❞✐❝✐♦♥❛❞❛s ❛ ✉♠ s✐st❡♠❛ é ❝♦♠✉♠ ❡♥❝♦♥tr❛r ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s✱ ❥á ❡①✐st❡♥t❡s✱ s❡♠❡❧❤❛♥t❡s à r❡q✉❡r✐❞❛✳ P♦rt❛♥t♦✱ é ♣r✉❞❡♥t❡ q✉❡ ❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ s✐❣❛ ❛ ♠❡s♠❛ ❡str✉t✉r❛ ❞❛s ❞❡♠❛✐s ❛té ♠❡s♠♦ ♣❛r❛ ❢❛❝✐❧✐t❛r ❢✉t✉r❛s ♠❛♥✉t❡♥çõ❡s ❞❡s❞❡ q✉❡ s❡ ✉t✐❧✐③❡ té❝♥✐❝❛s ♣❛r❛ ❣❡r❡♥❝✐❛r ♦s ❝❧♦♥❡s ❝♦♠ ❡✜❝✐ê♥❝✐❛ ❬❑❙◆▼✵✺❪✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖
✶✳✶✳ ❊❳P❖❙■➬➹❖ ❉❖ P❘❖❇▲❊▼❆ ✶✹
❧✐③❛çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❛rt❡❢❛t♦s ❞♦ ❝ó❞✐❣♦✲❢♦♥t❡ q✉❡ ❛❥✉❞❡♠ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ s✐st❡♠❛ ❞✐♠✐♥✉✐♥❞♦ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s q✉❡ ♦s ❞❡s❡♥✈♦❧✈❡❞♦r❡s ❞❡✈❡rã♦ ❛♥❛❧✐s❛r✳
✶✳✶ ❊①♣♦s✐çã♦ ❞♦ Pr♦❜❧❡♠❛
❖ t❡♠❛ ♣r✐♥❝✐♣❛❧ ❞❛ ♣❡sq✉✐s❛ ❡stá ♥❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❛rt❡❢❛t♦s ❞♦ ❝ó❞✐❣♦✲❢♦♥t❡ q✉❡ s❡r✈✐rã♦ ❞❡ ❜❛s❡ ♣❛r❛ ❛❞✐çã♦ ❞❡ ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❡♠ ✉♠ s✐st❡♠❛ ❡ ♥❛ ❝♦♠♣❛r❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝ó❞✐❣♦ ❞❡ ✈❡rsõ❡s ❞✐❢❡r❡♥t❡s s♦❜ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞♦ ❝♦♥❝❡✐t♦ q✉❡ ❡❧❡s ✐♠♣❧❡♠❡♥t❛♠✳ ❉✐❛♥t❡ ❞✐st♦✱ ❢♦r❛♠ ❜✉s❝❛❞❛s r❡s♣♦st❛s ♣❛r❛ ❛s s❡❣✉✐♥t❡s ♣❡r❣✉♥t❛s✿
✶✳ ❉❛❞❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s q✉❡ ✐♠♣❧❡♠❡♥t❛♠ ❝♦♥❝❡✐t♦s s❡♠❡❧❤❛♥t❡s ♥♦ s✐st❡♠❛✿
✭❛✮ ❈♦♠♦ ✐♥s❡r✐r ✉♠❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ q✉❡ t❡♥❤❛ ❛rq✉✐t❡t✉r❛ ❡ ✐♠♣❧❡♠❡♥t❡ ❝♦♥❝❡✐t♦s s❡♠❡❧❤❛♥t❡s ❞❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❥á ❡①✐st❡♥t❡s ♥♦ s✐st❡♠❛❄
✭❜✮ ◗✉❛❧ ❛ s❡qüê♥❝✐❛ ❞❡ ❡✈❡♥t♦s q✉❡ ♦❝♦rr❡♠ ♥❛s ❡①❡❝✉çõ❡s ❞❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s s✐♠✐❧❛r❡s q✉❡ ♣♦❞❡♠ ❝♦♥tr✐❜✉✐r ♥❛ ✐♥t❡❣r❛çã♦ ❞❡ ✉♠❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ♥♦ s✐st❡♠❛❄
✭❝✮ ◗✉❛✐s ❛s ✈❛r✐❛❜✐❧✐❞❛❞❡s ♥❛ ❡①❡❝✉çã♦ ❞❡ ❢✉♥çõ❡s s✐♠✐❧❛r❡s ❞❡ ✉♠ s✐st❡♠❛❄ ✭❞✮ ◗✉❛✐s s❡qüê♥❝✐❛ ❞❡ ❡✈❡♥t♦s sã♦ ❝♦♠✉♥s ❛ ❞❡t❡r♠✐♥❛❞❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s❄ ✷✳ ❉❛❞❛s ✈❡rsõ❡s ❞✐❢❡r❡♥t❡s ❞❡ ✉♠ s✐st❡♠❛✿
✭❛✮ ❈♦♠♦ ✐❞❡♥t✐✜❝❛r ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❡✈♦❧✉çã♦ ❡♠ ✉♠❛ ❞❛❞❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❞❡ ✉♠ s✐st❡♠❛❄
✭❜✮ ❈♦♠♦ ✐❞❡♥t✐✜❝❛r ♠✉❞❛♥ç❛s ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ♦✉ ❛rq✉✐t❡t✉r❛✐s ❞❡ ✉♠❛ ❢✉♥❝✐♦✲ ♥❛❧✐❞❛❞❡ ❛tr❛✈és ❞❡ r❛str♦s ❞❡ ❡①❡❝✉çõ❡s❄
✶✳✷ ❍✐♣ót❡s❡s ❡ Pr♦♣♦st❛
◗✉❛♥❞♦ ❝♦♥s✐❞❡r❛✲s❡ ❛ ❛❞✐çã♦ ❞❡ ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❛ ✉♠ s✐st❡♠❛✱ é ♣♦ssí✈❡❧ q✉❡ ❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ t❡♥❤❛ ❛rq✉✐t❡t✉r❛ s❡♠❡❧❤❛♥t❡ ❛ ❛❧❣✉♠❛ ♣ré✲❡①✐st❡♥t❡ ♥♦ s✐st❡♠❛✳
❆ ❤✐♣ót❡s❡ ❞❡st❡ tr❛❜❛❧❤♦ é q✉❡✱ ✐❞❡♥t✐✜❝❛♥❞♦ ❛rt❡❢❛t♦s s❡♠❡❧❤❛♥t❡s ❡①✐st❡♥t❡s ❡♠ ✉♠ s✐st❡♠❛✱ ❛ ✐♥s❡rçã♦ ❞❡ ✉♠❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ s❡♠❡❧❤❛♥t❡ ❛ ❛❧❣✉♠❛ ❡①✐st❡♥t❡ ♣♦ss❛ t❡r s❡✉ t❡♠♣♦ ❡ ❡s❢♦rç♦ r❡❞✉③✐❞♦ ❥á q✉❡ s❡ s❛❜❡rá ♦♥❞❡ s❡rá ✐♥s❡r✐❞♦ ✉♠ ♥♦✈♦ ❛rt❡❢❛t♦ ❡ ❛té ❝♦♠♦ s❡rá s✉❛ ❢♦r♠❛ ✐♥✐❝✐❛❧✳
❆❧é♠ ❞✐ss♦✱ ✐❞❡♥t✐✜❝❛r ❝♦♠♦ ❡ s❡ ❢♦r❛♠ ❢❡✐t❛s ❡✈♦❧✉çõ❡s ❡♠ ✈❡rsõ❡s ❞✐❢❡r❡♥t❡s ❞❡ ✉♠ s✐st❡♠❛ é ✉♠ ❞❡s❛✜♦ ♣❛r❛ ♦s ❞❡s❡♥✈♦❧✈❡❞♦r❡s✱ s♦❜r❡♠❛♥❡✐r❛ q✉❛♥❞♦ ♥ã♦ s❡ t❡♠ ❞♦❝✉♠❡♥✲ t❛çã♦✳
❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖
✶✳✸✳ ❖❇❏❊❚■❱❖❙ ✶✺
❆ ♣r♦♣♦st❛ é ❢✉♥❞❛♠❡♥t❛❞❛ ♥♦ ✉s♦ ❞❡ té❝♥✐❝❛ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ s❡qüê♥❝✐❛s✳ ❆s s❡qüê♥❝✐❛ sã♦ r❛str♦s ❞❡ ❡①❡❝✉çã♦ ❞❡ s♦❢t✇❛r❡ ❞❡✜♥✐❞❛s ♣♦r r♦t❡✐r♦s ❞❡ ❡①❡❝✉çã♦✳
❆ ♣r✐♥❝✐♣❛❧ ❝♦♥tr✐❜✉✐çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ❡stá ❡♠ ♠♦str❛r ♣♦t❡♥❝✐❛✐s ❡❧❡♠❡♥t♦s ❞❡ ❝ó✲ ❞✐❣♦ q✉❡ ♣♦❞❡♠ ❞✐r❡❝✐♦♥❛r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✱ ❜❡♠ ❝♦♠♦ ❛ s❡qüê♥❝✐❛ ❞❡ ❡✈❡♥t♦s q✉❡ ❞❡✈❡rã♦ ♦❝♦rr❡r ♣❛r❛ q✉❡ ❛ ♥♦✈❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ s❡❥❛ ✐♥❝♦r♣♦r❛❞❛✳ ❆❧é♠ ❞✐ss♦✱ ♦✉tr❛ ❝♦♥tr✐❜✉✐çã♦ ❡stá ♥❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❝♦♠♦ ❢♦r❛♠ ❢❡✐t❛s ❡✈♦❧✉çõ❡s ❡♠ ✉♠❛ ❞❛❞❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✳
✶✳✸ ❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❛♣❧✐❝❛r té❝♥✐❝❛ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ r❛str♦s ❞❡ ❡①❡❝✉çã♦ ❞❡ ✉♠ ♣r♦❣r❛♠❛ ♣❛r❛ ❡①tr❛✐r ✐♥❢♦r♠❛çã♦ ❞♦ ❝ó❞✐❣♦✲❢♦♥t❡ q✉❡ ❞✐r❡❝✐♦♥❡♠ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ s✐st❡♠❛s ❞❡ ❢♦r♠❛ ❛ ❛❣✐❧✐③❛r t❛r❡❢❛s ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ♠❛♥✉t❡♥çã♦ ❞❡ s♦❢t✇❛r❡✳
✶✳✹ ❏✉st✐✜❝❛t✐✈❛s
❆s ♣rát✐❝❛s ❞❡ ❡✈♦❧✉çã♦ ❞❡ s✐st❡♠❛s ❡♥❢r❡♥t❛♠ ✉♠❛ ❞❡♠❛♥❞❛ ❝❛❞❛ ✈❡③ ♠❛✐♦r ♣♦r s♦❢t✇❛r❡ ❞❡ q✉❛❧✐❞❛❞❡ ❡ ❡♥tr❡❣✉❡ ❡♠ ♠❡♥♦r t❡♠♣♦✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ q✉❡ s❡ t❡♠ ❛ ❢❛③❡r ♣❛r❛ ❡✈♦❧✉✐r ✉♠ s✐st❡♠❛ t❡♠ ❝✉st♦s q✉❡ ✈❛r✐❛♠ ❞❡ ✹✵✪ ❛ ✻✵✪ ❞♦ ❝✉st♦ t♦t❛❧ ❞❡ ✉♠ s✐st❡♠❛ ❬❆❇❉▼✵✶❪✳
◆❡st❡ ❝♦♥t❡①t♦✱ ❛ r❡✉t✐❧✐③❛çã♦ ❞❡ s♦❢t✇❛r❡ r❡♣r❡s❡♥t❛ ✉♠❛ ár❡❛ ❞❛ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❙♦❢t✇❛r❡ q✉❡ ✈❡♠ ❣❛♥❤❛♥❞♦ ❢♦rç❛✳ ❊❧❛ ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❝r✐❛çã♦ ❞❡ s✐st❡♠❛s ❞❡ s♦❢t✇❛r❡ ❛ ♣❛rt✐r ❞❡ s♦❢t✇❛r❡ ♣r❡❡①✐st❡♥t❡✱ tr❛③❡♥❞♦ ❝♦♥s✐❣♦ ❛ ♣r♦♠❡ss❛ ❞❡ ❛✉♠❡♥t❛r ❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ❡ ❞✐♠✐♥✉✐r ❝✉st♦s ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✱ ❛❧é♠ ❞❡ ♠❡❧❤♦r❛r ❛ q✉❛❧✐❞❛❞❡ ❞♦ ♣r♦❞✉t♦✱ ❛tr❛✈és ❞❛ r❡✉t✐❧✐③❛çã♦ ❞❡ ❛rt❡❢❛t♦s ❞❡ s♦❢t✇❛r❡ ❥á t❡st❛❞♦s ❡ ✉t✐❧✐③❛❞♦s ❡♠ ♦✉tr♦s ❝♦♥t❡①t♦s✳
P♦rt❛♥t♦✱ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❛rt❡❢❛t♦s ♣♦t❡♥❝✐❛✐s q✉❡ ❞✐r❡❝✐♦♥❛♠ ❡✱ ♣♦r ❝♦♥s❡qüê❝✐❛✱ r❡❞✉③❛♠ ♦s ❝✉st♦s ❞♦s ♣r♦❝❡ss♦s ❞❡ ❝♦♠♣r❡❡♥sã♦ ❞❡ s♦❢t✇❛r❡ ♣❛r❛ ♣r♦✈❡r ❡✈♦❧✉çã♦ t♦r♥❛♠✲ s❡ ✈❛❧✐♦s♦s✳
✶✳✺ ❱✐sã♦ ●❡r❛❧ ❞❛ ❉✐ss❡rt❛çã♦
❈❛♣ít✉❧♦ ✷
❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛ ❡ ❆❧✐♥❤❛♠❡♥t♦ ❞❡
❙❡qüê♥❝✐❛s
◆❡st❡ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ✉♠❛ r❡✈✐sã♦ ♥❛ ❧✐t❡r❛t✉r❛ s♦❜r❡ ♦s ♣r✐♥❝✐♣❛✐s t❡♠❛s ❡♥✈♦❧✈✐❞♦s ♥❛ ♣❡sq✉✐s❛✱ ❞❡♥tr❡ ❡❧❡s✱ ❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛ ✭❙❡çã♦ ✷✳✶✮✱ ❆♥á❧✐s❡ ❉✐♥â♠✐❝❛ ✭❙❡çã♦ ✷✳✶✳✶✮ ❡ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❙❡qüê♥❝✐❛s ✭❙❡çã♦ ✷✳✷✮✳
✷✳✶ ❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛
❆ ❊♥❣❡♥❤❛r✐❛ ❘❡✈❡rs❛ ✭❊❘✮ ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦✿ ✏♦ ♣r♦❝❡ss♦ ❞❡ ❛♥á❧✐s❡ ❞❡ ✉♠ s✐st❡♠❛✱ ❛ ✜♠ ❞❡ ✐❞❡♥t✐✜❝❛r ♦s ❝♦♠♣♦♥❡♥t❡s ❞❡ss❡ s✐st❡♠❛ ❡ s❡✉s r❡❧❛❝✐♦♥❛♠❡♥t♦s ❡ ❝r✐❛r r❡♣r❡s❡♥t❛çõ❡s ❞♦ s✐st❡♠❛ ❡♠ ✉♠❛ ♦✉tr❛ ❢♦r♠❛ ♦✉ ❡♠ ✉♠ ♥í✈❡❧ ♠❛✐s ❛❧t♦ ❞❡ ❛❜str❛çã♦✑ ❬❈❈■✾✵❪✳
❆ ❊❘✱ ♥♦r♠❛❧♠❡♥t❡✱ ♦❜❥❡t✐✈❛ ❛ ❡①tr❛çã♦ ❞❡ ❞♦❝✉♠❡♥t❛çã♦ ❞❡ ♣r♦❥❡t♦ ❛ ♣❛rt✐r ❞♦ ❝ó❞✐❣♦✱ r❡♣r❡s❡♥t❛♥❞♦ ✉♠❛ ❛t✐✈✐❞❛❞❡ ♦✉ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ té❝♥✐❝❛s q✉❡ ✈✐s❛♠ ❢❛❝✐❧✐t❛r ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ✉♠ s♦❢t✇❛r❡ ❡①✐st❡♥t❡ ❬❱❛s✵✼❪✳ ◆❡st❡ ❝♦♥t❡①t♦ ❡①✐st❡♠ ✈ár✐♦s tr❛❜❛✲ ❧❤♦s ❡♥✈♦❧✈❡♥❞♦ ❞✐❢❡r❡♥t❡s ♦❜❥❡t✐✈♦s✱ ❝♦♠♦✿ r❡❞♦❝✉♠❡♥t❛çã♦ ❞❡ s♦❢t✇❛r❡✱ r❡❝✉♣❡r❛çã♦ ❞❡ ♣r♦❥❡t♦✱ r❡♠♦❞✉❧❛r✐③❛çã♦✱ r❡❝✉♣❡r❛çã♦ ❞❡ ❛rq✉✐t❡t✉r❛✱ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ♥♦ ❝ó❞✐❣♦✱ ❡①tr❛çã♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s✳
◆♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ❢♦✐ ❡①♣❧♦r❛❞❛ ❛ ❛t✐✈✐❞❛❞❡ ❞❡ ❧♦❝❛❧✐③❛çã♦ ❞❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ♥♦ ❝ó❞✐❣♦✳ ❊ss❛ ❛t✐✈✐❞❛❞❡ t❡♠ ❢✉♥❞❛♠❡♥t❛❧ ✐♠♣♦rtâ♥❝✐❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ ♠❛♥✉t❡♥çã♦ ❞❡ s♦❢t✇❛r❡ ✉♠❛ ✈❡③ q✉❡ ♦ ♣ré✲r❡q✉✐s✐t♦ ♣❛r❛ t❛❧ ❛t✐✈✐❞❛❞❡ é ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ s✐st❡♠❛ ❡ ❡ss❡ ❡♥t❡♥❞✐♠❡♥t♦ ❡stá ❞✐r❡t❛♠❡♥t❡ ❧✐❣❛❞♦ ❛♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ♥♦ ❝ó❞✐❣♦✳ ❖ ♣r✐♠❡✐r♦ ♣❛ss♦ ♣❛r❛ ❧♦❝❛❧✐③❛r ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❝♦♥s✐st❡ ♥❛ ❛♥á❧✐s❡ ❞♦s ❛rt❡❢❛t♦s ❞♦ ❝ó❞✐❣♦✳ ❉♦✐s t✐♣♦s ❞❡ ❛♥á❧✐s❡s sã♦ ❝♦♠✉♠❡♥t♦ ❛♣❧✐❝❛❞♦s✿ ❡stát✐❝❛ ❡ ❞✐♥â♠✐❝❛✳
❈❆P❮❚❯▲❖ ✷✳ ❊◆●❊◆❍❆❘■❆ ❘❊❱❊❘❙❆ ❊ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙
✷✳✷✳ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙ ✶✼
✷✳✶✳✶ ❆♥á❧✐s❡ ❊stát✐❝❛ ❡ ❆♥á❧✐s❡ ❉✐♥â♠✐❝❛
❆ ✜♠ ❞❡ ✐❞❡♥t✐✜❝❛r ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❞❡ ✉♠ ❝ó❞✐❣♦ t❛♥t♦ ❛ ❛♥á❧✐s❡ ❡stát✐❝❛ ❝♦♠♦ ❛ ❞✐♥â♠✐❝❛ ♣♦❞❡♠ s❡r ❞❡s❡♠♣❡♥❤❛❞❛s✳ ❙❡ ♣♦r ✉♠ ❧❛❞♦ ❛ ❛♥á❧✐s❡ ❡stát✐❝❛ ♣♦❞❡ ❡①tr❛✐r ✐♥❢♦r♠❛çõ❡s ❜ás✐❝❛s ❞♦ s♦❢t✇❛r❡✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ❛❝❡ss♦ ❛ ✈❛r✐á✈❡✐s ❡ ❣r❛❢♦s ❞❡ ❝❤❛♠❛❞❛s ❞❡ ♣r♦❝❡❞✐♠❡♥t♦s✱ ♣♦r ♦✉tr♦ ❧❛❞♦ ❛ ❛♥á❧✐s❡ ❞✐♥â♠✐❝❛ ❝♦♥s✐st❡ ♥❛ ❛♥á❧✐s❡ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❞❡ ✉♠❛ ♣r♦❣r❛♠❛ ❡♠ ❡①❡❝✉çã♦✱ ✐♥❢♦r♠❛♥❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛s s❡qüê♥❝✐❛s ❞❡ ❝❤❛♠❛❞❛s ❞❡ ❢✉♥çõ❡s✱ ♦s ✈❛❧♦r❡s ❞❡ ✈❛r✐á✈❡✐s✱ ❡t❝✳
P❛r❛ s❡ ❞❡s❝♦❜r✐r ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ❝❤❛♠❛❞❛s ❞❡ ❢✉♥çõ❡s✴♠ét♦❞♦s ❛ ❛♥á❧✐s❡ ❡stát✐❝❛ é s✉✜❝✐❡♥t❡✱ ♠❛s s❛❜❡r q✉❛✐s ♦❜❥❡t♦ ❞❡ ❝ó❞✐❣♦ r❡❛❧♠❡♥t❡ ✉t✐❧✐③❛✱ ♣♦❞❡ ❞❡♣❡♥❞❡r ❞♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ✉t✐❧✐③❛❞♦s ♦✉ ❝❛♠✐♥❤♦ ❡s❝♦❧❤✐❞♦ ♣❛r❛ ❡①❡❝✉t❛r ♦ ♣r♦❣r❛♠❛✱ s❡♥❞♦ ♥❡❝❡ssár✐❛ ❛ ❛♥á❧✐s❡ ❞✐♥â♠✐❝❛✳ ❆ ❛♥á❧✐s❡ ❞✐♥â♠✐❝❛ é ♠❡♥♦s ❣❡r❛❧ ❞♦ q✉❡ ❛ ❡stát✐❝❛✱ ♥♦ s❡♥t✐❞♦ ❞❡ q✉❡ ❡❧❛ ❢♦r♥❡❝❡ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❝❤❛♠❛❞❛ ❞♦ ♣r♦❣r❛♠❛ ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ♣❛rt✐❝✉❧❛r✳ ❯♠ ♠❡s♠♦ ♣r♦❣r❛♠❛ ❝♦♠ ♦✉tr♦s ❞✐❢❡r❡♥t❡s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ♣♦❞❡ ❢♦r♥❡❝❡r ♦✉tr❛s ✐♥❢♦r♠❛çõ❡s ❬❆◆◗✵✵❪✳
◆❡st❡ tr❛❜❛❧❤♦✱ s♦♠❡♥t❡ ❛ ❛♥á❧✐s❡ ❞✐♥â♠✐❝❛ ❢♦✐ ❡①♣❧♦r❛❞❛ ♣♦r ♣❡r♠✐t✐r r❡❧❛❝✐♦♥❛r ❛s ✈❛r✐❛çõ❡s ❞❡ ❡♥tr❛❞❛✱ r❡❧❛t✐✈❛s ❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✱ ❛♦s ❛❝♦♥t❡❝✐♠❡♥t♦s ✐♥t❡r♥♦s ❞♦s ♣r♦❣r❛♠❛s ❬❙♦❜❪✳
✷✳✷ ❆❧✐♥❤❛♠❡♥t♦ ❞❡ ❙❡qüê♥❝✐❛s
❆ ❇✐♦❧♦❣✐❛ ▼♦❧❡❝✉❧❛r é ✉♠❛ ❝✐ê♥❝✐❛ q✉❡ ❛♣r❡s❡♥t♦✉ ❛✈❛♥ç♦s s✐❣♥✐✜❝❛t✐✈♦s ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s✳ ❯♠ ❣r❛♥❞❡ ❞❡s❛✜♦ ❡♥❝♦♥tr❛❞♦ ♣❡❧♦ ❜✐ó❧♦❣♦s é ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠❛♥✐♣✉❧❛r ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çõ❡s ❣❡r❛❞❛s ❛ ♣❛rt✐r ❞❡ s❡✉s ❡①♣❡r✐♠❡♥t♦s✳ ❆ss✐♠✱ s✉r✲ ❣✐✉ ❛ ❇✐♦✐♥❢♦r♠át✐❝❛ q✉❡ ❛♣❧✐❝❛ té❝♥✐❝❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ♠❛t❡♠át✐❝❛s ❡ ❡st❛tíst✐❝❛s ♣❛r❛ tr❛t❛r s❡✉s ♣r♦❜❧❡♠❛s✳ ❯♠ ❞♦s ♣r♦❜❧❡♠❛s ♣r✐♥❝✐♣❛✐s ♥❡st❡ ❝♦♥t❡①t♦ é ❛ ❝♦♠♣❛r❛çã♦ ❞❡ s❡qüê♥❝✐❛s✳
❆ té❝♥✐❝❛ ♠❛✐s ❢r❡qü❡♥t❡♠❡♥t❡ ✉s❛❞❛ ♣❛r❛ ❝♦♠♣❛r❛r ❞✉❛s ♦✉ ♠❛✐s s❡qüê♥❝✐❛s ❞❡ ♥✉❝❧❡✲ ♦tí❞❡♦s ♦✉ ❛♠✐♥♦á❝✐❞♦s ❝♦♥s✐st❡ ❡♠ s♦❜r❡♣♦r ✉♠❛ ❝❛❞❡✐❛ s♦❜r❡ ♦✉tr❛ ❡ ❜✉s❝❛r s❡♠❡❧❤❛♥ç❛s ❡ ❞✐❢❡r❡♥ç❛s✱ ❛ q✉❛❧ é ❢♦r♠❛❧♠❡♥t❡ ❞❡♥♦♠✐♥❛❞❛ ❛❧✐♥❤❛♠❡♥t♦✳
❆❧❣✉♠❛s ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞❛ ❝♦♠♣❛r❛çã♦ ❞❡ s❡qüê♥❝✐❛s sã♦ ❛♣♦♥t❛❞❛s ♣♦r ❬❖▲P✵✶❪✿
✶✳ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❢✉♥çã♦ ❜✐♦❧ó❣✐❝❛ ♠❡❞✐❛♥t❡ ❤♦♠♦❧♦❣✐❛ ❞❡ s❡qüê♥❝✐❛s❀
✷✳ ❇✉s❝❛ ❞❡ ♣❛❞rõ❡s ❝♦♥s❡r✈❛❞♦s ❛♦ ❧♦♥❣♦ ❞❛ ❡✈♦❧✉çã♦ q✉❡ s❡r✈❡♠ ♣❛r❛ ✐❞❡♥t✐✜❝❛r ❡str✉t✉r❛s ❝♦♥s❡r✈❛❞❛s✱ r❡sí❞✉♦s ❢✉♥❝✐♦♥❛✐s q✉❡ ♣♦❞❡♠ ❞❡s❝r❡✈❡r ✉♠❛ ❢❛♠í❧✐❛ ♦✉ s✉❜✲❢❛♠í❧✐❛ ❞❡ ♣r♦t❡í♥❛s❀
❈❆P❮❚❯▲❖ ✷✳ ❊◆●❊◆❍❆❘■❆ ❘❊❱❊❘❙❆ ❊ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙
✷✳✷✳ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙ ✶✽
✹✳ ❈♦♥str✉çã♦ ❞❛ ❡str✉t✉r❛ ♠♦❧❡❝✉❧❛r ❛ ♣❛rt✐r ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ ♥✉❝❧❡♦tí❞❡♦s ❝♦♠ ✉♠❛ ♣r♦t❡í♥❛ ❞❡ ❡str✉t✉r❛ ❝♦♥❤❡❝✐❞❛ ❡✱ ♣♦r ❝♦♥s❡qüê♥❝✐❛✱ ❞❡t❡r♠✐♥❛r s✉❛ ❢✉♥çã♦ ❜✐♦❧ó❣✐❝❛❀
✺✳ ❊st✉❞♦s ❡✈♦❧✉t✐✈♦s ♣❛r❛ ❞❡✜♥✐r r❡❧❛çõ❡s ✜❧♦❣❡♥ét✐❝❛s ❡♥tr❡ s❡qüê♥❝✐❛s✳
❆s ♣r✐♠❡✐r❛s ❛❜♦r❞❛❣❡♥s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ✉s❛✈❛♠ té❝♥✐❝❛s ❞❡ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛✳ P♦st❡r✐♦r♠❡♥t❡✱ s✉r❣✐r❛♠ ♠♦❞❡❧♦s ❤❡✉ríst✐❝♦s ❡ ♣r♦❜❛❜✐❧íst✐❝♦s✳ ❚é❝♥✐❝❛s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛s ❝♦♠♦ r❡❞❡s ♥❡✉r❛✐s ❡ ❛❧❣♦r✐t♠♦s ❡✈♦❧✉t✐✈♦s ❢♦r❛♠ t❛♠❜é♠ ❞❡s❡♥✈♦❧✈✐❞❛s✳
✷✳✷✳✶ ❉❡✜♥✐çõ❡s
◆❡st❛ s❡çã♦ ❛♣r❡s❡♥t❛✲s❡ ❛s ❞❡✜♥✐çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ s❡qüê♥❝✐❛s✳ ❖ ❝♦♥t❡ú❞♦ ❞❡st❛ s❡çã♦ ❡stá ❜❛s❡❛❞♦ ❡♠ ❬❞❇✵✸❪✳
✷✳✷✳✷ ❆❧❢❛❜❡t♦s✱ ❙í♠❜♦❧♦s ❡ ❙❡qüê♥❝✐❛s
❯♠ ❛❧❢❛❜❡t♦Σé ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ ❡ ♥ã♦✲✈❛③✐♦✳ ❯♠ ❡❧❡♠❡♥t♦σ ∈Σé ❝❤❛♠❛❞♦ ❝❛r❛❝✲ t❡r❡ ♦✉ sí♠❜♦❧♦✳ ❯♠❛ s❡qüê♥❝✐❛ s s♦❜r❡ ♦ ❛❧❢❛❜❡t♦Σé ✉♠❛ s❡qüê♥❝✐❛s= (σ1, σ2, ..., σn)∈
Σn✱ ♦♥❞❡ n > 0 é ✉♠ ✐♥t❡✐r♦✳ ❙❡ s = σ
1, σ2, ..., σn ❞❡✜♥❡✲s❡ ♦ ❝♦♠♣r✐♠❡♥t♦ |s| ❞❡ s ♣♦r |s|=n✳ ❙❡ n = 0✭❡✱ ♣♦rt❛♥t♦✱ |s|= 0✮✱ ❡♥tã♦ s é ❝❤❛♠❛❞❛ s❡qüê♥❝✐❛ ✈❛③✐❛ ❡ é ❞❡♥♦t❛❞❛ ♣♦rε✳ ❙❡n>0é ✉♠ ✐♥t❡✐r♦ ❡σ ∈Σ✱ ❡♥tã♦ ❞❡♥♦t❛✲s❡ ♣♦rσn ❛ s❡qüê♥❝✐❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ♥ ❝✉❥♦s ❝❛r❛❝t❡r❡s sã♦ t♦❞♦s ✐❣✉❛✐s ❛σ✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s s❡qüê♥❝✐❛s s♦❜r❡ ♦ ❛❧❢❛❜❡t♦
Σ é ❞❡♥♦t❛❞♦ ♣♦r Σ∗✱ ❡♥q✉❛♥t♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞❛s ❛s s❡qüê♥❝✐❛s ♥ã♦✲✈❛③✐❛s s♦❜r❡ Σ é
❞❡♥♦t❛❞♦ ♣♦rΣ+✳
❯♠ s❡❣♠❡♥t♦ s[i..j] ❞❡ ✉♠❛ s❡qüê♥❝✐❛ s✱ ♣❛r❛ i 6 j✱ é ❛ s❡qüê♥❝✐❛ ❞❡✜♥✐❞❛ ♣♦r s[i..j] =σi, σi+1, ..., σj✳ ❙❡ i > j✱ ❞❡✜♥❡✲s❡ s[i..j] =ε✳
❯♠❛ s✉❜s❡qüê♥❝✐❛ s′ ❞❡ s é ✉♠❛ s❡qüê♥❝✐❛ s′ = σ
i1, σi2...σim ❡♠ q✉❡ i1, i2, ..., im ⊆
1,2, ..., n ❡i1 < i2 < ... < im✳ ◆❡ss❡ ❝❛s♦✱ t❛♠❜é♠ t❡♠✲s❡ q✉❡ s é ✉♠❛ s✉♣❡rs❡qüê♥❝✐❛ ❞❡
s′✳ ❆ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ✉♠ s❡❣♠❡♥t♦ ❡ ✉♠❛ s✉❜s❡qüê♥❝✐❛ ❞❡ s é q✉❡ ♦ ♣r✐♠❡✐r♦ s❡ ❝♦♥st✐t✉✐
❞❡ ✉♠❛ sér✐❡ ❞❡ ❝❛r❛❝t❡r❡s ❝♦♥s❡❝✉t✐✈♦s ❞❡ s✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ✉♠❛ s✉❜s❡qüê♥❝✐❛ ♣♦❞❡ s❡r ❝♦♥st✐t✉í❞❛ ❞❡ ❝❛r❛❝t❡r❡s q✉❡ ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❡st❡❥❛♠ ❝♦♥s❡❝✉t✐✈♦s ❡♠ s✳
❙❡Σé ✉♠ ❛❧❢❛❜❡t♦ t❛❧ q✉❡⊔∈/ Σ✱ ❞❡♥♦t❛♠♦s ♣♦rΣ′ ♦ ❛❧❢❛❜❡t♦ Σ′ = Σ∪ ⊔✳ ❖ sí♠❜♦❧♦
⊔é tr❛t❛❞♦ ❝♦♠♦ ❡s♣❡❝✐❛❧ ❡ é ❝❤❛♠❛❞♦ ❝❛r❛❝t❡r❡ ❜r❛♥❝♦ ♦✉ ❡s♣❛ç♦✳
✷✳✷✳✸ ❆❧✐♥❤❛♠❡♥t♦s
❙❡❥❛♠ k ✉♠ ✐♥t❡✐r♦ ♣♦s✐t✐✈♦ ❡s1, s2, ..., sk s❡qüê♥❝✐❛s s♦❜r❡ ✉♠ ❛❧❢❛❜❡t♦ Σ✱ ❝♦♠ |si|=
ni✱ ♣❛r❛ i = 1, ..., k✳ ❯♠ ❛❧✐♥❤❛♠❡♥t♦ ❆ ❞❡ s1, s2, ..., sk é ✉♠❛ ♠❛tr✐③ A = (Aij) ❞❡ ❞✐♠❡♥sõ❡s k ×n ❝♦♠ ❡♥tr❛❞❛s ❞❡ Σ′ = Σ∪ ⊔ ✭❡ ♥ > maxk
❈❆P❮❚❯▲❖ ✷✳ ❊◆●❊◆❍❆❘■❆ ❘❊❱❊❘❙❆ ❊ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙
✷✳✷✳ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙ ✶✾
P❛r❛ ✜❝❛r ♠❛✐s ❝❧❛r♦✱ ♣♦❞❡✲s❡ r❡❡s❝r❡✈❡r ❛ ❞❡✜♥✐çã♦ ❛❝✐♠❛ ❝♦♠♦✿ ✉♠ ❛❧✐♥❤❛♠❡♥t♦ ❆ ❞❡ s1, s2, ..., sk é ✉♠❛ ♠❛tr✐③ A = (Aij) ❞❡ ❞✐♠❡♥sõ❡s k×n ❝♦♠ ❡♥tr❛❞❛s ❞❡ Σ′ t❛❧ q✉❡✱ ♣❛r❛ ❝❛❞❛ ✐✱ ❡①✐st❡ ✉♠ ❝♦♥❥✉♥t♦Ji ={j1, j2, ..., jni} ⊆ {1,2, ..., n}✱ ❝♦♠j1 < j2 < ... < jni
❡ t❛❧ q✉❡Aij1Aij2...Aijni =si ❡ t❛❧ q✉❡ ♣❛r❛ t♦❞♦ j ∈ {1,2, ..., n} −Ji✱ t❡♠♦s Aij =⊔✳
❉✐③❡♠♦s q✉❡ ❞♦✐s ❝❛r❛❝t❡r❡s si[j] ❡ si′[j′] ❡stã♦ ❛❧✐♥❤❛❞♦s ❡♠ ❆ s❡ si[j] ❡ si′[j′] ❡stã♦
♥❛ ♠❡s♠❛ ❝♦❧✉♥❛ ❞❡ ❆✳
❙❡❥❛ A = (Aij) ✉♠ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ s1, s2, ..., sk✳ ❯♠ ❡s♣❛ç♦✶ ❞❡ si ♥♦ ❛❧✐♥❤❛♠❡♥t♦ ❆ é q✉❛❧q✉❡r s❡❣♠❡♥t♦ ♥ã♦✲✈❛③✐♦ ♠❛①✐♠❛❧ ❞❡ Ai ❝♦♠♣♦st♦ ❛♣❡♥❛s ❞❡ ❡s♣❛ç♦s✱ ✐st♦ é✱ ✉♠ ❡s♣❛ç♦ ❞❡ si ❡♠ ❆ é ✉♠ s❡❣♠❡♥t♦ Ai[j..j′] ❞❡Ai t❛❧ q✉❡✿
• j 6j′❀
• t♦❞♦s ♦s sí♠❜♦❧♦s ❞❡ ❞❡ Ai[j..j′] sã♦⊔❀
• ♥ã♦ s❡❥❛ ♣♦ssí✈❡❧ ❡st❡♥❞❡r Ai[j..j′] ❡♠ A
i ♣♦r ♠❡✐♦ ❞❡ ❡s♣❛ç♦s ❡♠ ❜r❛♥❝♦✱ ♦✉ s❡❥❛✱
j = 1 ♦✉Ai[j −1]6=⊔ ❡j′ =n ♦✉Ai[j′+ 1]6=⊔✳
❙❡❥❛♠s1, s2, ..., sks❡qüê♥❝✐❛s s♦❜r❡ ✉♠ ❛❧❢❛❜❡t♦Σ✳ ❉❡♥♦t❛✲s❡ ♣♦rAs1,s2,...,sk ♦ ❝♦♥❥✉♥t♦
❞❡ ❛❧✐♥❤❛♠❡♥t♦s ❡♥tr❡ ❛s s❡qüê♥❝✐❛ss1, s2, ..., sk✳ ◆❛ ❚❛❜❡❧❛ ✷✳✶ ❛♣r❡s❡♥t❛✲s❡ ✉♠ ♣❡q✉❡♥♦
❡①❡♠♣❧♦ ✐❧✉str❛t✐✈♦ ❞♦s ❝♦♥❝❡✐t♦s ❛♣r❡s❡♥t❛❞♦s✳
❆ ❇ ⊔ ⊔ ⊔
❆ ❇ ❈ ❉ ❊
❆ ⊔ ❈ ⊔ ❊
❚❛❜❡❧❛ ✷✳✶✿ ❊①❡♠♣❧♦ ❞❡ ❛❧✐♥❤❛♠❡♥t♦s ❡♥tr❡ ✸ s❡qüê♥❝✐❛s✳
✷✳✷✳✹ ❆❧✐♥❤❛♠❡♥t♦s ❞❡ P❛r❡s ❞❡ ❙❡qüê♥❝✐❛s
❆❧✐♥❤❛♠❡♥t♦s sã♦ ✉♠❛ ♠❛♥❡✐r❛ ❞❡ r❡❛❧✐③❛r ❝♦♠♣❛r❛çõ❡s ❡♥tr❡ s❡qüê♥❝✐❛s✳ ◆❛ ❋✐✲ ❣✉r❛ ✷✳✶ ❛♣r❡s❡♥t❛♠♦s ✉♠ ♣♦ssí✈❡❧ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❛s s❡qüê♥❝✐❛s ❞❡ ❝❛r❛❝t❡r❡s ❚❆●●❚❈❆ ❡ ❚❆●❈❚❆✳
❋✐❣✉r❛ ✷✳✶✿ P♦ssí✈❡❧ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❚❆●●❚❈❆ ❡ ❚❆●❈❚❆✳
❊♠❜♦r❛ ♦ ❛❧✐♥❤❛♠❡♥t♦ ❛❝✐♠❛ ♥ã♦ ❞❡♠♦♥str❡ q✉❡ ❛s ❞✉❛s s❡qüê♥❝✐❛s sã♦ ♣❛r❡❝✐❞❛s t❡♠♦s ♦✉tr♦ ♣♦ssí✈❡❧ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❛s ♠❡s♠❛s s❡qüê♥❝✐❛s ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✷ ♦♥❞❡ ✜❝❛ ❡✈✐❞❡♥t❡ q✉❡ ❛s s❡qüê♥❝✐❛s t❡♠ ♠✉✐t♦ ❡♠ ❝♦♠✉♠✿
❆s ú♥✐❝❛s ❞✐❢❡r❡♥ç❛s sã♦ ✉♠ ❝❛r❛❝t❡r ● ♥❛ ♣r✐♠❡✐r❛ s❡qüê♥❝✐❛ ♦❝✉♣❛♥❞♦ ♦ ❧✉❣❛r ❞❡ ✉♠ ❝❛r❛❝t❡r ❈ ♥❛ s❡❣✉♥❞❛ ❡ ✉♠ ❝❛r❛❝t❡r ❈ q✉❡ ❡stá ♣r❡s❡♥t❡ ♣r✐♠❡✐r❛ s❡qüê♥❝✐❛✱ ♠❛s q✉❡
❈❆P❮❚❯▲❖ ✷✳ ❊◆●❊◆❍❆❘■❆ ❘❊❱❊❘❙❆ ❊ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙
✷✳✷✳ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙ ✷✵
❋✐❣✉r❛ ✷✳✷✿ ❖✉tr♦ ❛❧✐♥❤❛♠❡♥t♦ ❡♥tr❡ ❚❆●●❚❈❆ ❡ ❚❆●❈❚❆✳
♥ã♦ ❡stá ♣r❡s❡♥t❡ ♥❛ s❡❣✉♥❞❛✳ ❆❧é♠ ❞✐ss♦✱ ♣❡r❝❡❜❡✲s❡ q✉❡ t❡♠♦s ✉♠ s❡❣♠❡♥t♦ ❞❡ três ❝❛r❛❝t❡r❡s ✐♥✐❝✐❛✐s q✉❡ sã♦ ✐❣✉❛✐s ♥❛s ❞✉❛s s❡qüê♥❝✐❛s✳
❆ ❜✉s❝❛ ♣♦r ❡✈✐❞ê♥❝✐❛s q✉❡ ❡①♣♦♥❤❛♠ ❛s s✐♠✐❧❛r✐❞❛❞❡s ❡ ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s s❡qüê♥❝✐❛s é ♦ q✉❡ ✐♥t❡r❡ss❛ às t❛r❡❢❛s ❞❡ ❛❧✐♥❤❛♠❡♥t♦✳ P♦r ✐ss♦✱ ♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❛ ❋✐❣✉r❛ ✷✳✷ ♣❛r❡❝❡ ♠❡❧❤♦r✱ ✉♠❛ ✈❡③ q✉❡ ♣❡r♠✐t❡ ✉♠❛ ❢á❝✐❧ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s s❡qüê♥❝✐❛s✳
▲♦❣♦ ♣❛r❛ ❞❡❝✐❞✐r q✉❛❧ ♦ ❛❧✐♥❤❛♠❡♥t♦ é ♦ ♠❡❧❤♦r✱ é ♥❡❝❡ssár✐♦ ❡st❛❜❡❧❡❝❡r ✉♠ ❝♦♥❝❡✐t♦ ❞❡ ✏♣♦♥t✉❛çã♦✑ ♣❛r❛ ❝❛❞❛ ❛❧✐♥❤❛♠❡♥t♦✳ ❚❛❧ ❝♦♥❝❡✐t♦ é ❡①♣❧♦r❛❞♦ ♥❛ s❡çã♦ s❡q✉✐♥t❡✳
✷✳✷✳✺ P♦♥t✉❛çõ❡s
❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ s❡qüê♥❝✐❛s é tr❛t❛❞♦ ❝♦♠♦ ✉♠ ♣r♦✲ ❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♠ ♦❜❥❡t✐✈♦ s✐♠♣❧❡s✳ P❛r❛ ❝❛❞❛ ♣❛r ❞❡ s❡qüê♥❝✐❛s✱ ♦ ❛❧✐♥❤❛♠❡♥t♦ q✉❡ ❡✈✐❞❡♥❝✐❛r ❛ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ s❡♠❡❧❤❛♥ç❛s s❡rá ♦ ♠❡❧❤♦r✳ ❯♠❛ ♠❛♥❡✐r❛ ✉s✉❛❧ ❞❡ ❛tr✐❜✉✐r ♣♦♥t✉❛çõ❡s ❛ ❛❧✐♥❤❛♠❡♥t♦s ❞❡ ❞✉❛s s❡qüê♥❝✐❛s é ❞❛❞❛ ♣❡❧❛ ❡str❛té❣✐❛ ❞❡✱ ❛ ❝❛❞❛ ❝♦❧✉♥❛ ❞❡ ✉♠ ❛❧✐♥❤❛♠❡♥t♦✱ ❛ss♦❝✐❛r ✉♠❛ ♣♦♥t✉❛çã♦ ❡ ❞❡✜♥✐r ❛ ♣♦♥t✉❛çã♦ ❞♦ ❛❧✐♥❤❛♠❡♥t♦ ❝♦♠♦ s❡♥❞♦ ❛ s♦♠❛ ❞❛s ♣♦♥t✉❛çõ❡s ❞❡ s✉❛s ❝♦❧✉♥❛s✳
P♦r ❡①❡♠♣❧♦✱ ♥❛ ❋✐❣✉r❛ ✷✳✸ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ♣♦ssí✈❡❧ ♣♦❧ít✐❝❛ ❞❡ ♣♦♥t✉❛çã♦✿
❋✐❣✉r❛ ✷✳✸✿ P♦❧ít✐❝❛ ❞❡ ♣♦♥t✉❛çã♦✳
❈❆P❮❚❯▲❖ ✷✳ ❊◆●❊◆❍❆❘■❆ ❘❊❱❊❘❙❆ ❊ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙
✷✳✷✳ ❆▲■◆❍❆▼❊◆❚❖ ❉❊ ❙❊◗Ü✃◆❈■❆❙ ✷✶
✷✳✷✳✻ ❋♦r♠❛❧✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛
❆ ♣♦♥t✉❛çã♦ ❞❡ ✉♠ ❛❧✐♥❤❛♠❡♥t♦ é ❞❡✜♥✐❞❛ ❝♦♠♦ ❛ s♦♠❛ ❞❛s ♣♦♥t✉❛çõ❡s ❞❡ s✉❛s ❝♦❧✉♥❛s✳ ■♥t✉✐t✐✈❛♠❡♥t❡✱ s❡ ♦ ❡sq✉❡♠❛ ❞❡ ♣♦♥t✉❛çã♦ ❛tr✐❜✉✐ ✏♣♦♥t✉❛çã♦ ❜❛✐①❛✑ ❛ ❝❛r❛❝t❡✲ r❡s ✏s❡♠❡❧❤❛♥t❡s✑ ❞❡ ✉♠ ❛❧❢❛❜❡t♦ ❡ ✏♣♦♥t✉❛çã♦ ❛❧t❛✑ ❛ ❝❛r❛❝t❡r❡s ✏❞✐❢❡r❡♥t❡s✑ ❞❡ ♠❡s♠♦ ❛❧❢❛❜❡t♦✱ ❡♥tã♦ ♦s ❛❧✐♥❤❛♠❡♥t♦s ❞❡ ♠❛✐♦r ✐♥t❡r❡ss❡ sã♦ ❛q✉❡❧❡s ❞❡ ✏♣❡q✉❡♥❛ ♣♦♥t✉❛çã♦✑✳ Pr♦❜❧❡♠❛ ✶✳✶ ✭❆❧✐♥❤❛♠❡♥t♦ ❞❡ P❛r❡s ❞❡ s❡qüê♥❝✐❛s ✭❆P❙✮✮ ❉❛❞❛s ❞✉❛s s❡qüê♥✲
❝✐❛s s ❡ t s♦❜r❡ ✉♠ ❛❧❢❛❜❡t♦ Σ ❡ ✜①❛❞♦ ✉♠ ❡sq✉❡♠❛ ❞❡ ♣♦♥t✉❛çã♦ ❝✱ ❡♥❝♦♥tr❛r ✉♠ ❛❧✐♥❤❛♠❡♥t♦ ❆ ❞❡ s ❡ t ❝✉❥❛ ♣♦♥t✉❛çã♦ ❝✭❆✮ s❡❥❛ ♠í♥✐♠❛✳
◆❛ ♣ró①✐♠❛ s❡çã♦✱ ❛♣r❡s❡♥t❛✲s❡ ❞♦✐s ❛❧❣♦r✐t♠♦s ❢✉♥❞❛♠❡♥t❛✐s✱ ❜❛s❡❛❞♦s ♥♦ ♣❛r❛❞✐❣♠❛ ❞❡ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛✱ q✉❡ ♣♦❞❡♠ s❡r ✉s❛❞♦s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞❡ ♣❛r❡s ❞❡ s❡qüê♥❝✐❛s✳
✷✳✷✳✼ ❆❧❣♦r✐t♠♦s ❞❡ Pr♦❣r❛♠❛çã♦ ❉✐♥â♠✐❝❛
❯♠ ❛❧❣♦r✐t♠♦ ❜❛s❡❛❞♦ ♥♦ ♣❛r❛❞✐❣♠❛ ❞❡ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛ ♦♣❡r❛ r❡s♦❧✈❡♥❞♦ ♣r♦✲ ❣r❡ss✐✈❛♠❡♥t❡ s✉❜♣r♦❜❧❡♠❛s ❞♦ ♣r♦❜❧❡♠❛ ♦r✐❣✐♥❛❧ ✭❣❡r❛❧♠❡♥t❡✱ ❡♠ ♦r❞❡♠ ❝r❡s❝❡♥t❡ ❞❡ t❛♠❛♥❤♦ ❞♦s s✉❜♣r♦❜❧❡♠❛s✮ ❡ ❛r♠❛③❡♥❛♥❞♦ ❛s s♦❧✉çõ❡s ❞❡ ❝❛❞❛ s✉❜♣r♦❜❧❡♠❛ ❡♠ ✉♠❛ t❛❜❡❧❛ ♣❛r❛ ✉♠ ♣♦ssí✈❡❧ ✉s♦ ♣♦st❡r✐♦r✳ ❆ ✐❞é✐❛ é ❡✈✐t❛r q✉❡ ❛❧❣✉♠ s✉❜♣r♦❜❧❡♠❛ s❡❥❛ r❡s♦❧✲ ✈✐❞♦ ✭❞❡s♥❡❝❡ss❛r✐❛♠❡♥t❡✮ ♠❛✐s ❞❡ ✉♠❛ ✈❡③✳ ❖✉tr❛ ❢♦r♠❛ ❞❡ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ♣❛r❛❞✐❣♠❛ é q✉❡ ❡❧❡ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ♠❛♥❡✐r❛ ❞❡ ❡①❡❝✉t❛r ♦s ♣❛ss♦s ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ r❡❝✉rs✐✈♦ ❡♠ ✉♠❛ ♦r❞❡♠ ❝♦♥✈❡♥✐❡♥t❡✱ ✉s❛♥❞♦ ✉♠❛ t❛❜❡❧❛ ♣❛r❛ ♠❛♥t❡r ❛s s♦❧✉çõ❡s ❞♦s s✉❜♣r♦❜❧❡♠❛s ❥á r❡s♦❧✈✐❞♦s ♣♦r ❝❤❛♠❛❞❛s r❡❝✉rs✐✈❛s ❞♦ ❛❧❣♦r✐t♠♦✳
❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛ ♣❛r❛ ♦ Pr♦❜❧❡♠❛ ❆P❙ ❢♦✐ ♣✉❜❧✐❝❛❞♦ ❡♠ ✶✾✼✵ ♣♦r ◆❡❡❞❧❡♠❛♥ ❡ ❲✉♥s❝❤ ❬◆❲✼✵❪✱ ❡ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ❛ ♣r✐♠❡✐r❛ ❝♦♥tr✐❜✉✐çã♦ ✐♠♣♦r✲ t❛♥t❡ ❡♠ ♣r♦❝❡❞✐♠❡♥t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♣❛r❛ ❛ ❝♦♠♣❛r❛çã♦ ❞❡ s❡qüê♥❝✐❛s✳ ❖ ❛❧❣♦r✐t♠♦✱ ♠✉✐t♦ ♠♦❞✐✜❝❛❞♦ ❞❡s❞❡ ❡♥tã♦ ♣♦r ✈ár✐♦s ♣❡sq✉✐s❛❞♦r❡s✱ ❢♦✐ ♠❡❧❤♦r❛❞♦ ❡♠ r❡❧❛çã♦ à ❝♦♠✲ ♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ❡ ❞❡ ❡s♣❛ç♦✱ ❝♦♠♦ t❛♠❜é♠ ❢♦✐ ❛❞❛♣t❛❞♦ ♣❛r❛ ♦✉tr♦s ♣r♦❜❧❡♠❛s✳ ■♠♣♦rt❛ ❞❡st❛❝❛r ✉♠❛ ❞❛s ❛❞❛♣t❛çõ❡s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❡ ♣♦♣✉❧❛r❡s ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❙♠✐t❤ ❡ ❲❛t❡r♠❛♥ ❡♠ ✶✾✽✶✱ ♣❛r❛ ❝♦♠♣✉t❛r ❛❧✐♥❤❛♠❡♥t♦s ❧♦❝❛✐s ❬❙❲✽✶❪✳
❆ s❛❜❡r✱ ♥❛ ❧✐t❡r❛t✉r❛ ❡♥❝♦♥tr❛♠✲s❡ ❜❛s✐❝❛♠❡♥t❡ ❞✉❛s ❢♦r♠❛s ❞✐❢❡r❡♥t❡s ❞❡ ❛❧✐♥❤❛♠❡♥✲ t♦s q✉❡ sã♦ ❛♣r❡s❡♥t❛❞♦s ❛ s❡❣✉✐r✿
