❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❆P▲■❈❆◆❉❖ ❚➱❈◆■❈❆❙ ❉❊ ❆P❘❊◆❉■❩❆❉❖ ❉❊ ▼➪◗❯■◆❆
❊▼ P▲❆◆❊❏❆▼❊◆❚❖
❏❊❆◆ ▲❯❈❆❙ ❉❊ ❙❖❯❙❆
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❏❊❆◆ ▲❯❈❆❙ ❉❊ ❙❖❯❙❆
❆P▲■❈❆◆❉❖ ❚➱❈◆■❈❆❙ ❉❊ ❆P❘❊◆❉■❩❆❉❖ ❉❊ ▼➪◗❯■◆❆
❊▼ P▲❆◆❊❏❆▼❊◆❚❖
❉✐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❧♦s ❘♦❜❡rt♦ ▲♦♣❡s
Dados Internacionais de Catalogação na Publicação (CIP) Sistema de Bibliotecas da UFU
S725a 2014
Sousa, Jean Lucas de, 1990-
Aplicando as técnicas de aprendizado de máquina em planejamen- to / Jean Lucas de Sousa. -- 2014.
101 f. : il.
Orientador: Carlos Roberto Lopes.
Dissertação (mestrado) – Universidade Federal de Uberlândia, Pro- grama de Pós-Graduação em Ciência da Computação.
Inclui bibliografia.
1. Computação - Teses. 2. Aprendizado do computador - Teses. 3. Planejamento - Teses. I. Lopes, Carlos Roberto, 1962- 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✉❧❛❞❛ ✏❆♣❧✐❝❛♥❞♦ ❚é❝♥✐❝❛s ❞❡ ❆♣r❡♥❞✐③❛❞♦ ❞❡ ▼áq✉✐♥❛ ❡♠ P❧❛♥❡❥❛♠❡♥t♦✑ ♣♦r ❏❡❛♥ ▲✉❝❛s ❞❡ ❙♦✉s❛ ❝♦♠♦ ♣❛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❧♦s ❘♦❜❡rt♦ ▲♦♣❡s ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢❛✳ ❉r❛✳ ❘✐t❛ ▼❛r✐❛ ❞❛ ❙✐❧✈❛ ❏✉❧✐❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❉❛t❛✿ ❥✉♥❤♦ ❞❡ ✷✵✶✹
❆✉t♦r✿ ❏❡❛♥ ▲✉❝❛s ❞❡ ❙♦✉s❛
❚ít✉❧♦✿ ❆♣❧✐❝❛♥❞♦ ❚é❝♥✐❝❛s ❞❡ ❆♣r❡♥❞✐③❛❞♦ ❞❡ ▼áq✉✐♥❛ ❡♠ P❧❛♥❡❥❛✲ ♠❡♥t♦
❋❛❝✉❧❞❛❞❡✿ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈♦♠♣✉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♦✳✳✳
❆ ♠✐♥❤❛ ❢❛♠í❧✐❛ ❡ ♥❛♠♦r❛❞❛✱ q✉❡ ♠❡ ❛♣♦✐❛r❛♠ ❡ ❛❝r❡❞✐t❛r❛♠ ❡♠ ♠✐♠✳✳✳
❆♦s ❝♦❧❡❣❛s✱ ❝♦♠♣❛♥❤❡✐r♦s ❞❡ ✈✐❛❣❡♥s✱ ❛♠✐❣♦s✱ q✉❡ ❢♦r❛♠ t❛♥t♦s✱ ♠❛s ❡ss❡♥❝✐❛✐s à r❡❛❧✐✲ ③❛çã♦ ❞❡ss❛ ❡t❛♣❛✳✳✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ PP●❈❈✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ▼ár❝✐❛✱ ●✐♥❛✱ ❘✐t❛ ❡ ❉✐♥♦✱ ♣r♦❢❡ss♦r❡s ❞❛ ■❆✱ q✉❡ ❝♦♠♣❛rt✐❧❤❛r❛♠ s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ♠❡ ❛♣r❡s❡♥t❛r❛♠ ♠✉✐t❛s ❞❛s té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s ♥❡ss❡ tr❛❜❛❧❤♦✳✳✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❈❛r❧♦s✱ q✉❡ ♠❡ ❡♥❝❛♠✐♥❤♦✉ s❡♠♣r❡ ♥❛s ♠❡❧❤♦r❡s ❞✐r❡çõ❡s ♣❛r❛ ❛ ♣❡s✲ q✉✐s❛✳✳✳
❘❡s✉♠♦
❊♠ t❡r♠♦s ❞❡ ❛❜♦r❞❛❣❡♠ ❝❧áss✐❝❛✱ s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♦✉ ♣❧❛♥❡❥❛❞♦r❡s ❝♦♥❝❡♥tr❛♠✲ s❡ ❡♠ ❣❡r❛r ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❛çõ❡s q✉❡ tr❛♥s❢♦r♠❛ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ✭❡st❛❞♦✮ ✐♥✐❝✐❛❧ ❞❡ ♦❜❥❡t♦s ❡♠ ♦✉tr♦ ❡st❛❞♦ ❡♠ q✉❡ ✉♠ ❞❛❞♦ ♦❜❥❡t✐✈♦ é s❛t✐s❢❡✐t♦✳ ❙✐s✲ t❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♣❛r❛ r❡s♦❧✈❡r ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ♣r♦❜❧❡♠❛s ❝♦♠ s✉❝❡ss♦✳ ❆♣❡s❛r ❞✐ss♦✱ ♥❡♥❤✉♠ ♣❧❛♥❡❥❛❞♦r é ♠❡❧❤♦r q✉❡ t♦❞♦s ♦s ♦✉tr♦s q✉❛♥❞♦ ❛♣❧✐❝❛❞♦s ❛ ♣r♦❜❧❡♠❛s ❞✐st✐♥t♦s✳
❖ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦ é ✉♠❛ ❡①t❡♥sã♦ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ q✉❡ tr❛❜❛❧❤❛ s♦❜r❡ ✉♠ ❛♠❜✐❡♥t❡ ♥ã♦ ❞❡t❡r♠✐♥íst✐❝♦✳ ❆ss✐♠ ❝♦♠♦ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✱ ❞✐✈❡rs♦s ♣❧❛♥❡❥❛❞♦r❡s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s✱ ♣♦ré♠ ♥❡♥❤✉♠ ♣❧❛♥❡❥❛❞♦r é ❝❛♣❛③ ❞❡ s✉♣❡r❛r t♦t❛❧♠❡♥t❡ ♦s ♦✉tr♦s ❡♠ t♦❞♦s ♦s ♣r♦❜❧❡♠❛s✳
◆❡st❡ tr❛❜❛❧❤♦✱ ❞❡s❝r❡✈❡✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ q✉❡ ❝♦♥s✐st❡ ❡♠ ❡①tr❛✐r ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♣r♦❜❧❡♠❛ ❛ s❡r r❡s♦❧✈✐❞♦ ❡ ❞❡t❡r♠✐♥❛r✱ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❧❛♥❡❥❛❞♦r❡s ❝❧áss✐❝♦s ❡ ♣r♦❜❛❜✐❧íst✐❝♦s✱ ✉♠ q✉❡ s❡❥❛ ❝❛♣❛③ ❞❡ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❝♦♠ ❡✜❝✐ê♥❝✐❛✳ ❊♠ ♥♦ss❛ ❛❜♦r✲ ❞❛❣❡♠✱ sã♦ ✉t✐❧✐③❛❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ ♠❡❧❤♦r ♣❧❛♥❡❥❛❞♦r ❞❡♥tr❡ ♦ ♣♦rt❢ó❧✐♦ q✉❡ r❡s♦❧✈❡ ♦ ♣r♦❜❧❡♠❛✳
❆ s❡❧❡çã♦ ❞♦s ♣❧❛♥❡❥❛❞♦r❡s s❡ ♠♦str♦✉ ❡✜❝✐❡♥t❡ ♥♦s t❡st❡s t❡♥❞♦ ♠♦str❛❞♦ ❜♦♥s r❡✲ s✉❧t❛❞♦s ♥♦s ❡①♣❡r✐♠❡♥t♦s ❛♦ s✉♣❡r❛r ♦s ♣❧❛♥❡❥❛❞♦r❡s ❞❡ ♣♦rt❢ó❧✐♦ q✉❡ ❝♦♥s❡❣✉✐r❛♠ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♥❛s ❝♦♠♣❡t✐çõ❡s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ ❛♠❜❛s ❛s ár❡❛s ✭♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❡ ♣r♦❜❛❜✐❧íst✐❝♦✮✳
❆❜str❛❝t
■♥ t❡r♠s ♦❢ ❝❧❛ss✐❝❛❧ ♣❧❛♥♥✐♥❣✱ ♣❧❛♥♥❡rs ♦❜❥❡❝t✐✈❡s ❛r❡ ❣❡♥❡r❛t❡ ❛ s❡q✉❡♥❝❡ ♦❢ ❛❝t✐♦♥s t❤❛t ❝♦♥✈❡rts ❛♥ ✐♥✐t✐❛❧ ❝♦♥✜❣✉r❛t✐♦♥ ✭st❛t❡✮ ✐♥t♦ ❛♥♦t❤❡r st❛t❡ t❤❛t ❛tt❡♥❞s ❛ ❣♦❛❧✳ P❧❛♥✲ ♥✐♥❣ s②st❡♠s ❤❛✈❡ ❜❡❡♥ ✉s❡❞ ✐♥ s♦❧✈✐♥❣ ❛ ✈❛r✐❡t② ♦❢ ♣r♦❜❧❡♠s ✇✐t❤ s✉❝❝❡ss✳ ❍♦✇❡✈❡r✱ ♥♦ ♣❧❛♥♥❡r ✐s ❝❛♣❛❜❧❡ ♦❢ ♦✉t♣❡r❢♦r♠✐♥❣ ❛❧❧ t❤❡ ♦t❤❡rs ✇❤❡♥ ❛♣♣❧✐❡❞ t♦ ❞✐st✐♥❝t ♣r♦❜❧❡♠s✳
Pr♦❜❛❜✐❧✐st✐❝ ♣❧❛♥♥✐♥❣ ✐s ❛♥ ❡①t❡♥s✐♦♥ ♦❢ ❝❧❛ss✐❝❛❧ ♣❧❛♥♥✐♥❣ t❤❛t ✇♦r❦s ✇✐t❤ st♦❝❤❛st✐❝ ❡♥✈✐r♦♥♠❡♥ts✳ ❏✉st ❛s ✐♥ ❝❧❛ss✐❝❛❧ ♣❧❛♥♥✐♥❣✱ s❡✈❡r❛❧ ♣❧❛♥♥❡rs ✇❡r❡ ♣r♦♣♦s❡❞ t♦ s♦❧✈❡ ♣r♦✲ ❜❛❧✐st✐❝ ♣❧❛♥♥✐♥❣ ♣r♦❜❧❡♠s✳ ❍♦✇❡✈❡r✱ ♥♦ ♣❧❛♥♥❡r ✐s ❝❛♣❛❜❧❡ ♦❢ ♦✉t♣❡r❢♦r♠ ❛❧❧ ♦t❤❡rs ✇❤❡♥ ❛♣♣❧✐❡❞ t♦ ❞✐st✐♥❝t ♣r♦❜❧❡♠s✳
■♥ t❤✐s ✇♦r❦ ✇❡ ❞❡s❝r✐❜❡ ♦✉r ❛♣♣r♦❛❝❤ t❤❛t ✐s ❝❛♣❛❜❧❡ ♦❢ ❡①tr❛❝t✐♥❣ ❢❡❛t✉r❡s ♦❢ ❛ ♣❧❛♥♥✐♥❣ ♣r♦❜❧❡♠ ❛♥❞ ❞❡t❡r♠✐♥✐♥❣ ❛ ❝❧❛ss✐❝❛❧ ♦r ♣r♦❜❛❜✐❧✐st✐❝ ♣❧❛♥♥❡r ❢r♦♠ ❛ ♣♦rt❢♦❧✐♦ t❤❛t ❝❛♥ s♦❧✈❡ t❤❡ ♣r♦❜❧❡♠✳ ❲❡ ✉s❡ ♠❛❝❤✐♥❡ ❧❡❛r♥✐♥❣ ❛❧❣♦r✐t❤♠s t♦ ❞❡t❡r♠✐♥❡ t❤❡ ❜❡st ♣❧❛♥♥❡r ❢r♦♠ t❤❡ ♣♦r❢♦❧✐♦ t❤❛t s♦❧✈❡s ❛ ♣r♦❜❧❡♠✳
❖✉r ❛♣♣r♦❛❝❤ s❤♦✇❡❞ ❣♦♦❞ r❡s✉❧ts ✐♥ t❤❡ ❡①♣❡r✐♠❡♥ts✳ ❖✉r ❛♣♣r♦❛❝❤ ♦✉t♣❡r❢♦r♠❡❞ t❤❡ ❜❡st ♣❧❛♥♥❡rs ❢r♦♠ ❛ r❡❝❡♥t ♣❧❛♥♥✐♥❣ ❝♦♠♣❡t✐t✐♦♥ ✐♥ ❜♦t❤ ❛r❡❛s ✭❝❧❛ss✐❝❛❧ ❛♥❞ ♣r♦❜❛❜✐❧✐st✐❝ ♣❧❛♥♥✐♥❣✮✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①①✐
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s ①①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✷✺
✶✳✶ ❈♦♥tr✐❜✉✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✷ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s ✷✾
✷✳✶ ❇✉s❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✶✳✶ ❆❧❣♦r✐t♠♦s ❞❡ ❇✉s❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✷✳✶ ❋♦r♠❛❧✐③❛çã♦ ❞❡ Pr♦❜❧❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✷✳✷ P❧❛♥❡❥❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✷✳✸ ❍❡✉ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✷✳✹ P♦rt❢ó❧✐♦ ❞❡ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✸ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✷✳✸✳✶ ❈❧❛ss✐✜❝❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✷✳✸✳✷ ❈❧❛ss✐✜❝❛çã♦ ❡♠ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✷✳✹ ❈♦♥❝❧✉sã♦ ❞♦ ❈❛♣ít✉❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✸ ▼❡t♦❞♦❧♦❣✐❛ ✺✾
✸✳✶ ❆rq✉✐t❡t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✶✳✶ P❧❛♥❡❥❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✶✳✷ ❈❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✶✳✸ Pr♦❜❧❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✶✳✹ ▲❡✈❛♥t❛♠❡♥t♦ ❞♦s ❉❛❞♦s ❞❡ ❊①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✶✳✺ ❈❧❛ss✐✜❝❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✷ ❚r❡✐♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✸✳✸ ❈♦♠♣♦s✐çã♦ ❞♦ P♦rt❢ó❧✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
①✈✐✐✐ ❙✉♠ár✐♦
✹ ❊①♣❡r✐♠❡♥t♦s ❡ ❉✐s❝✉ssõ❡s ✻✾
✹✳✶ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✷ ❙❡❧❡çã♦ ❞❡ ❈❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✸ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✹ P♦rt❢ó❧✐♦ ●❡r❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺ ❆♣❧✐❝❛♥❞♦ ❈❧❛ss✐✜❝❛çã♦ ❡♠ P❧❛♥❡❥❛♠❡♥t♦ Pr♦❜❛❜✐❧íst✐❝♦ ✽✸ ✺✳✶ ❈♦♥❝❡✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✷ ❆rq✉✐t❡t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✸ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
✻ ❈♦♥❝❧✉sã♦ ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✾✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❋❧✉①♦❣r❛♠❛ ❞♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✷ ❊①❡♠♣❧♦✿ ✐♥stâ♥❝✐❛ ❞♦ ♣r♦❜❧❡♠❛ ▼✉♥❞♦ ❞♦s ❇❧♦❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✸ ❊①❡♠♣❧♦✿ ❛♣❧✐❝❛♥❞♦ ✉♠❛ ❛çã♦ s♦❜r❡ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✹ ❊①❡♠♣❧♦✿ s✉❝❡ss✐✈❛s ❡①♣❛♥sõ❡s ❛té ❡♥❝♦♥tr❛r ❛ ♠❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✺ ●r❛❢♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✿ t❡r ❜♦❧♦ ❡ ❝♦♠❡r ❜♦❧♦ t❛♠❜é♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✻ ❊①❡♠♣❧♦✿ ❉❚●s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ●r✐❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✼ ❊①❡♠♣❧♦✿ ●r❛❢♦ ❝❛✉s❛❧ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ●r✐❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✽ ❊①❡♠♣❧♦✿ r❡❣r❡ssã♦ ♥♦ ❘P● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✷✳✾ ❊①❡♠♣❧♦✿ ✈❛❧♦r ❤❡✉ríst✐❝♦ ❡①tr❛í❞♦ ❞♦ ❘P● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✷✳✶✵ ❈❧❛ss✐✜❝❛çã♦ ✉s❛♥❞♦ ♦ ❦✲◆◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✷✳✶✶ ❚♦♣♦❧♦❣✐❛s ❞❡ ✉♠❛ r❡❞❡ ❞❡ ❑♦❤♦♥❡♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✶ ❆rq✉✐t❡t✉r❛ ❞♦ s✐st❡♠❛ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✷ ❉❊❘ ❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ✉t✐❧✐③❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✸ ❱❡t♦r ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✶ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ✲ ❝❧❛ss✐✜❝❛❞♦r❡s ❡ ❝♦♠♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✷ ❚❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ✲ ❝❧❛ss✐✜❝❛❞♦r❡s ❡ ♣♦rt❢ó❧✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✸ ❘❡s✉❧t❛❞♦s ❝♦♥s♦❧✐❞❛❞♦s ✲ P♦rt❢ó❧✐♦ ❣❡r❛❞♦ ❡ ❋❉❙❙✷ ❙❆❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✶ ❘❡s✉❧t❛❞♦s ❝♦♥s♦❧✐❞❛❞♦s ✲ ❝❧❛ss✐✜❝❛❞♦r❡s✱ P❘❖❙❚ ❡ ●❧✉tt♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❈❛r❛❝t❡ríst✐❝❛s ▲❡✈❛♥t❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✶ ❈♦♥❥✉♥t♦ ❞❡ ❈❛r❛❝t❡ríst✐❝❛s ❯t✐❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✷ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❞♦ ♣♦rt❢ó❧✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✸ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆▲▲ ✳ ✳ ✳ ✳ ✼✷ ✹✳✹ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❍❆P ✳ ✳ ✳ ✳ ✼✸ ✹✳✺ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆●✶ ✳ ✳ ✳ ✳ ✼✸ ✹✳✻ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆●✷ ✳ ✳ ✳ ✳ ✼✹ ✹✳✼ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆●✸ ✳ ✳ ✳ ✳ ✼✹ ✹✳✽ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆●✹ ✳ ✳ ✳ ✳ ✼✺ ✹✳✾ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s✱ ✉s❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❆●✺ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✵ ❘❡s✉❧t❛❞♦s ❝♦♥s♦❧✐❞❛❞♦s ✲ ❝❧❛ss✐✜❝❛❞♦r❡s ❡ ❝♦♠♣♦♥❡♥t❡s ❞♦ ♣♦rt❢ó❧✐♦ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✶ ▼é❞✐❛ ❞❡ s✉❝❡ss♦ ❞♦s ♣♦rt❢ó❧✐♦s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✶✷ ❘❡s✉❧t❛❞♦s ❝♦♥s♦❧✐❞❛❞♦s ✲ ❝❧❛ss✐✜❝❛❞♦r❡s ❡ ♣♦rt❢ó❧✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✶ ❈❛r❛❝t❡ríst✐❝❛s ▲❡✈❛♥t❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✷ ❘❡s✉❧t❛❞♦s ■PP❈ ✷✵✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s
❆✯ ❆ st❛r ✲ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❜✉s❝❛ ❞❡ ❝❛♠✐♥❤♦s ót✐♠♦s ❡♠ ❣r❛❢♦s ❆❉❉ ❆❧❣❡❜r❛✐❝ ❉❡❝✐s✐♦♥ ❉✐❛❣r❛♠
❆❉▲ ❆❝t✐♦♥ ❉❡s❝r✐♣t✐♦♥ ▲❛♥❣✉❛❣❡ ❆● ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦
❆❘❋❋ ❆ttr✐❜✉t❡✲r❡❧❛t✐♦♥ ❋✐❧❡ ❋♦r♠❛t ❇❉❉ ❇✐♥❛r② ❉❡❝✐s✐♦♥ ❉✐❛❣r❛♠ ❇❋❙ ❇❡st ❋✐rst ❙❡❛r❝❤
❈● ❈❛✉s❛❧ ●r❛♣❤
❈P❋ ❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐st✐❝ ❋✉♥❝t✐♦♥ ❉❊❘ ❉✐❛❣r❛♠❛ ❞❡ ❡♥t✐❞❛❞❡✲r❡❧❛❝✐♦♥❛♠❡♥t♦ ❉❚● ❉♦♠❛✐♥✲❚r❛♥s✐t✐♦♥ ●r❛♣❤
❊❍❈ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❋❋ ❋❛st ❋♦r✇❛r❞
❋❉ ❋❛st ❉♦✇♥✇❛r❞
❋❉❙❙ ❋❛st ❉♦✇♥✇❛r❞ ❙t♦♥❡ ❙♦✉♣ ❍❆P ❍✐❣❤❧② ❆❞❥✉st❛❜❧❡ P❧❛♥♥❡r
❍❆P✲◆◆ ❍✐❣❤❧② ❆❞❥✉st❛❜❧❡ P❧❛♥♥❡r ◆❡❛r❡st ◆❡✐❣❤❜♦r ❍❈ ❍✐❧❧ ❈❧✐♠❜✐♥❣
❍❙P ❍❡✉r✐st✐❝ ❙❡❛r❝❤ P❧❛♥♥❡r ■❆ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧
■P❈ ■♥t❡r♥❛t✐♦♥❛❧ P❧❛♥♥✐♥❣ ❈♦♠♣❡t✐t✐♦♥
■PP❈ ■♥t❡r♥❛t✐♦♥❛❧ Pr♦❜❛❜✐❧✐st✐❝ P❧❛♥♥✐♥❣ ❈♦♠♣❡t✐t✐♦♥ ❦✲◆◆ ❦ ◆❡❛r❡st ◆❡✐❣❤❜♦r
▲❘❚❆✯ ▲❡❛r♥✐♥❣ ❘❡❛❧✲❚✐♠❡ ❆✯ ▼✫❙ ▼❡r❣❡ ✫ ❙❤r✐♥❦
▼❈❚ ▼♦♥t❡✲❈❛r❧♦ ❚r❡❡
▼❉P ▼❛r❦♦✈ ❉❡❝✐s✐♦♥ Pr♦❝❡ss
◆❇ ◆❛ï✈❡ ❇❛②❡s
◆❋▲ ◆♦ ❋r❡❡ ▲✉♥❝❤
P❜P P♦rt❢♦❧✐♦✲❜❛s❡❞ P❧❛♥♥❡r
①①✐✈ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s
P❉❉▲ P❧❛♥♥✐♥❣ ❉♦♠❛✐♥ ❉❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡
PP❉❉▲ Pr♦❜❛❜✐❧✐st✐❝ P❧❛♥♥✐♥❣ ❉♦♠❛✐♥ ❉❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡ P● P❧❛♥♥✐♥❣ ●r❛♣❤
❘❉❉▲ ❘❡❧❛t✐♦♥❛❧ ❉②♥❛♠✐❝ ■♥✢✉❡♥❝❡ ❉✐❛❣r❛♠ ▲❛♥❣✉❛❣❡ ❘P● ❘❡❧❛①❡❞ P❧❛♥♥✐❣ ●r❛♣❤
❙❖▼ ❙❡❧❢ ❖r❣❛♥✐③❛❜❧❡ ▼❛♣♣✐♥❣
❙❚❘■P❙ ❙❚❛♥❢♦r❞ ❘❡s❡❛r❝❤ ■♥st✐t✉t❡ Pr♦❜❧❡♠ ❙♦❧✈❡r ❙❱▼ ❙✉♣♣♦rt ❱❡❝t♦r ▼❛❝❤✐♥❡
❯❈▼ ❯♣♣❡r ❈♦♥✜❞❡♥❝❡ ❚r❡❡ ❲✲❆✯ ❲❡✐❣❤t❡❞ ❆ st❛r
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❆ ❡✈♦❧✉çã♦ ❞❛ ✐♥❢♦r♠át✐❝❛ é ♥♦tá✈❡❧ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✳ ❊ ❥✉♥t♦ ❝♦♠ ❡ss❛ ❡✈♦❧✉çã♦✱ ♦s ♣r♦❜❧❡♠❛s t❛♠❜é♠ ✜❝❛r❛♠ ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠♣❧❡①♦s ❞❡ s❡r❡♠ r❡s♦❧✈✐❞♦s✳ ❱✐s❛♥❞♦ r❡❞✉③✐r ❡st❛ ❝♦♠♣❧❡①✐❞❛❞❡✱ ♣❡sq✉✐s❛s ✈ê♠ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❡♥t❡♥❞❡r ❝♦♠♦ ♦ s❡r ❤✉♠❛♥♦ r❛❝✐♦❝✐♥❛ ❡ ❛ss✐♠ ❛♣❧✐❝❛r t❛❧ ❝♦♥❤❡❝✐♠❡♥t♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ té❝♥✐❝❛s q✉❡ ♣♦ss❛♠ ❛✉①✐❧✐❛r ♥❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳ ❊♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ t❛✐s ♣❡sq✉✐s❛s ❝♦♥❝❡♥tr❛♠✲s❡ ❡♠ ✉♠❛ ár❡❛ ❞❡♥♦♠✐♥❛❞❛ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ✭■❆✮✳ ❉❡ ✉♠❛ ❢♦r♠❛ ❣❡r❛❧✱ ❛ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ❜✉s❝❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ✉t✐❧✐③❛♥❞♦ ❤❛❜✐❧✐❞❛❞❡s ❤✉♠❛♥❛s s✐♥t❡t✐✲ ③❛❞❛s ❡♠ té❝♥✐❝❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❝❛♣❛③❡s ❞❡ r❡❛❧✐③❛r t❛r❡❢❛s ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
❉❡♥tr❡ ❛s ❞✐✈❡rs❛s ár❡❛s ❞❡ ♣❡sq✉✐s❛ ❡♠ ■❆✱ ❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✭❆■ P❧❛♥♥✐♥❣✮ é ✉♠❛ ❞❛s ♠❛✐s ✐♥tr✐❣❛♥t❡s✳ ❙✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♦✉ ♣❧❛♥❡❥❛❞♦r❡s ❝♦♥❝❡♥tr❛♠✲s❡ ❡♠ ❣❡r❛r ❛✉t♦♠❛t✐❝❛♠❡♥t❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❛çõ❡s q✉❡ tr❛♥s❢♦r♠❛♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ✭❡st❛❞♦✮ ✐♥✐❝✐❛❧ ❞❡ ♦❜❥❡t♦s ❡♠ ♦✉tr♦ ❡st❛❞♦ ❡♠ q✉❡ ✉♠ ❞❛❞♦ ♦❜❥❡t✐✈♦ é s❛t✐s❢❡✐t♦✳ ❊①✐st❡♠ ❞✐✈❡rs❛s ❛❜♦r❞❛❣❡♥s ♣❛r❛ ✐♠♣❧❡♠❡♥t❛r s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ❚❛✐s ❛❜♦r❞❛❣❡♥s s❡ ❞✐❢❡r❡♠ ♥❛ ❢♦r♠❛ ❞❡ s❡ r❡♣r❡s❡♥t❛r ❡st❛❞♦s✱ ❛çõ❡s ❡ ♣❧❛♥♦s✳ ❈♦♠♦ ❡①❡♠♣❧♦ ❞❡ ❛❜♦r❞❛❣❡♥s t❡♠✲s❡ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✱ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♥❞✐❝✐♦♥❛❧✱ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦✱ ❡♥tr❡ ♦✉tr♦s✳ ◆❡st❛ ❞✐ss❡rt❛çã♦✱ ❛ ê♥❢❛s❡ é ❞❛❞❛ às ❛❜♦r❞❛❣❡♥s ❝❧áss✐❝❛ ❡ ♣r♦❜❛❜✐❧íst✐❝❛✳
◆♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♦s ❛♠❜✐❡♥t❡s sã♦ ❝❧❛ss✐✜❝❛❞♦s ❡♠ t♦t❛❧♠❡♥t❡ ♦❜s❡r✈á✈❡✐s ✭♣❡r♠✐t❡♠ q✉❡ s❡♥s♦r❡s ♦❜t❡♥❤❛♠ t♦❞❛s ❛s ✐♥❢♦r♠❛çõ❡s ❞♦ ❡st❛❞♦✮❀ ❡stát✐❝♦s ✭s❡ ♠♦❞✐✜❝❛♠ ❛♣❡♥❛s ❞✉r❛♥t❡ ❛ ❡①❡❝✉çã♦ ❞❡ ✉♠❛ ❛çã♦✱ ♥✉♥❝❛ ♥❛ ❡t❛♣❛ ❞❡ ❞❡❝✐sã♦✮❀ ❡ ❞❡t❡r♠✐♥íst✐❝♦s ✭❛s ❛çõ❡s s❡♠♣r❡ sã♦ r❡❛❧✐③❛❞❛s ❝♦♠ s✉❝❡ss♦✮ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳ ❖ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦ é ✉♠❛ ❡①t❡♥sã♦ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ q✉❡ tr❛❜❛❧❤❛ s♦❜r❡ ✉♠ ❛♠❜✐❡♥t❡ ♥ã♦ ❞❡t❡r♠✐♥íst✐❝♦✱ ♦♥❞❡ ❝❛❞❛ ✉♠❛ ❞❛s ❛çõ❡s ♣♦ss✉✐ ✉♠❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♦❝♦rr❡r ❝♦♠ s✉❝❡ss♦ ♦✉ ♥ã♦✳ ■ss♦ ✐♥❞✐❝❛ q✉❡ ♥❡♠ s❡♠♣r❡ ♦ ❡st❛❞♦ ❝♦rr❡♥t❡ s♦❢r❡ ❛s ❛❧t❡r❛çõ❡s ❡s♣❡r❛❞❛s ❞❡❝♦rr❡♥t❡s ❞❛ ❡①❡❝✉çã♦ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❛çã♦✳
❆❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ t❡♠ s✐❞♦ ♠✉✐t♦ ✉s❛❞♦s r❡❝❡♥t❡♠❡♥t❡ ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✳ ❉❡ ❢❛t♦✱ ❛❧❣♦r✐t♠♦s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✐♠♣❧❡♠❡♥t❛❞♦s ❝♦♠ ❞✐❢❡✲ r❡♥t❡s té❝♥✐❝❛s ❞❡ ❜✉s❝❛ t❡♠ s❡ ♠♦str❛❞♦ ❡✜❝✐❡♥t❡ ♥❛ s♦❧✉çã♦ ❞❡ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡
✷✻ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
♣r♦❜❧❡♠❛s✳ ❖ ❋❛st ❋♦r✇❛r❞ ❬❍♦✛♠❛♥♥ ❡ ◆❡❜❡❧ ✷✵✵✶❪ é ✉♠ ❡①❡♠♣❧♦ ❞❡ ♣❧❛♥❡❥❛❞♦r ❞❡ s✉❝❡ss♦ ✐♠♣❧❡♠❡♥t❛❞♦ ✉s❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣✳ ❆♣❡s❛r ❞✐ss♦✱ ♥❡♥❤✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ é s✉♣❡r✐♦r ❛♦s ❞❡♠❛✐s ❬❲♦❧♣❡rt ❡ ▼❛❝r❡❛❞② ✶✾✾✼❪✳ ❯♠ ❞❡t❡r♠✐♥❛❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♣♦❞❡ ♥ã♦ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ❥á r❡s♦❧✈✐❞♦ ♣♦r ♦✉tr♦ ❛❧❣♦r✐t♠♦✳ ❆ ♣❛rt✐r ❞❡ss❛s ♦❜s❡r✈❛çõ❡s✱ ✉♠❛ ❞❛s t❡♥❞ê♥❝✐❛s ♥❡ss❛ ár❡❛ é s❡✲ ❧❡❝✐♦♥❛r ♦ ♠❡❧❤♦r ❛❧❣♦r✐t♠♦ ♦✉ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞♦s ♠❡❧❤♦r❡s ❛❧❣♦r✐t♠♦s ♣❛r❛ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ❡♠ ♣❛rt✐❝✉❧❛r ❬❑♦tt❤♦✛ ✷✵✶✷❪✳ ❉❡st❛ ❢♦r♠❛✱ ♣❛ss❛✲s❡ ❛ t❡r ✉♠ ♣r♦❜❧❡♠❛ ❞❡ s❡❧❡çã♦ ❞❡ ❛❧❣♦r✐t♠♦ ❛ s❡r r❡s♦❧✈✐❞♦ ❬❘✐❝❡ ✶✾✼✻❪✳ ❆♦ ❧♦♥❣♦ ❞❡st❛ ❧✐♥❤❛ ❞❡ r❛❝✐♦❝í♥✐♦ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♦s ❝❤❛♠❛❞♦s ♣♦rt❢ó❧✐♦s ❞❡ ♣❧❛♥❡❥❛❞♦r❡s✳ ◆❛ ❝r✐❛çã♦ ❞❡ ✉♠ ♣♦rt❢ó❧✐♦✱ ✉♠❛ ❞❛s ❣r❛♥❞❡s ❞✐✜❝✉❧❞❛❞❡s ❛✐♥❞❛ é ❞❡t❡r♠✐♥❛r ♦ ♠❡❧❤♦r ♣❧❛♥❡❥❛❞♦r ♣❛r❛ r❡s♦❧✈❡r ✉♠❛ ✐♥stâ♥❝✐❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣r♦❜❧❡♠❛ ❬❱❛❧❧❛t✐ ❡ ❑✐t❝❤✐♥ ✷✵✶✷❪✳
❆ss✐♠ ❝♦♠♦ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✱ ❡♠ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦ ❞✐✈❡rs♦s ♣❧❛✲ ♥❡❥❛❞♦r❡s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ r❡s♦❧✈❡r ♦s ♣r♦❜❧❡♠❛s✱ ✐♥❝❡♥t✐✈❛❞♦s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ■♥t❡r♥❛t✐♦♥❛❧ Pr♦❜❛❜✐❧✐st✐❝ P❧❛♥♥✐♥❣ ❈♦♠♣❡t✐t✐♦♥ ✭■PP❈✮ ✲ ❈♦♠♣❡t✐çã♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❡ P❧❛♥❡❥❛♠❡♥t♦ Pr♦❜❛❜✐❧íst✐❝♦✳ ➱ ♣♦ssí✈❡❧ ♥♦t❛r q✉❡✱ ❛♣❡s❛r ❞❡ ❞♦✐s ♣❧❛♥❡❥❛❞♦r❡s s❡ ❞❡st❛❝❛✲ r❡♠ ♥♦s r❡s✉❧t❛❞♦s ✜♥❛✐s ✭P❘❖❙❚ ❬❑❡❧❧❡r ❡ ❊②❡r✐❝❤ ✷✵✶✷❪ ❡ ●❧✉tt♦♥ ❬❑♦❧♦❜♦✈ ❡t ❛❧✳ ✷✵✶✷❪✮✱ ♦✉tr♦s ♣❧❛♥❡❥❛❞♦r❡s ♣r♦♣♦st♦s ❝♦♥s❡❣✉✐r❛♠ r❡s✉❧t❛❞♦s ♣♦s✐t✐✈♦s ❡♠ ♣r♦❜❧❡♠❛s ✐♥❞✐✈✐❞✉❛✐s✱ ♦ q✉❡ ♥♦s s✐t✉❛ ♥♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❡♥❢r❡♥t❛❞♦ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✿ ♥❡♥❤✉♠ ♣❧❛♥❡✲ ❥❛❞♦r é ❝❛♣❛③ ❞❡ s✉♣❡r❛r t♦t❛❧♠❡♥t❡ ♦s ♦✉tr♦s ❡♠ t♦❞♦s ♦s ♣r♦❜❧❡♠❛s ❬❱❛❧❧❛t✐ ❡ ❑✐t❝❤✐♥ ✷✵✶✷❪✳
❖❜❥❡t✐✈❛♥❞♦ ♠✐t✐❣❛r ❡st❛ ❞✐✜❝✉❧❞❛❞❡ ❡♠ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❡ ♣r♦❜❛❜✐❧íst✐❝♦✱ ❡st❛ ❞✐ss❡rt❛çã♦ ❞❡s❝r❡✈❡ ❛ ♣r♦♣♦st❛ ❞❡ ✉♠ ♣♦rt❢ó❧✐♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♣r♦♣ós✐t♦ ❣❡r❛❧✱ ✐♥❞❡✲ ♣❡♥❞❡♥t❡ ❞❡ ❞♦♠í♥✐♦✱ ♣❛r❛ ❛♠❜❛s ❛s ár❡❛s✳ ❆ ♣❛rt✐r ❞❛ ❡s♣❡❝✐✜❝❛çã♦ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣r♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❧❡✈❛♥t❛♠✲s❡ ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ♣❡r♠✐t❡♠ ❞❡t❡r♠✐♥❛r ♦s ♠❡✲ ❧❤♦r❡s ❛❧❣♦r✐t♠♦s ♣❛r❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳ ❆ ❡s❝♦❧❤❛ ❞♦s ♠❡❧❤♦r❡s ♣❧❛♥❡❥❛❞♦r❡s é ❢❡✐t❛ ❝♦♠ ❜❛s❡ ❡♠ ❛❧❣♦r✐t♠♦s ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛✳ ◆❛ ❡s❝♦❧❤❛ ❞♦s ♠❡❧❤♦r❡s ❝♦♥s✐❞❡r♦✉✲ s❡ ♦ t❡♠♣♦ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞♦ ♣❧❛♥♦ ❡♠ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❡ ♠❛①✐♠✐③❛çã♦ ❞❛ ♣♦♥t✉❛çã♦ ❡♠ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦✳
✶✳✶✳ ❈♦♥tr✐❜✉✐çã♦ ✷✼
q✉❡ r❡s♦❧✈❡r✐❛ ♦ ♣r♦❜❧❡♠❛✳ ❬❆❧❤♦ss❛✐♥✐ ❡ ❇❡❝❦ ✷✵✶✸❪ t❛♠❜é♠ ❡①tr❛✐✉ ❝❛r❛❝t❡ríst✐❝❛s ❡s✲ ♣❡❝í✜❝❛s ❞♦s ❞♦♠í♥✐♦s ❞❡ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s t❡♥t❛♥❞♦ ❞❡✜♥✐r ♦ ♠❡❧❤♦r ♣❧❛♥❡❥❛❞♦r ♣❛r❛ r❡s♦❧✈ê✲❧♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ❡♠ ♥♦ss❛ ♣r♦♣♦st❛ ❢♦r❛♠ s❡❧❡❝✐♦♥❛❞❛s ✸✽ ❝❛r❛❝t❡ríst✐❝❛s ❞✐st✐♥✲ t❛s✳ P♦st❡r✐♦r♠❡♥t❡✱ ✉t✐❧✐③❛♥❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ❢♦✐ ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛s ♠❡❧❤♦r❡s ❝❛r❛❝t❡ríst✐❝❛s r❡♣r❡s❡♥t❛t✐✈❛s ❞♦ ♣r♦❜❧❡♠❛✳
❖ ✉s♦ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❞❡ ♠áq✉✐♥❛ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❝❧❛ss✐✜❝❛r ♣r♦❜❧❡♠❛s ❥á ❢♦✐ ✉t✐❧✐✲ ③❛❞❛ ❡♠ ♣❧❛♥❡❥❛♠❡♥t♦✳ ❱ár✐♦s ♣♦rt❢ó❧✐♦s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ✉s❛♥❞♦ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❢♦r❛♠ ♣r♦♣♦st♦s✱ ❝♦♠♦ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❝♦♠♦ ♦ ❛❧❣♦r✐t♠♦ ❈✹✳✺ ❡ ♦ ❦✲◆◆✱ ♣❛rt✐♥❞♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❡①tr❛í❞❛s ❞♦ ♣r♦❜❧❡♠❛✱ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ♣r❡❞✐③❡r s❡ ✉♠ ♣❧❛♥❡❥❛❞♦r t❡r✐❛ ♦✉ ♥ã♦ s✉❝❡ss♦ ❛♦ t❡♥t❛r ❡♥❝♦♥tr❛r ✉♠ ♣❧❛♥♦ ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣r♦❜❧❡♠❛ ❬❘♦❜❡rts ❡ ❍♦✇❡ ✷✵✵✼✱❈❡♥❛♠♦r ❡t ❛❧✳ ✷✵✶✷✱❆❧❤♦ss❛✐♥✐ ❡ ❇❡❝❦ ✷✵✶✸❪✳
❊ss❛ ❞✐ss❡rt❛çã♦ ♣r♦♣õ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ s❡♠❡❧❤❛♥t❡ ❛♦s tr❛❜❛❧❤♦s ❞❡ ❱r❛❦❛s ❬❱r❛❦❛s ❡t ❛❧✳ ✷✵✵✸❪ ❡ ❘♦❜❡rts ❬❘♦❜❡rts ❡ ❍♦✇❡ ✷✵✵✼❪ ♣❛r❛ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✱ ✉t✐❧✐③❛♥❞♦ ✉♠ r❡✜♥❛♠❡♥t♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♣r♦♣♦st❛s✱ ✉♠❛ ❛t✉❛❧✐③❛çã♦ ❞♦s ♣❧❛♥❡❥❛❞♦r❡s ✉t✐❧✐③❛❞♦s ❡ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ ♦❜❥❡t✐✈♦✿ ❡♥q✉❛♥t♦ ❡♠ ❱r❛❦❛s ❛ ❝❧❛ss✐✜❝❛çã♦ é ✉s❛❞❛ ♣❛r❛ ♣❛r❛♠❡tr✐③❛r s❡✉ ♣❧❛♥❡❥❛❞♦r✱ ❡ ❡♠ ❘♦❜❡rts ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ s✉❝❡ss♦ ❞❡ ✉♠ ♣❧❛♥❡❥❛❞♦r✱ ♥♦ss♦ ♦❜❥❡t✐✈♦ é ❞❡t❡r♠✐♥❛r q✉❛❧ ♦ ♣❧❛♥❡❥❛❞♦r é ❝❛♣❛③ ❞❡ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧✱ ♥♦ ✐♥t✉✐t♦ ❞❡ ❝r❡❞❡♥❝✐❛r ♥♦ss♦ ♣❧❛♥❡❥❛❞♦r ♣❛r❛ ♣❛rt✐❝✐♣❛r ❞❡ ❝♦♠♣❡t✐çõ❡s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ♣❛rt✐✉✲s❡ ♣❛r❛ ❛ ❝r✐❛çã♦ ❞❡ ✉♠ ♣♦rt❢ó❧✐♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❝♦♠❜✐♥❛♥❞♦ ♦s ♠❡❧❤♦r❡s ❝❧❛ss✐✜❝❛❞♦r❡s ❡♠ ✉♠ ú♥✐❝♦ ♣❧❛♥❡❥❛❞♦r✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ r❡✜♥❛r ♦s r❡s✉❧t❛❞♦s ❝♦♠ r❡❧❛çã♦ à t❛①❛ ❞❡ s✉❝❡ss♦✳ ❖ ♣r♦❝❡❞✐♠❡♥t♦ s❡❣✉✐❞♦ ♣❛r❛ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❢♦✐ t❛♠❜é♠ ❛♣❧✐❝❛❞♦ ❛♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦✳ ◆❡ss❛ ár❡❛ ♥ã♦ ❡①✐st❡ ❛❜♦r❞❛❣❡♠ s❡♠❡❧❤❛♥t❡ à ❛♣❧✐❝❛❞❛ ♥❡ss❡ tr❛❜❛❧❤♦✳
❆ ♣r♦♣♦st❛ r❡❛❧✐③❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦ s❡ ♠♦str♦✉ ❡✜❝✐❡♥t❡ ❛♦ ❞❡t❡r♠✐♥❛r ♦s ♠❡❧❤♦r❡s ♣❧❛♥❡❥❛❞♦r❡s ♣❛r❛ ♦s ♣r♦❜❧❡♠❛s ♥♦s t❡st❡s r❡❛❧✐③❛❞♦s✳ ❉❡st❛ ❢♦r♠❛ ❢♦✐ ♣♦ssí✈❡❧ s✉♣❡r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♣❧❛♥❡❥❛❞♦r❡s q✉❡ ❛♥t❡r✐♦r♠❡♥t❡ ❤❛✈✐❛♠ ❝♦♥s❡❣✉✐❞♦ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛✲ ❞♦s ♥❛s ❝♦♠♣❡t✐çõ❡s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♥s✐❞❡r❛♥❞♦✲s❡ ❛s tr✐❧❤❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦ ❡ ♣r♦❜❛❜✐❧íst✐❝♦✳
✶✳✶ ❈♦♥tr✐❜✉✐çã♦
❆s ♣r✐♥❝✐♣❛✐s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿
• ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠ ♣♦rt❢ó❧✐♦ ❞❡ ♣❧❛♥❡❥❛❞♦r❡s ❜❛s❡❛❞♦ ❡♠ ❝❧❛ss✐✜❝❛çã♦ ♥❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✱ ❝❛♣❛③ ❞❡ ❞❡t❡r♠✐♥❛r ♦s ♣❧❛♥❡❥❛❞♦r❡s ❝♦♠ ♠❛✐♦r ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s✉❝❡ss♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ❡ q✉❡ s♦❧✉❝✐♦♥❛rã♦ ♦ ♠❡s♠♦ ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧❀ • ❣❡r❛çã♦ ❞❡ ✉♠ ❝❧❛ss✐✜❝❛❞♦r ❡✜❝✐❡♥t❡ ♥❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦✱ ❝❛♣❛③
✷✽ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦
❖ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛ ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❛❧❣♦r✐t♠♦s ❜✉s❝❛✱ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ ■♥t❡✲ ❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✱ ❝❧❛ss✐✜❝❛çã♦ ❡ tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❝♦♥t❡①t♦ ❞❛ ❞✐ss❡rt❛çã♦✳
❖ ❈❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛ ❞❡t❛❧❤❡s ❞❛ ❛rq✉✐t❡t✉r❛ ♣❛r❛ ❣❡r❛çã♦ ❡ tr❡✐♥❛♠❡♥t♦ ❞♦s ❝❧❛s✲ s✐✜❝❛❞♦r❡s q✉❡ ♣❛rt✐❝✐♣❛rã♦ ❞♦s ♣♦rt❢ó❧✐♦s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳
❖ ❈❛♣ít✉❧♦ ✹ ❞❡s❝r❡✈❡ ♦s r❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ❡♥❝♦♥tr❛❞♦s ♣❡❧♦s ❝❧❛ss✐✜❝❛❞♦r❡s ❣❡r❛✲ ❞♦s ❝♦♠♣❛r❛♥❞♦ ❝♦♠ ♦s ♣❧❛♥❡❥❛❞♦r❡s ❝♦♠ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♥❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝❧áss✐❝♦✳
❖ ❈❛♣ít✉❧♦ ✺ ❞❡s❝r❡✈❡ ♦s r❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ❡♥❝♦♥tr❛❞♦s ❞♦s ❝❧❛ss✐✜❝❛❞♦r❡s ❣❡r❛❞♦s✱ ♣♦ré♠ ♥❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♣r♦❜❛❜✐❧íst✐❝♦✳
❈❛♣ít✉❧♦ ✷
❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s
❈♦rr❡❧❛t♦s
◆❡st❡ ❝❛♣ít✉❧♦ sã♦ ❞✐s❝✉t✐❞♦s ♦s ❢✉♥❞❛♠❡♥t♦s t❡ór✐❝♦s ❡ tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✱ ♣❛r❛ ♠❡❧❤♦r❛r ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ❡①✐❜✐r ♦s tr❛❜❛❧❤♦s ✐♠♣♦rt❛♥t❡s ❥á ❞❡s❡♥✈♦❧✈✐❞♦s ❝♦♠ ❛s♣❡❝t♦s s❡♠❡❧❤❛♥t❡s✳ ❊st❡ ❝❛♣ít✉❧♦ ❢♦✐ ❡str✉t✉r❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ♥❛ ❙❡çã♦ ✷✳✶ sã♦ ❞❡s❝r✐t♦s ❝♦♥❝❡✐t♦s ❡ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ r❡❧❛❝✐♦♥❛❞♦s ❛♦ t❡♠❛❀ ♥❛ ❙❡çã♦ ✷✳✷ sã♦ ❛♣r❡s❡♥t❛❞♦s ❝♦♥❝❡✐t♦s ❡ ❛❧❣✉♥s s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❛❧é♠ ❞❡ ❛s♣❡❝t♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦s ♣♦rt❢ó❧✐♦s ❞❡ ♣❧❛♥❡❥❛❞♦r❡s❀ ❡ ♥❛ ❙❡çã♦ ✷✳✸ sã♦ ❛♣r❡s❡♥t❛❞❛s té❝♥✐❝❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❡ s✉❛s ❛♣❧✐❝❛çõ❡s ♥❛ ár❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳
✷✳✶ ❇✉s❝❛
❯♠ ♣r♦❜❧❡♠❛ ❞❡ ❜✉s❝❛ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ✉♠❛ ♣♦ssí✈❡❧ s❡q✉ê♥❝✐❛ ❞❡ tr❛♥s✐çõ❡s ❡♥tr❡ ❡st❛❞♦s✱ r❡♣r❡s❡♥t❛❞♦s ♥✉♠❛ ❡str✉t✉r❛ ❝❤❛♠❛❞❛ ár✈♦r❡ ❞❡ ❜✉s❝❛✱ q✉❡ é ❝❛♣❛③ ❞❡ s❛✐r ❞❡ ✉♠ ♥ó ✐♥✐❝✐❛❧ ❡ ❝❤❡❣❛r ❛ ✉♠ ♥ó ♠❡t❛✳ ❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ q✉❛❧q✉❡r ♣r♦❜❧❡♠❛ ♣♦❞❡ s❡r ❢♦r♠✉❧❛❞♦ ❝♦♠♦ ✉♠❛ ár✈♦r❡ ❞❡ ❜✉s❝❛✱ ♦♥❞❡ ❝❛❞❛ ♥ó ❝❛r❛❝t❡r✐③❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ s✐t✉❛çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❝❤❛♠❛❞❛ ❡st❛❞♦✱ ❡ ❛s ❛r❡st❛s ❞✐r❡❝✐♦♥❛❞❛s sã♦ ❛çõ❡s ❛ s❡r❡♠ ❛♣❧✐❝❛❞❛s ♥♦ ❡st❛❞♦ ♦r✐❣❡♠ q✉❡ ♦ ❛❧t❡r❛♠ ♣❛r❛ ♦ ❡st❛❞♦ ❞❡st✐♥♦✳ ❯♠ ❡st❛❞♦ é ❛ r❡♣r❡s❡♥t❛çã♦ ❢♦r♠❛❧ ❞❡ ❝♦♠♦ ♦ ❛♠❜✐❡♥t❡ ❡stá ❞✉r❛♥t❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡♥❝♦♥tr❛r ✉♠❛ s♦❧✉çã♦ ♣❛r❛ ✉♠❛ ❞❡t❡r✲ ♠✐♥❛❞❛ t❛r❡❢❛ q✉❡ ❧❤❡ é ♣❛ss❛❞❛✳ ❚♦❞♦ ♣r♦❜❧❡♠❛ s❡♠♣r❡ ♥❡❝❡ss✐t❛ ❞❛ ✐♥❢♦r♠❛çã♦ ❞♦ ♥ó ✐♥✐❝✐❛❧ q✉❡ ❛ ❜✉s❝❛ t❡rá ❝♦♠♦ ❜❛s❡✱ ❝❤❛♠❛❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧✱ ❡ ❞♦ ♦❜❥❡t✐✈♦ ❛ s❡r s♦❧✉❝✐♦✲ ♥❛❞♦✱ q✉❡ é ♠❡t❛ ❞♦ ♣r♦❜❧❡♠❛✳ ❆ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❜✉s❝❛ é ❝♦♠♣♦st❛ ♣♦r ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❡st❛❞♦s✱ s❡♥❞♦ q✉❡ ❝❛❞❛ ❡st❛❞♦ r❡♣r❡s❡♥t❛ ♣❛rt❡ ❞❛ s♦❧✉çã♦ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
❈♦♠♦ ❡①✐st❡♠ ❞✐✈❡rs♦s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛✱ sã♦ ♥❡❝❡ssár✐♦s ❝r✐tér✐♦s ♣❛r❛ ❞❡✜♥✐r ❛
✸✵ ❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s
❡s❝♦❧❤❛ ❡♠ ❝❛❞❛ ♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦✳ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪ ❝✐t❛ q✉❡ ❛s ❛✈❛❧✐❛çõ❡s ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ sã♦ ❣❡r❛❧♠❡♥t❡ ❢❡✐t❛s ❝♦♠ ❜❛s❡ ❡♠ q✉❛tr♦ ❝r✐tér✐♦s✿
• ❈♦♠♣❧❡t✉❞❡✿ ♣r♦♣r✐❡❞❛❞❡ ❞♦ ❛❧❣♦r✐t♠♦ ❡♥❝♦♥tr❛r ✉♠❛ s♦❧✉çã♦ s❡♠♣r❡ q✉❡ ❛❧❣✉♠❛ ❡①✐st❛❀
• ❖t✐♠❛❧✐❞❛❞❡✿ ♦ ❛❧❣♦r✐t♠♦ s❡♠♣r❡ ❡♥❝♦♥tr❛ ❛ ♠❡❧❤♦r s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛❀ • ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ t❡♠♣♦ ♠é❞✐♦ ❞❡ ❡①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦❀
• ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❝♦♥s✉♠♦ ❞❡ ♠❡♠ór✐❛ ❞♦ ❛❧❣♦r✐t♠♦❀
❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ✐♥❢♦r♠❛çõ❡s q✉❡ ❡❧❡ ✉t✐❧✐③❛ ♣❛r❛ ❡①♣❧♦r❛r ❡♥tr❡ ❡st❛❞♦s✳ ❊♠ ❢✉♥çã♦ ❞✐st♦✱ ❡❧❡ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❝❡❣❛ ♦✉ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ✐♥❢♦r♠❛❞❛✳ ❯♠❛ ❜✉s❝❛ ❝❡❣❛ r❡❛❧✐③❛ t♦❞❛s ❛s ❛✈❛❧✐❛çõ❡s ❞♦ ❡st❛❞♦ ❢❛③❡♥❞♦ ✉s♦ ❛♣❡♥❛s ❞❡ ✐♥❢♦r♠❛çõ❡s ✐♥❡r❡♥t❡s ❛♦ ♣r♦❜❧❡♠❛✱ ❝♦♠♦ ❝✉st♦s ❞❡ ❝❛♠✐♥❤♦✳ ❚✉❞♦ q✉❡ s❡ ♣♦❞❡ ❢❛③❡r é ❡①♣❛♥❞✐r ✉♠ ❡st❛❞♦✱ ♦✉ s❡❥❛✱ ❣❡r❛r ❡st❛❞♦s s✉❝❡ss♦r❡s ❛ ♣❛rt✐r ❞❡ ✉♠ ♦✉tr♦ ❡st❛❞♦ q✉❛❧q✉❡r✱ ❡ ❞✐st✐♥❣✉✐r ✉♠ ❡st❛❞♦ ♠❡t❛ ❞❡ ✉♠ ♥ã♦✲♠❡t❛✳ ❊♠ ✉♠❛ ❜✉s❝❛ ✐♥❢♦r♠❛❞❛✱ ❡①✐st❡ ❛ ❛❞✐çã♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❤❡✉ríst✐❝❛✱ q✉❡ ❡st✐♠❛ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦ ❡st❛❞♦ ❛t✉❛❧ ❡ ❛ ♠❡t❛✱ ♣❛r❛ ❛✉①✐❧✐❛r ❛ ❞❡✜♥✐r ❛ ♦r❞❡♠ q✉❡ ♦s s✉❝❡ss♦r❡s s❡rã♦ ✈✐s✐t❛❞♦s✳ ❯♠❛ ❤❡✉ríst✐❝❛ h(s) s❡r✈❡ ♣❛r❛ ❡st✐♠❛r ❛ ❞✐stâ♥❝✐❛ ❞❡ ✉♠ ❡st❛❞♦ s ❛té ❛ ♠❡t❛✱ ♦♥❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ♣r✐♦r✐③❛♠ ♣♦r ❡①♣❛♥❞✐r ❡st❛❞♦s q✉❡ t❡♠ ♠❡♥♦r ✈❛❧♦r ❞❡ h✱ ♦✉ s❡❥❛✱ ❡st❛❞♦s q✉❡ ❛❝r❡❞✐t❛✲s❡ ❡st❛r❡♠ ♠❛✐s ♣ró①✐♠♦s à ♠❡t❛ ♣❛r❛ q✉❡ ❛ ❜✉s❝❛ s❡❥❛ ❡①❡❝✉t❛❞❛ ♦ ♠❛✐s rá♣✐❞♦ ♣♦ssí✈❡❧✳ ❊♠ ❣❡r❛❧✱ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❝❡❣❛ ♣♦ss✉❡♠ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ♠❡♥♦r✱ ❡♥q✉❛♥t♦ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ✐♥❢♦r♠❛❞❛ tê♠ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❝♦♠♣❧❡t✉❞❡ ❡ ♦t✐♠❛❧✐❞❛❞❡ ❬❊❞❡❧❦❛♠♣ ❡ ❙❝❤rö❞❧ ✷✵✶✷❪✳
❖s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ t❛♠❜é♠ ♣♦❞❡♠ s❡r ❝❛r❛❝t❡r✐③❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♣r♦❝❡❞✐✲ ♠❡♥t♦ ❞❡ ❡①♣❧♦r❛çã♦ ❞♦s ❡st❛❞♦s✱ s❡♥❞♦ ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ s✐st❡♠át✐❝❛ ♦✉ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❧♦❝❛❧✳ ❯♠❛ ❜✉s❝❛ s✐st❡♠át✐❝❛ é r❡❛❧✐③❛❞❛ ❛r♠❛③❡♥❛♥❞♦ t♦❞♦s ♦s ♣♦ssí✈❡✐s s✉❝❡ss♦r❡s ❞❡ ❝❛❞❛ ♥ó ♣❛r❛ q✉❡ ♣♦st❡r✐♦r♠❡♥t❡ s❡❥❛♠ ✈✐s✐t❛❞♦s✳ ❆ ❜✉s❝❛ s✐st❡✲ ♠át✐❝❛ ❣❛r❛♥t❡ ❛ ❝♦♠♣❧❡t✉❞❡ ❞♦ ♣r♦❜❧❡♠❛✱ ♣♦✐s s❡ ❡♠ ❛❧❣✉♠ ✐♥st❛♥t❡ ❞❡ t❡♠♣♦ ♥❡♥❤✉♠ ❡st❛❞♦ é ♣❛ssí✈❡❧ ❞❡ s❡r ✈✐s✐t❛❞♦✱ é ♣♦ssí✈❡❧ ❛✜r♠❛r q✉❡ ♥ã♦ ❡①✐st❡ s♦❧✉çã♦✱ ❡ s❡ ❡♠ ❛❧❣✉♠ ♠♦♠❡♥t♦ ✉♠ ❡st❛❞♦ ❢♦r ❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ ♠❡t❛✱ ❡st❡ s❡rá ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳ ❆ ❜✉s❝❛ ❧♦❝❛❧✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ❜✉s❝❛ s✐st❡♠át✐❝❛✱ ♣♦ss✉✐ ✐♥❢♦r♠❛çã♦ ❞❡ ❛♣❡♥❛s ✉♠ ❡st❛❞♦ ♣♦r ✈❡③✱ ❡ ❡♠ ❝❛❞❛ ❡s❝♦❧❤❛ ❞❡ s✉❝❡ss♦r ♦ ❡st❛❞♦ ❛♥t❡r✐♦r é ❞❡s❝❛rt❛❞♦ ❡ ✉♠ ♥♦✈♦ ❡st❛❞♦ é t♦♠❛❞♦ ❝♦♠♦ ❜❛s❡✳ ❆❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❧♦❝❛❧ ❣❡r❛❧♠❡♥t❡ ♣♦ss✉❡♠ ✐♠♣❧❡♠❡♥t❛çã♦ s✐♠✲ ♣❧❡s✱ ♣♦ré♠ ♥ã♦ ❣❛r❛♥t❡♠ ❝♦♠♣❧❡t✉❞❡ ❞♦ ♣r♦❜❧❡♠❛✱ ♣♦✐s ♣♦❞❡♠ ✜❝❛r ♣r❡s♦s ❡♠ ót✐♠♦s ❧♦❝❛✐s✶ ❬❍♦♦s ❡ ❙tt③❧❡ ✷✵✵✹❪✳
❆ ❡str❛té❣✐❛ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ✈❛r✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝❛❞❛ ❛❧❣♦r✐t♠♦✱ ♣♦ré♠ ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ❞❡✜♥❡ s❡ ♦ ❛❧❣♦r✐t♠♦ é ❞♦ t✐♣♦ ❢♦r✇❛r❞ ♦✉ ❜❛❝❦✇❛r❞✳ ❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❞♦ t✐♣♦ ❢♦r✇❛r❞ r❡❛❧✐③❛ ❛ s✉❛ ❜✉s❝❛ ❛ ♣❛rt✐r ❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ❡ ❝❛♠✐♥❤❛♥❞♦ ♣❡❧♦s
✷✳✶✳ ❇✉s❝❛ ✸✶
❡st❛❞♦s s✉❜s❡q✉❡♥t❡s ❛té ❡♥❝♦♥tr❛r ✉♠ ❡st❛❞♦ q✉❡ s❛t✐s❢❛ç❛ ❛ ♠❡t❛✳ ❏á ✉♠❛ ❜✉s❝❛ ❞♦ t✐♣♦ ❜❛❝❦✇❛r❞ r❡❛❧✐③❛ ♦ ♣r♦❝❡ss♦ ❝♦♥trár✐♦✿ ✐♥✐❝✐❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ❡st❛❞♦ q✉❡ s❛t✐s❢❛ç❛ ❛ ♠❡t❛ ❡ r❡❛❧✐③❛ ❛ ❜✉s❝❛ ♣r♦❝✉r❛♥❞♦ ♣❡❧♦ ❡st❛❞♦ ✐♥✐❝✐❛❧✳ ❯♠❛ ❞✐✜❝✉❧❞❛❞❡ ❛♦ ❡①❡❝✉t❛r ✉♠❛ ❜✉s❝❛ ❜❛❝❦✇❛r❞ é ❣❛r❛♥t✐r q✉❡ ❛♣❡♥❛s ✉♠ ❡st❛❞♦ s❛t✐s❢❛ç❛ ❛ ♠❡t❛✱ ♣♦✐s ❡♠ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ✈ár✐♦s ❡st❛❞♦s ♣♦❞❡♠ ❛t❡♥❞ê✲❧❛✱ ❡♥tã♦ ❡①✐st✐r✐❛♠ ✈ár✐♦s ❡st❛❞♦s q✉❡ ❛ ❜✉s❝❛ ❜❛❝❦✇❛r❞ ♣♦❞❡r✐❛ ♣❛rt✐r✳ ●❡r❛❧♠❡♥t❡✱ ♦s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ sã♦ ✐♠♣❧❡♠❡♥t❛❞♦s ❝♦♠♦ ❢♦r✇❛r❞✱ ♠❛s ❛ ❡str❛té❣✐❛ ❜❛❝❦✇❛r❞ ♣♦❞❡ s❡r út✐❧ ♣❛r❛ ♣r♦❜❧❡♠❛s q✉❡ ❣❡r❛♠ ♠✉✐t♦s s✉❝❡ss♦r❡s ♥♦s ❡st❛❞♦s ✐♥✐❝✐❛✐s ❬▼❛❧✐❦ ❡t ❛❧✳ ✷✵✵✹❪✳
P♦r ú❧t✐♠♦✱ ✉♠ ❛❧❣♦r✐t♠♦ ♣♦❞❡ s❡r ♦✛✲❧✐♥❡ ♦✉ ♦♥✲❧✐♥❡✳ ◆♦s ❛❧❣♦r✐t♠♦s ♦✛✲❧✐♥❡✱ ❛ ❢❛s❡ ❞❡❧✐❜❡r❛t✐✈❛ ❛♥t❡❝❡❞❡ t♦t❛❧♠❡♥t❡ ❛ ❢❛s❡ ❞❡ ❡①❡❝✉çã♦✱ ♦ q✉❡ ♣❡r♠✐t❡ q✉❡ t♦❞♦ t❡♠♣♦ ❡ ❡s♣❛ç♦ s❡❥❛ ❛❧♦❝❛❞♦ ♣❛r❛ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦✱ ❡ ❛♣ós ✐ss♦✱ ❛ ♠❡s♠❛ é ❡①❡❝✉t❛❞❛✳ ❖s ❛❧❣♦r✐t♠♦s ♦♥✲❧✐♥❡✱ t❛♠❜é♠ ❞❡♥♦♠✐♥❛❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❡♠ t❡♠♣♦ r❡❛❧✱ ❛❧t❡r♥❛♠ ❛s ❢❛s❡s ❞❡ ❞❡❧✐❜❡r❛çã♦ ❡ ❡①❡❝✉çã♦ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛✳ ❯♠ ❛❧❣♦r✐t♠♦ ♦♥✲❧✐♥❡ ♥ã♦ ❝♦♥❤❡❝❡ t♦❞❛ ❛ ✐♥❢♦r♠❛çã♦ s♦❜r❡ ♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✱ ❡ ❛♣ós ✉♠ ❝❡rt♦ t❡♠♣♦ é ♥❡❝❡ssár✐♦ q✉❡ ❡❧❡ r❡t♦r♥❡ ✉♠❛ s♦❧✉çã♦✳ ❉❡ ✉♠ ♠♦❞♦ ❣❡r❛❧✱ ❛❧❣♦r✐t♠♦s ♦✛✲❧✐♥❡ t❡♠ ✉♠ t❡♠♣♦ ❞❡ r❡s♣♦st❛ ♠❛✐♦r q✉❡ ♦s ♦♥✲❧✐♥❡✱ ❡ ❝♦♥s❡❣✉❡♠ ❡♥❝♦♥tr❛r s♦❧✉çõ❡s ♠❡❧❤♦r❡s ♣❡❧♦ ♠❛✐♦r ❝♦♥❤❡❝✐♠❡♥t♦ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❬❋✉r❝② ✷✵✵✹❪✳
✷✳✶✳✶ ❆❧❣♦r✐t♠♦s ❞❡ ❇✉s❝❛
❈♦♠ ❛ ❡✈♦❧✉çã♦ ❞❛s ❤❡✉ríst✐❝❛s✱ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❝❡❣❛ s❡ t♦r♥❛r❛♠ ♣♦✉❝♦ ❡❢❡t✐✈♦s ❡♠ ♣r♦❜❧❡♠❛s ❝♦♠ ❛❧t❛ ❝♦♠♣❧❡①✐❞❛❞❡✳ ❉❡♥tr❡ ♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❝❡❣❛✱ ♣♦❞❡✲s❡ ❝✐t❛r✿
• ❇✉s❝❛ ❡♠ ❧❛r❣✉r❛✿ ♦♥❞❡ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ é ❡①♣❛♥❞✐❞♦ ♣r✐♠❡✐r♦✱ ❡ ❞❡♣♦✐s s❡✉s s✉❝❡ss♦r❡s✱ ♦s s✉❝❡ss♦r❡s ❞❡ s❡✉s s✉❝❡ss♦r❡s✱ ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡✱ ❛té q✉❡ s❡ ❡♥❝♦♥tr❡ ❛ ♠❡t❛❀
• ❇✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡✿ ♦s ❡st❛❞♦s ❡①♣❛♥❞✐❞♦s ♥❡ss❛ ❡str❛té❣✐❛ sã♦ ❛r♠❛③❡♥❛❞♦s ❡♠ ✉♠❛ ✜❧❛✱ ♦♥❞❡ ❛♦ s❡r❡♠ ❣❡r❛❞♦s sã♦ ❝♦❧♦❝❛❞♦s ♥❛ ❝❛❜❡ç❛ ❞❛ ✜❧❛✱ ❡ ♦ ❡st❛❞♦ ❛ s❡r ❡①♣❛♥❞✐❞♦ é r❡t✐r❛❞♦ t❛♠❜é♠ ❞❛ ❝❛❜❡ç❛ ❞❛ ✜❧❛✳ ❊♥tr❡ s✉❛s ✈❛r✐❛çõ❡s ♣♦❞❡✲s❡ ❝✐t❛r ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❧✐♠✐t❛❞❛ ❡ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ✐t❡r❛t✐✈❛❀
• ❇✉s❝❛ ❞❡ ❝✉st♦ ✉♥✐❢♦r♠❡✿ s❡❧❡❝✐♦♥❛ ♦s s✉❝❡ss♦r❡s ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ f(n) ❛ ♣❛rt✐r ❞♦ ❝✉st♦ ♣❛r❛ ❡①♣❛♥❞✐r ♦ ❡st❛❞♦ ✭g(n)✮✱ ✐✳❡✳ f(n) = g(n)❀ ❆ ❜✉s❝❛ ❤❡✉ríst✐❝❛ ✉t✐❧✐③❛ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❡s♣❡❝í✜❝♦ ❞♦ ♣r♦❜❧❡♠❛ ♥❛ ❡s❝♦❧❤❛ ❞♦ ♣ró✲ ①✐♠♦ ❡st❛❞♦ ❛ s❡r ❡①♣❛♥❞✐❞♦✳ ●❡r❛❧♠❡♥t❡ ❜✉s❝❛s ✐♥❢♦r♠❛❞❛s sã♦ ❜❛s❡❛❞❛s ❡♠ ❡str❛té❣✐❛s ❝❡❣❛s✱ ❛❞✐❝✐♦♥❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦ ❤❡✉ríst✐❝❛ ♣❛r❛ ❛✉①í❧✐♦ ❞❛ ❛✈❛❧✐❛çã♦✳
✸✷ ❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s
❤❡✉ríst✐❝❛ h(n)✮✱ ✐✳❡✳ f(n) = h(n)✳ ➱ ♠❛♥t✐❞❛ ✉♠❛ ❧✐st❛ ❢❡❝❤❛❞❛ ✭❝❧♦s❡❞✮✱ q✉❡ ❛r♠❛③❡♥❛ ♦s ❡st❛❞♦s ❥á ✈✐s✐t❛❞♦s✱ ❡ ✉♠❛ ✜❧❛ ❞❡ ♣r✐♦r✐❞❛❞❡ ♦r❞❡♥❛❞❛ ♣❡❧♦ ♠❡♥♦r ✈❛❧♦r f(n) ✭♦♣❡♥✮✱ q✉❡ ❛r♠❛③❡♥❛ ♦s ❡st❛❞♦s q✉❡ ❡stã♦ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ s❡r❡♠ ✈✐s✐t❛❞♦s✳ ❆ ❝❛❞❛ ✐t❡r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦✱ ♦ ❡st❛❞♦ ♣r❡s❡♥t❡ ♥❛ ❧✐st❛ ❛❜❡rt❛ ❝♦♠ ♠❡♥♦r f(n)é s❡❧❡❝✐♦♥❛❞♦✱ ❡ s❡ ❡ss❡ ♥ã♦ ❢♦r ❛ ♠❡t❛✱ t♦❞♦s ♦s s✉❝❡ss♦r❡s q✉❡ ♥ã♦ ♣❡rt❡♥ç❛♠ à ❧✐st❛ ❢❡❝❤❛❞❛ ❡ à ❧✐st❛ ❛❜❡rt❛ sã♦ ❛❞✐❝✐♦♥❛❞♦s ♣❛r❛ s❡r❡♠ ✈✐s✐t❛❞♦s ♣♦st❡r✐♦r♠❡♥t❡✳ ❖ ❛❧❣♦r✐t♠♦ ♣❛r❛ ❝♦♠ s✉❝❡ss♦ q✉❛♥❞♦ ♦ ❡st❛❞♦ s❡❧❡❝✐♦♥❛❞♦ ❞❛ ❧✐st❛ ❛❜❡rt❛ é ❛ ♠❡t❛ ❡ ♣❛r❛ ❝♦♠ ❢❛❧❤❛ q✉❛♥❞♦ ❛ ❧✐st❛ ❛❜❡rt❛ ✜❝❛ ✈❛③✐❛ ❬▲❛❱❛❧❧❡ ✷✵✵✻❪✳ ❙❡✉ ♣s❡✉❞♦✲❝ó❞✐❣♦ ❡stá ❞❡s❝r✐t♦ ♥♦ ❆❧❣♦r✐t♠♦ ✶✿
❆❧❣♦r✐t♠♦ ✶ ❇❋❙✭sinicial, smeta✮
✶✿ open←sinicial
✷✿ closed← ∅
✸✿ ❡♥q✉❛♥t♦open6=∅ ❢❛ç❛
✹✿ scurrent ←open.remove()
✺✿ s❡ scurrent =smeta ❡♥tã♦
✻✿ r❡t♦r♥❛ s✉❝❡ss♦ ✼✿ ✜♠ s❡
✽✿ closed.add(scurrent)
✾✿ open.add(sucessores(scurrent))
✶✵✿ ✜♠ ❡♥q✉❛♥t♦ ✶✶✿ r❡t♦r♥❛ ❢❛❧❤❛
❆ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ ❞♦ ❇❋❙ é ❛ ❝♦♠♣❧❡t✉❞❡✱ q✉❡ ❣❛r❛♥t❡ q✉❡ s❡♠♣r❡ ❛ s♦❧✉çã♦ s❡rá ❡♥❝♦♥tr❛❞❛✳ ❈♦♠♦ ❞❡s✈❛♥t❛❣❡♠✱ ♦ ✉s♦ ❞❡ ❤❡✉ríst✐❝❛s ❝♦♠♦ ú♥✐❝❛ ❢✉♥çã♦ ❛✈❛❧✐❛t✐✈❛ ♦ t♦r♥❛ ❞❡♣❡♥❞❡♥t❡ ❞❛ ❡❢❡t✐✈✐❞❛❞❡ ❞❛ ❡st✐♠❛t✐✈❛✿ q✉❛♥t♦ ♠❡❧❤♦r s✉❛ ❢✉♥çã♦ ❤❡✉ríst✐❝❛✱ ♠❡♥♦r s❡rá ♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❛r❛ q✉❡ ♦ ❇❋❙ ❡♥❝♦♥tr❡ ❛ s♦❧✉çã♦✳
❖ ❛❧❣♦r✐t♠♦ ❆✯ ✭❛ st❛r✮ t❛♠❜é♠ é ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❝♦♠♣❧❡t♦✱ ❡①❡❝✉t❛❞♦ ❞❡ ❢♦r♠❛ s✐st❡♠át✐❝❛ ❡ ✐♥❢♦r♠❛❞❛✱ q✉❡ ❣❛r❛♥t❡ s❡♠♣r❡ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦ ót✐♠❛ ❝❛s♦ ❛ ❤❡✉ríst✐❝❛ ❢♦r♥❡❝✐❞❛ s❡❥❛ ❛❞♠✐ssí✈❡❧✷✱ ♣❛r❛ ❜✉s❝❛ ❡♠ ár✈♦r❡✱ ♦✉ ❝♦♥s✐st❡♥t❡✸✱ ♣❛r❛ ❜✉s❝❛
❡♠ ❣r❛❢♦✳ ❖ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❆✯ é s❡♠❡❧❤❛♥t❡ ❛♦ ❞♦ ❇❋❙✱ ♣♦ré♠ ❝♦♠ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ♥❛ ❢✉♥çã♦ ❞❡ ❛✈❛❧✐❛çã♦ f(n)✿ ❡❧❛ é ❢♦r♠❛❞❛ ♣❡❧❛ s♦♠❛ ❞♦s ❡❧❡♠❡♥t♦s g(n) ❡ h(n)✱ ♦♥❞❡ g(n) é ♦ ❝✉st♦ ❞♦ ❝❛♠✐♥❤♦ ❛ ♣❛rt✐r ❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ❛té ♦ ❡st❛❞♦ ❛t✉❛❧ ❡ ♦ h(n) é ❛ ❢✉♥çã♦ ❤❡✉ríst✐❝❛✱ ✐✳❡✳ f(n) =g(n) +h(n)✳ ❖✉tr❛ ♠♦❞✐✜❝❛çã♦ é ❛ s❡❧❡çã♦ ❞♦s s✉❝❡ss♦r❡s✿ ✉♠ s✉❝❡ss♦r ♣♦❞❡ s❡r ❡s❝♦❧❤✐❞♦ ♠❡s♠♦ q✉❡ ♣❡rt❡♥ç❛ à ❧✐st❛ ❢❡❝❤❛❞❛✱ ❝❛s♦ ♦ f(n) ❛t✉❛❧ s❡❥❛ ♠❡♥♦r q✉❡ ♦ f(n) ❛r♠❛③❡♥❛❞♦ ♥❛ ❧✐st❛ ❢❡❝❤❛❞❛✳ P♦r ú❧t✐♠♦✱ ❛♦ ❛❞✐❝✐♦♥❛r s✉❝❡ss♦r❡s ♥❛ ❧✐st❛ ❛❜❡rt❛ ❡❧❡ ✈❡r✐✜❝❛ s❡ ♦ ♥ó ❛t✉❛❧ ❥á ♣❡rt❡♥❝❡ ❛ ❧✐st❛ ❛❜❡rt❛✳ ❙❡ ♥ã♦ ♣❡rt❡♥❝❡r✱ ❡❧❡ é ❛❞✐❝✐♦♥❛❞♦✳ ❙❡ ❡❧❡ ❥á ♣❡rt❡♥❝❡ ❛ ❧✐st❛ ❛❜❡rt❛✱ é ❝♦♠♣❛r❛❞♦ ♦ f(n) ❛t✉❛❧ ❝♦♠ ♦ f(n) ❛r♠❛③❡♥❛❞♦ ♥❛ ❧✐st❛ ❛❜❡rt❛✳ ❙❡ ♦ f(n) ❛t✉❛❧ ❢♦r ♠❡♥♦r✱ ♦ ♥ó é s✉❜st✐t✉í❞♦ ♥❛ ❧✐st❛ ❛❜❡rt❛ ❬❍❛rt ❡t ❛❧✳ ✶✾✻✽❪✳
✷❯♠❛ ❤❡✉ríst✐❝❛ ❛❞♠✐ssí✈❡❧ é ✉♠❛ ❤❡✉ríst✐❝❛ ♦♥❞❡ ❛ ❡st✐♠❛t✐✈❛ ❞❡ ❝✉st♦ ❢♦r♥❡❝✐❞❛ ♣❛r❛ ✉♠ ❡st❛❞♦
q✉❛❧q✉❡r ❛té ❛ ♠❡t❛ ♥✉♥❝❛ s✉♣❡r❛ s❡✉ ❝✉st♦ r❡❛❧ ✭h(n)< g(n)✮✳
✸❯♠❛ ❤❡✉ríst✐❝❛ é ❝♦♥s✐st❡♥t❡ s❡ ♣❛r❛ ❝❛❞❛ ❡st❛❞♦s✱ ❡ s❡✉s s✉❝❡ss♦r❡s s′ ❣❡r❛❞♦s ♣♦r ✉♠❛ ❛çã♦a✱ ♦
