❱❛❧ér✐♦ ●✉t❡♠❜❡r❣ ❞❡ ▼❡❞❡✐r♦s ❏✉♥✐♦r
❆♣❧✐❝❛çã♦ ❞♦ ▼ét♦❞♦ ❇ ❛♦ Pr♦❥❡t♦ ❋♦r♠❛❧ ❞❡
❙♦❢t✇❛r❡ ❊♠❜❛r❝❛❞♦
❱❛❧ér✐♦ ●✉t❡♠❜❡r❣ ❞❡ ▼❡❞❡✐r♦s ❏✉♥✐♦r
❆♣❧✐❝❛çã♦ ❞♦ ▼ét♦❞♦ ❇ ❛♦ Pr♦❥❡t♦ ❋♦r♠❛❧ ❞❡
❙♦❢t✇❛r❡ ❊♠❜❛r❝❛❞♦
❉✐ss❡rt❛çã♦ ❞❡ ♠❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠✲ ♣✉t❛çã♦ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞✲ ❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❉❛✈✐❞ ❇♦r✐s P❛✉❧ ❉é❤❛r❜❡
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❙✐st❡♠❛s ❡ ❈♦♠♣✉t❛çã♦
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ s♦❜ ♦ tít✉❧♦ ✏❆♣❧✐❝❛çã♦ ❞♦ ▼ét♦❞♦ ❇ ❛♦ Pr♦❥❡t♦ ❋♦r♠❛❧ ❞❡ ❙♦❢t✇❛r❡ ❊♠❜❛r❝❛❞♦✑✱ ❞❡❢❡♥❞✐❞❛ ♣♦r ❱❛❧ér✐♦ ●✉t❡♠❜❡r❣ ❞❡ ▼❡❞❡✐r♦s ❏r ❡♠ ✾ ❞❡ ❙❡t❡♠❜r♦ ❞❡ ✷✵✵✾✱ ❡♠ ◆❛t❛❧✱ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡✱ ♣❡❧❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛ ❝♦♥st✐t✉í❞❛ ♣❡❧♦s ♣r♦❢❡ss♦r❡s✿
Pr♦❢✳ ❉r✳ ❉❛✈✐❞ ❇♦r✐s P❛✉❧ ❉é❤❛r❜❡
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ✲ ❯❋❘◆
❖r✐❡♥t❛❞♦r
Pr♦❢✳ ❉r✳ ❆♥❛♠❛r✐❛ ▼❛rt✐♥s ▼♦r❡✐r❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥❢♦r♠át✐❝❛ ❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ✲ ❯❋❘◆
Pr♦❢✳ ❉r✳ ❆♥❛ ❈❛✈❛❧❝❛♥t✐
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❨♦r❦
Pr♦❢✳ ❉r✳ ❆♥❞ré ▲❛✉r✐♥❞♦ ▼❛✐t❡❧❧✐
❆❣r❛❞❡❝✐♠❡♥t♦s
❉❡❞✐❝♦ ♠❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s ♣❛r❛✿
✲ ❉❡✉s ♣♦r ✐❧✉♠✐♥❛r ♠❡✉ ❝❛♠✐♥❤♦ ❡ ♠❡ ❞❛r ❢♦rç❛s ♣❛r❛ s❡❣✉✐r s❡♠♣r❡ ❡♠ ❢r❡♥t❡❀ ✲ ❖s ♠❡✉s ♣❛✐s ♣♦r t♦❞♦ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ❡ ✜♥❛♥❝✐❛♠❡♥t♦ ❞♦s ♠❡✉s ❡st✉❞♦s❀
✲ ❖s ♣r♦❢❡ss♦r❡s ❉❛✈✐❞ ❉é❤❛r❜❡ ❡ ❆♥❛♠❛r✐❛ ▼❛rt✐♥s q✉❡ ♠❡ ♦r✐❡♥t❛r❛♠ ❡ s❡♠♣r❡ q✉❡ ❡st❛✈❛♠ ❞✐s♣♦♥í✈❡✐s ❛t❡♥❞✐❛♠✲♠❡ ♣r♦♥t❛♠❡♥t❡❀
✲ ❆ ❘♦ss❛♥❛ ♣♦r ❝♦♠♣r❡❡♥❞❡r ❡ ❛❥✉❞❛r✲♠❡ ♥♦s ❧♦♥❣♦s ♣❡rí♦❞♦s ❞❡ ❡st✉❞♦❀ ✲ ❖s ♣r♦❢❡ss♦r❡s ❞♦ ❉■▼❆♣ q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❢♦r♠❛çã♦ ❞❡ ✉♠ ♠♦❞♦ ❣❡r❛❧❀ ✲ ❖s ♠❡✉s ❢❛♠✐❧✐❛r❡s ♣♦r t♦❞♦ ❛♣♦✐♦❀
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ♠ét♦❞♦ ❞❡ ♣r♦❥❡t♦ ♣r♦♣♦st❛ ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❞♦ s♦❢t✇❛r❡ ❛té ♦ ♥í✈❡❧ ❞❛ ❧✐♥❣✉❛❣❡♠ ❛ss❡♠❜❧②✳ ❊ss❡ ♠ét♦❞♦ é ❢✉♥❞❛✲ ♠❡♥t❛❞❛ ♥♦ ♠ét♦❞♦ ❇✱ ♦ q✉❛❧ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❝♦♠ ♦ ❛♣♦✐♦ ❡ ✐♥t❡r❡ss❡ ❞❛ ♠✉❧t✐♥❛❝✐♦♥❛❧ ❞♦ s❡t♦r ❞❡ ♣❡tró❧❡♦ ❡ ❣ás ❇r✐t✐s❤ P❡tr♦❧❡✉♠ ✭❇P✮✳ ❆ ❡✈♦❧✉çã♦ ❞❡ss❛ ♠❡t♦❞♦❧♦❣✐❛ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❝♦♥tr✐❜✉✐r ♥❛ r❡s♣♦st❛ ❞❡ ✉♠ ✐♠♣♦rt❛♥t❡ ♣r♦❜❧❡♠❛✱ q✉❡ ♣❡rt❡♥❝❡ ❛♦s ❣r❛♥❞❡s ❞❡s❛✜♦s ❞❛ ❝♦♠♣✉t❛çã♦✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ✏❚❤❡ ❱❡r✐❢②✐♥❣ ❈♦♠♣✐❧❡r✑✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❞❡s❝r❡✈❡ ✉♠ ♠♦❞❡❧♦ ❢♦r♠❛❧ ❞♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r ❩✽✵ ❡ ✉♠ s✐st❡♠❛ r❡❛❧ ❞❛ ár❡❛ ❞❡ ♣❡tró❧❡♦✳ ❖ ♠♦❞❡❧♦ ❢♦r♠❛❧ ❞♦ ❩✽✵ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ❞♦❝✉♠❡♥t❛❞♦✱ ♣♦r s❡r ✉♠ ♣ré✲r❡q✉✐s✐t♦ ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ❛té ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧②✳ ❆ ✜♠ ❞❡ ✈❛❧✐❞❛r ❡ ❞❡s❡♥✈♦❧✈❡r ❛ ♠❡t♦❞♦❧♦❣✐❛ ❝✐t❛❞❛✱ ❡❧❛ ❢♦✐ ❛♣❧✐❝❛❞❛ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ t❡st❡ ❞❡ ♣r♦❞✉çã♦ ❞❡ ♣♦ç♦s ❞❡ ♣❡tró❧❡♦✱ ♦ q✉❛❧ é ❛♣r❡s❡♥t❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✳ ❆t✉❛❧♠❡♥t❡✱ ❛❧❣✉♠❛s ❛t✐✈✐❞❛❞❡s sã♦ r❡✲ ❛❧✐③❛❞❛s ♠❛♥✉❛❧♠❡♥t❡✳ ◆♦ ❡♥t❛♥t♦✱ ✉♠❛ ♣❛rt❡ s✐❣♥✐✜❝❛t✐✈❛ ❞❡ss❛s ❛t✐✈✐❞❛❞❡s ♣♦❞❡ s❡r ❛✉t♦♠❛t✐③❛❞❛ ❛tr❛✈és ❞❡ ✉♠ ❝♦♠♣✐❧❛❞♦r ❡s♣❡❝í✜❝♦✳ P❛r❛ ❡ss❡ ✜♠✱ ❛ ♠♦❞❡❧❛❣❡♠ ❢♦r♠❛❧ ❞♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r ❡ ❛ ♠♦❞❡❧❛❣❡♠ ❞♦ s✐st❡♠❛ ❞❡ t❡st❡ ❞❡ ♣r♦❞✉çã♦ ❢♦r♥❡❝❡♠ ❝♦♥❤❡❝✐✲ ♠❡♥t♦s ❡ ❡①♣❡r✐ê♥❝✐❛s ✐♠♣♦rt❛♥t❡s ♣❛r❛ ♦ ♣r♦❥❡t♦ ❞❡ ✉♠ ♥♦✈♦ ❝♦♠♣✐❧❛❞♦r✳ ❊♠ s✉♠❛✱ ❡ss❡ tr❛❜❛❧❤♦ ❞❡✈❡ ♠❡❧❤♦r❛r ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ❞♦s ♠❛✐s r✐❣♦r♦s♦s ❝r✐tér✐♦s ❞❡ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧✿ ❛❝❡❧❡r❛♥❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ✈❡r✐✜❝❛çã♦✱ r❡❞✉③✐♥❞♦ ♦ t❡♠♣♦ ❞❡ ♣r♦❥❡t♦ ❡ ❛✉♠❡♥t❛♥❞♦ ❛ q✉❛❧✐❞❛❞❡ ❡ ❝♦♥✜❛♥ç❛ ❞♦ ♣r♦❞✉t♦ ❞❡ s♦❢t✇❛r❡ ✜♥❛❧✳ ❚♦❞❛s ❡ss❛s q✉❛❧✐❞❛❞❡s sã♦ ❜❛st❛♥t❡ r❡❧❡✈❛♥t❡s ♣❛r❛ s✐st❡♠❛s q✉❡ ❡♥✈♦❧✈❡♠ sér✐♦s r✐s❝♦s ♦✉ ❡①✐❣❡♠ ❛❧t❛ ❝♦♥✜❛♥ç❛✱ ♦s q✉❛✐s sã♦ ♠✉✐t♦ ❝♦♠✉♥s ♥❛ ✐♥❞ústr✐❛ ❞♦ ♣❡tró❧❡♦✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ s❤♦✇s ❛ ♣r♦❥❡❝t ♠❡t❤♦❞ ♣r♦♣♦s❡❞ t♦ ❞❡s✐❣♥ ❛♥❞ ❜✉✐❧❞ s♦❢t✇❛r❡ ❝♦♠♣♦♥❡♥ts ❢r♦♠ t❤❡ s♦❢t✇❛r❡ ❢✉♥❝t✐♦♥❛❧ ♠♦❞❡❧ ✉♣ t♦ ❛ss❡♠❜❧② ❝♦❞❡ ❧❡✈❡❧ ✐♥ ❛ r✐❣♦r♦✉s ❢❛s❤✐♦♥✳ ❚❤✐s ♠❡t❤♦❞ ✐s ❜❛s❡❞ ♦♥ t❤❡ ❇ ♠❡t❤♦❞✱ ✇❤✐❝❤ ✇❛s ❞❡✈❡❧♦♣❡❞ ✇✐t❤ s✉♣♣♦rt ❛♥❞ ✐♥t❡r❡st ♦❢ ❇r✐t✐s❤ P❡tr♦❧❡✉♠ ✭❇P✮✳ ❖♥❡ ❣♦❛❧ ♦❢ t❤✐s ♠❡t❤♦❞♦❧♦❣② ✐s t♦ ❝♦♥tr✐❜✉t❡ t♦ s♦❧✈❡ ❛♥ ✐♠♣♦r✲ t❛♥t ♣r♦❜❧❡♠✱ ❦♥♦✇♥ ❛s ✏❚❤❡ ❱❡r✐❢②✐♥❣ ❈♦♠♣✐❧❡r✑✳ ❇❡s✐❞❡s✱ t❤✐s ✇♦r❦ ❞❡s❝r✐❜❡s ❛ ❢♦r♠❛❧ ♠♦❞❡❧ ♦❢ ❩✽✵ ♠✐❝r♦❝♦♥tr♦❧❧❡r ❛♥❞ ❛ r❡❛❧ s②st❡♠ ♦❢ ♣❡tr♦❧❡✉♠ ❛r❡❛✳ ❚♦ ❛❝❤✐❡✈❡ t❤✐s ❣♦❛❧✱ t❤❡ ❢♦r♠❛❧ ♠♦❞❡❧ ♦❢ ❩✽✵ ✇❛s ❞❡✈❡❧♦♣❡❞ ❛♥❞ ❞♦❝✉♠❡♥t❡❞✱ ❛s ✐t ✐s ♦♥❡ ❦❡② ❝♦♠♣♦♥❡♥t ❢♦r t❤❡ ✈❡r✐✜❝❛t✐♦♥ ✉♣t♦ t❤❡ ❛ss❡♠❜❧② ❧❡✈❡❧✳ ■♥ ♦r❞❡r t♦ ✐♠♣r♦✈❡ t❤❡ ♠❡♥t✐♦♥❡❞ ♠❡t❤♦❞♦❧♦❣②✱ ✐t ✇❛s ❛♣♣❧✐❡❞ ♦♥ ❛ ♣❡tr♦❧❡✉♠ ♣r♦❞✉❝t✐♦♥ t❡st s②st❡♠✱ ✇❤✐❝❤ ✐s ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ✇♦r❦✳ P❛rt ♦❢ t❤✐s t❡❝❤♥✐q✉❡ ✐s ♣❡r❢♦r♠❡❞ ♠❛♥✉❛❧❧②✳ ❍♦✇❡✈❡r✱ ❛❧♠♦st ♦❢ t❤❡s❡ ❛❝t✐✈✐t✐❡s ❝❛♥ ❜❡ ❛✉t♦♠❛t❡❞ ❜② ❛ s♣❡❝✐✜❝ ❝♦♠♣✐❧❡r✳ ❚♦ ❜✉✐❧❞ s✉❝❤ ❝♦♠♣✐❧❡r✱ t❤❡ ❢♦r♠❛❧ ♠♦❞❡❧❧✐♥❣ ♦❢ ♠✐✲ ❝r♦❝♦♥tr♦❧❧❡r ❛♥❞ ♠♦❞❡❧❧✐♥❣ ♦❢ ♣r♦❞✉❝t✐♦♥ t❡st s②st❡♠ s❤♦✉❧❞ ♣r♦✈✐❞❡ r❡❧❡✈❛♥t ❦♥♦✇❧❡❞❣❡ ❛♥❞ ❡①♣❡r✐❡♥❝❡s t♦ t❤❡ ❞❡s✐❣♥ ♦❢ ❛ ♥❡✇ ❝♦♠♣✐❧❡r✳ ■♥ s✉♠♠❛r②✱ t❤✐s ✇♦r❦ s❤♦✉❧❞ ✐♠♣r♦✈❡ t❤❡ ✈✐❛❜✐❧✐t② ♦❢ ♦♥❡ ♦❢ t❤❡ ♠♦st str✐♥❣❡♥t ❝r✐t❡r✐❛ ❢♦r ❢♦r♠❛❧ ✈❡r✐✜❝❛t✐♦♥✿ s♣❡❡❞✐♥❣ ✉♣ t❤❡ ✈❡r✐✜❝❛t✐♦♥ ♣r♦❝❡ss✱ r❡❞✉❝✐♥❣ ❞❡s✐❣♥ t✐♠❡ ❛♥❞ ✐♥❝r❡❛s✐♥❣ t❤❡ q✉❛❧✐t② ❛♥❞ r❡❧✐❛❜✐❧✐t② ♦❢ t❤❡ ♣r♦❞✉❝t ♦❢ t❤❡ ✜♥❛❧ s♦❢t✇❛r❡✳ ❆❧❧ t❤❡s❡ q✉❛❧✐t✐❡s ❛r❡ ✈❡r② ✐♠♣♦rt❛♥t ❢♦r s②st❡♠s t❤❛t ✐♥✲ ✈♦❧✈❡ s❡r✐♦✉s r✐s❦s ♦r ✐♥ ♥❡❡❞ ♦❢ ❛ ❤✐❣❤ ❝♦♥✜❞❡♥❝❡✱ ✇❤✐❝❤ ✐s ✈❡r② ❝♦♠♠♦♥ ✐♥ t❤❡ ♣❡tr♦❧❡✉♠ ✐♥❞✉str②✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ■♥tr♦❞✉çã♦ ♣✳ ✶✸
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺ ✶✳✷ ❚r❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼
✷ ▼ét♦❞♦ ❇ ♣✳ ✶✾
✷✳✶ ▼♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵ ❖❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧✿ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸ ✷✳✷ ▼♦❞❡❧♦ r❡✜♥❛❞♦ ♦✉ r❡✜♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻ ✷✳✷✳✶ ❖❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ r❡✜♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼ ✷✳✸ ▼♦❞❡❧♦ ❛❧❣♦rít♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾ ✷✳✸✳✶ ❊s♣❡❝✐✜❝❛çã♦ ❞❡ ❧❛ç♦s ♥♦ ♠ét♦❞♦ ❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✸ ❱❡r✐✜❝❛çã♦ ❡♠ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧② ♣✳ ✸✷
✸✳✶ P❧❛t❛❢♦r♠❛ ♠í♥✐♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✷ ✸✳✷ ❱❡r✐✜❝❛çã♦ ❡♠ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺ ✸✳✷✳✶ ❊s♣❡❝✐✜❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞♦ ♣r♦❣r❛♠❛ ❙✇❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼
✹ ▼♦❞❡❧❛❣❡♠ ❞❡ ✐♥str✉çõ❡s ❛ss❡♠❜❧② ❡♠ ❇ ♣✳ ✹✶
✹✳✶✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ✈❡t♦r ❞❡ ❜✐ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹ ✹✳✶✳✸ ▼♦❞❡❧❛♥❞♦ ❜②t❡s ❡ ✈❡t♦r❡s ❞❡ ❜✐ts ❞❡ t❛♠❛♥❤♦ ✶✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✹✳✶✳✹ ❆r✐t♠ét✐❝❛ ❞❡ ✈❡t♦r❡s ❞❡ ❜✐ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✹✳✷ ❇✐❜❧✐♦t❡❝❛ ❞♦s t✐♣♦s ❞❡ ❞❛❞♦s ✐♥t❡✐r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✹✳✸ ▼♦❞❡❧❛❣❡♠ ❞♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r ❩✽✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼ ✹✳✸✳✶ ▼♦❞❡❧❛♥❞♦ r❡❣✐str❛❞♦r❡s ❡ ♣♦rt❛s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾ ✹✳✸✳✷ ❘❡❣✐str❛❞♦r ❞❡ ✢❛❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵ ✹✳✸✳✸ ❋✉♥çõ❡s ❞❡ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✶ ✹✳✸✳✹ ▼❡♠ór✐❛ ❞❡ ♣r♦❣r❛♠❛s✱ ♣✐❧❤❛ ❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷ ✹✳✸✳✺ ❯♥✐❞❛❞❡ ❧ó❣✐❝❛ ❡ ❛r✐t♠ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸ ✹✳✸✳✻ ▼♦❞❡❧❛♥❞♦ ❛s ♦♣❡r❛çõ❡s ❞❡ ♠✉❞❛♥ç❛ ❞❡ ❡st❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹ ✹✳✸✳✻✳✶ ▼♦❞❡❧❛♥❞♦ ❛s ❛çõ❡s ❡①t❡r♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✺ ✹✳✸✳✻✳✷ ▼♦❞❡❧❛♥❞♦ ✐♥str✉çõ❡s ❞❡ ❝♦♥tr♦❧❡ ❞❛s ♣♦rt❛s ❞❡ ❡♥tr❛❞❛
❡ s❛í❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✹✳✹ ❘❡❣r❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ ♣r♦✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽ ✹✳✺ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s s♦❜r❡ ♦ ♠♦❞❡❧♦ ❞♦ ❩✽✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶
✺ ❊st✉❞♦ ❞❡ ❝❛s♦ ♣✳ ✻✺
✺✳✶ ❚❡st❡ ❞❡ ♣r♦❞✉çã♦ ❡♠ t❛♥q✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺ ✺✳✷ ▼♦❞❡❧❛❣❡♠ ❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽ ✺✳✸ Pr♦❝❡ss♦ ❞❡ ✈❡r✐✜❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ❇ ❛ss❡♠❜❧② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✶ ✺✳✹ ❙✐♠✉❧❛çã♦ ❞♦ ❝ó❞✐❣♦ ❛ss❡♠❜❧② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷ ✺✳✺ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s s♦❜r❡ ♦ ❡st✉❞♦ ❞❡ ❝❛s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸
❈♦♥❝❧✉sõ❡s ♣✳ ✼✺
❘❡❢❡rê♥❝✐❛s ♣✳ ✼✽
▲✐st❛ ❞❡ ❋✐❣✉r❛s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ❘❡❣r❛s ❞❡ s✉❜st✐t✉✐çã♦ ❣❡♥❡r❛❧✐③❛❞❛✳ ❖s sí♠❜♦❧♦s ✉t✐❧✐③❛❞♦s ♥❡st❛ t❛❜❡❧❛ ❡stã♦ ❞❡✜♥✐❞♦s ❝♦♠♦✿ P✱ P1✱ P2✱ Q sã♦ ♣r❡❞✐❝❛❞♦s❀ S✱ S1✱ S2 sã♦ s✉❜✲ st✐t✉✐çõ❡s❀ E ✉♠❛ ❡①♣r❡ssã♦❀ e1, e2 sã♦ ✈❛❧♦r❡s ❡ α ✉♠❛ ✈❛r✐á✈❡❧ q✉❡ é
✶✸
✶ ■♥tr♦❞✉çã♦
➱ ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠✉♠ ❡♥❝♦♥tr❛r s♦❢t✇❛r❡ ❡♠❜✉t✐❞♦ ♥♦s ♠❛✐s ❞✐✈❡rs♦s ♣r♦❞✉t♦s✳ ❊ss❡ é ✉♠ t✐♣♦ s♦❢t✇❛r❡ ❞❡ ♣r♦♣ós✐t♦ ❡s♣❡❝✐❛❧ ✐♠♣❧❡♠❡♥t❛❞♦ ❡♠ ✉♠ ❝♦♠♣✉t❛❞♦r s✐♠♣❧✐✜❝❛❞♦ ❡ ♣r♦❥❡t❛❞♦ ♣❛r❛ ❡①❡❝✉t❛r ✉♠❛ ♦✉ ♣♦✉❝❛s ❢✉♥çõ❡s ❞❡❞✐❝❛❞❛s✳ ❊❧❡s sã♦ ❡♥❝♦♥tr❛❞♦s ❡♠ ✉♠❛ ✈❛st❛ ❣❛♠❛ ❞❡ ♣r♦❥❡t♦s✿ ❝♦♥tr♦❧❡s ❡♠ ♥❛✈✐♦s✱ ❝♦♥tr♦❧❡s ❡♠ ❛✈✐õ❡s✱ ✐♥❥❡çã♦ ❡❧❡trô♥✐❝❛ ❡♠ ❝❛rr♦s✱ ❡❧❡✈❛❞♦r❡s ❡ ❡♠ ✈ár✐♦s ❞✐s♣♦s✐t✐✈♦s ♠é❞✐❝♦s ❬●❛❥s❦✐ ❡ ❱❛❤✐❞ ✶✾✾✺❪✳ ❆t✉❛❧♠❡♥t❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❡ ♦ t❛♠❛♥❤♦ ❞❡ss❡ t✐♣♦ ❞❡ s♦❢t✇❛r❡ ✈ê♠ ❝r❡s❝❡♥❞♦ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ s❡✉ ❢❛t♦r ❝rít✐❝♦✳ ❈♦♠ ♦ ✉s♦ ❡♠ ❧❛r❣❛ ❡s❝❛❧❛ ❞❡ss❡ t✐♣♦ ❞❡ s♦❢t✇❛r❡✱ ♠✉✐t❛s ✈❡③❡s ✉s❛❞♦ ♥♦ ❝♦♥tr♦❧❡ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❞❡ s❡❣✉r❛♥ç❛✱ s✉r❣✐✉ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♦❢❡r❡❝❡r ✉♠❛ ❣❛r❛♥t✐❛ ♠❛✐s r✐❣♦r♦s❛ ❡♠ r❡❧❛çã♦ ❛♦ s❡✉ ❝♦rr❡t♦ ❢✉♥❝✐♦♥❛♠❡♥t♦✳ P❛r❛ ♣r♦✈❡r ✉♠❛ ❣❛r❛♥t✐❛ ❡st❛❜❡❧❡❝✐❞❛ ♠❛t❡♠❛t✐❝❛♠❡♥t❡✱ té❝♥✐❝❛s ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❡ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧ sã♦ ✉t✐❧✐③❛❞❛s✳
◆♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s♦❢t✇❛r❡s ❝rít✐❝♦s ❡ ❡♠❜❛r❝❛❞♦s✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ♣♦❞❡ s❡r ❜❛st❛♥t❡ ❝✉st♦s♦ ❡ ❞❡♠♦r❛❞♦✳ P♦ré♠ ♦ t❡♠♣♦ ❞❡ ♣r♦❥❡t♦ ❞❡ ✉♠ s✐st❡♠❛ é ✉♠ ❢❛t♦r ❝♦♠❡r❝✐❛❧ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ❞❡✈✐❞♦ ❛ ✈ár✐❛s r❛③õ❡s✳ ❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s é q✉❡ ♦s ♣r♦❞✉t♦s ♣✐♦♥❡✐r♦s tê♠ s✉❛s ✈❡♥❞❛s ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♠❛✐♦r❡s ❡ ❝♦♠ ✉♠❛ ♠❛✐♦r ♠❛r❣❡♠ ❞❡ ❧✉❝r♦ ❝♦♠ r❡❧❛çã♦ ❛♦s ♣r♦❞✉t♦s ❝♦♥❝♦rr❡♥t❡s ❧❛♥ç❛❞♦s ♣♦st❡r✐♦r♠❡♥t❡✳
◆♦ ❡♥t❛♥t♦✱ ❡①✐st❡♠ ♥♦ ♠❡r❝❛❞♦ ❝❡rt✐✜❝❛❞♦s ❞❡ ♥í✈❡✐s ❞❡ s❡❣✉r❛♥ç❛✱ q✉❡ ✈❛❧♦r✐③❛♠ ❛ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧ ❞❡ss❡s ♣r♦❞✉t♦s✱ ♦ q✉❡ ❡♠ ❛♣❧✐❝❛çõ❡s ❝rít✐❝❛s é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ q✉❛❧✐❞❛❞❡ ❞♦ ♣r♦❞✉t♦ ❬❉♦♥❞♦ss♦❧❛ ✶✾✾✾❪ ✳ ❙❡❣✉♥❞♦ ❬❈✉r② ✷✵✵✼❪✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❝❡rt✐✜❝❛çã♦ ❞❡ s♦❢t✇❛r❡ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ✈❡r✐✜❝❛r ♦✉ ✈❛❧✐❞❛r ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦s r❡q✉✐✲ s✐t♦s ❞❡ s♦❢t✇❛r❡✱ s❡♥❞♦ q✉❡✱ ❛t✉❛❧♠❡♥t❡✱ ❛ té❝♥✐❝❛ ♠❛✐s ❝♦♥✜á✈❡❧ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞❡ss❡ ♣r♦❝❡ss♦ é ❜❛s❡❛❞❛ ❡♠ ❛r❣✉♠❡♥t♦s ❝♦♠ ❢✉♥❞❛♠❡♥t♦s ♠❛t❡♠át✐❝♦s✳
✶✹
❡s♣❡❝✐✜❝❛çã♦✱ ✈❡r✐✜❝❛çã♦ ❡ às ✈❡③❡s ❛té ❣❡r❛çã♦ ❞❡ ❝ó❞✐❣♦✳ P♦rt❛♥t♦✱ ❡ss❡s ♠ét♦❞♦s sã♦ ❛❞❡q✉❛❞♦s ♣❛r❛ ❛❣✐❧✐③❛r ♦ ♣r♦❝❡ss♦ ❞❡ ♣r♦❥❡t♦ ❡ ✈❛❧✐❞❛çã♦ ❞❡ s✐st❡♠❛s ❝rít✐❝♦s✳
❊①✐st❡♠ ✈ár✐❛s ❧✐♥❣✉❛❣❡♥s ❡ ♠❡t♦❞♦❧♦❣✐❛s ❢♦r♠❛✐s✱ ❝♦♥t✉❞♦ ❡st❡ tr❛❜❛❧❤♦ ❛❞♦t❛ ♦ ♠ét♦❞♦ ❇ ❬❆❜r✐❛❧ ✶✾✾✻❪✳ ❊ss❡ ♠ét♦❞♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❝♦♠ ♦ ❛♣♦✐♦ ❡ ✐♥t❡r❡ss❡ ❞❛ ♠✉❧t✐✲ ♥❛❝✐♦♥❛❧ ❞♦ s❡t♦r ❞❡ ♣❡tró❧❡♦ ❡ ❣ás ❇r✐t✐s❤ P❡tr♦❧❡✉♠ ✭❇P✮✳ ❖ ♠ét♦❞♦ ❇ t❡♠ s❡ ♠♦str❛❞♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♠❛❞✉r♦ ❡ ✈❡♠ s❡♥❞♦ ✉s❛❞♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❞✐✈❡rs♦s s✐st❡♠❛s ❞❡ s❡❣✉r❛♥ç❛ ❝rít✐❝❛ ♥❛ ❊✉r♦♣❛✳ ❊❧❡ é ✉♠ ♣r♦❝❡ss♦ ❛❜r❛♥❣❡♥t❡ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s♦❢t✇❛r❡ q✉❡ s✉♣♦rt❛ ❛ ❡s♣❡❝✐✜❝❛çã♦✱ ✈❡r✐✜❝❛çã♦✱ r❡✜♥❛♠❡♥t♦ ❡ ❣❡r❛çã♦ ❞❡ ❝ó❞✐❣♦✳ ▼❛s t❛♠❜é♠✱ ❡❧❡ é ♣❛rt✐❝✉❧❛r♠❡♥t❡ ❢♦rt❡ ♥❛ ♥♦çã♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡♠ ♥í✈❡✐s✱ ♦ q✉❡ ♣❡r✲ ♠✐t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ s✐st❡♠❛ r❡❧❛t✐✈❛♠❡♥t❡ ❝♦♠♣❧❡①♦ s❡r ❞❡❝♦♠♣♦st♦ ❡♠ ✉♠❛ ❝♦♠♣♦s✐çã♦ ❞❡ ♠ó❞✉❧♦s ✉s❛♥❞♦ ✉♠ ♣❡q✉❡♥♦ ♥ú♠❡r♦ ❞❡ ❝♦♥str✉çõ❡s ❬❇✲❈♦r❡ ✶✾✾✾❪✳ ❆❧é♠ ❞✐ss♦✱ ❡①✐st❡♠ ✈ár✐❛s ❢❡rr❛♠❡♥t❛s ❞❡ s✉♣♦rt❡ ❛ ❇ ❬❈❧❡❛rs② ✷✵✵✾✱ ❆❜r✐❛❧ ✷✵✵✼✱ ❇✲❈♦r❡ ✶✾✾✺❪✳ ❖ ❆t❡❧✐❡r❇ ❬❈❧❡❛rs② ✷✵✵✾❪ é ❛ s✉❛ ♣r✐♥❝✐♣❛❧ ❢❡rr❛♠❡♥t❛❀ ❡❧❡ s✉♣♦rt❛ ✈ár✐♦s r❡❝✉rs♦s ❛✈❛♥ç❛✲ ❞♦s ❡ ✐♥t❡r❡ss❛♥t❡s✿ ♣r♦✈❛❞♦r ✐♥t❡r❛t✐✈♦✱ ♣r♦✈❛❞♦r ❞✐str✐❜✉í❞♦ ❡♠ r❡❞❡✱ ❣❡r❛❞♦r ❞❡ ❝ó❞✐❣♦ ❡♠ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦✱ ❡t❝✳ ❆s ♣♦t❡♥❝✐❛❧✐❞❛❞❡s ❞♦ ♠ét♦❞♦ ❇ t♦r♥❛♠ ♠❛✐s ✈✐á✈❡✐s ❛s ❡s♣❡❝✐✜❝❛çõ❡s ❡ ❝❡rt✐✜❝❛çõ❡s ❞❡ s✐st❡♠❛s ❞❡ ❡s❝❛❧❛ ✐♥❞✉str✐❛❧✳ ❊♥tã♦✱ ♣♦r ❡ss❛s ❡ ♦✉tr❛s ❝❛♣❛❝✐❞❛❞❡s✱ ♦ ✐♥t❡r❡ss❡ ♥❛ ✐♥❞ústr✐❛ ♣♦r ❇ é ❝r❡s❝❡♥t❡✳
❯♠❛ ♦✉tr❛ r❛③ã♦ ♣❛r❛ ❡s❝♦❧❤❛ ❞♦ ♠ét♦❞♦ ❇ é q✉❡ ♦✉tr♦s tr❛❜❛❧❤♦s ❬❆❧❥❡r ❡t ❛❧✳ ✷✵✵✸✱ ▲❡✉s❝❤❡❧ ✷✵✵✽✱ ▲✉❞♦✈✐❝ ❡ ▲❛♥❡t ✶✾✾✾✱ ❊✈❛♥s ❡ ●r❛♥t ✷✵✵✽❪ ❝♦♠ ♦❜❥❡t✐✈♦ s❡♠❡❧❤❛♥t❡ ❛♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ t❛♠❜é♠ ✉t✐❧✐③❛♠ ❇✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s♦❢t✇❛r❡✱ ♦ ♠ét♦❞♦ ❇ é ♠❛✐s ❛❞❡q✉❛❞♦ q✉❡ ♦ ❊✈❡♥t✲❇✱ ♣♦✐s ♦ ♠ét♦❞♦ ❇ ♣♦ss✉✐ ❝♦♥str✉çõ❡s ♠❛✐s ♣ró①✐♠❛s ❞❛s ❧✐♥❣✉❛❣❡♥s ❞❡ ♣r♦❣r❛♠❛çã♦ ❡ s✉❛s ❢❡rr❛♠❡♥t❛s sã♦ ❝❛♣❛③❡s ❞❡ ❣❡r❛r ❝ó❞✐❣♦ ♥❡ss❛ ❧✐♥❣✉❛❣❡♠✳ ❆❧é♠ ❞✐ss♦✱ ♦ s✉♣♦rt❡ ❢❡rr❛♠❡♥t❛❧ ♣❛r❛ ❇ ❡r❛ ♠❛✐s r♦❜✉st♦ q✉❛♥❞♦ ♦ tr❛❜❛❧❤♦ ❢♦✐ ✐♥✐❝✐❛❞♦✳
❖ ♠ét♦❞♦ ❇ ♣♦ss✉✐ ✉♠❛ ❝❛♣❛❝✐❞❛❞❡ ❡s♣❡❝✐❛❧✿ ❝❛❞❛ ♣❛ss♦ ❞❛ ❡s♣❡❝✐✜❝❛çã♦ ❇ ♣♦❞❡ ❛❞✐❝✐♦♥❛r ♠❛✐s ❞❡t❛❧❤❡s ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ❛❜str❛çã♦✳ ❊♠ ❇ ❡ss❡ ♣❛ss♦ é ❞❡♥♦♠✐✲ ♥❛❞♦ r❡✜♥❛♠❡♥t♦✳ ❖ r❡✜♥❛♠❡♥t♦ é ✉♠❛ té❝♥✐❝❛ ✉s❛❞❛ ♣❛r❛ ✈❡r✐✜❝❛r ❛ tr❛♥s❢♦r♠❛çã♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❛❜str❛t♦ ❞❡ s♦❢t✇❛r❡ ✭❡s♣❡❝✐✜❝❛çã♦✮ ❡♠ ✉♠ ♦✉tr♦ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ♠❛✐s ❝♦♥❝r❡t♦ ❬❆❜r✐❛❧ ✶✾✾✻✱ ▼♦r❣❛♥ ✶✾✽✾❪✳ ❚❛❧ té❝♥✐❝❛ ♣❡r♠✐t❡ q✉❡ ♦ ♠ét♦❞♦ ❇ s✉♣♦rt❡ ❛ ✈❡✲ r✐✜❝❛çã♦ ❡♠ ✉♠ ♥í✈❡❧ s✉✜❝✐❡♥t❡♠❡♥t❡ ♣ró①✐♠♦ ❞♦ ♥í✈❡❧ ❞❡ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡str✉t✉r❛❞❛✳ ❊♥✜♠✱ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡s♣❡❝✐✜❝❛r ♠♦❞❡❧♦s ❞❡ s♦❢t✇❛r❡ ❡ ✈❡r✐✜❝❛r ❛ ❝♦rr❡s✲ ♣♦♥❞ê♥❝✐❛ ❡♥tr❡ ♦ ♠♦❞❡❧♦ ❡ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ♠❡r❡❝❡ ❞❡st❛q✉❡✱ ♣♦rq✉❡ ✐ss♦ é ✉♠ r❡q✉✐s✐t♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ❞❡ ♣r♦❣r❛♠❛s✳
✶✺
♠❛çã♦✱ ♠✉✐t❛s ✈❡③❡s✱ ❛s ♣ró♣r✐❛s ❢❡rr❛♠❡♥t❛s ❞❡ ❡s♣❡❝✐✜❝❛çã♦ sã♦ ❝❛♣❛③❡s ❞❡ tr❛♥s❢♦r♠❛r ❛ ❡s♣❡❝✐✜❝❛çã♦ ❡♠ ❝ó❞✐❣♦ ❞❡ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❈✳ P♦ré♠✱ ❡♠ ❣❡r❛❧✱ ♥ã♦ ❡①✐st❡ ✉♠❛ ❣❛r❛♥t✐❛ ❢♦r♠❛❧ ❞❛ ❝♦♥s✐stê♥❝✐❛ ❞❛ ❣❡r❛çã♦ ❞❡ ❝ó❞✐❣♦ ❛ss❡♠❜❧② ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❡s♣❡❝✐✜❝❛❞♦ ♦✉ ❝ó❞✐❣♦ ❡♠ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦✳ ◆❡ss❡ ♣r♦❝❡ss♦ ❞❡ ❣❡r❛çã♦ ❞❡ ❝ó❞✐❣♦ ♦ ❝♦♠♣✐❧❛❞♦r✴❣❡r❛❞♦r ♣♦❞❡ t❛♠❜é♠ ✐♥tr♦❞✉③✐r ❡r✲ r♦s✳ P❛r❛ r❡s♦❧✈❡r ❡ss❡ ♣r♦❜❧❡♠❛ ❞❡ ❢♦r♠❛ ❝♦♥✜á✈❡❧✱ ❡①✐st❡ ❛ ♣r♦♣♦st❛ ❛♣r❡s❡♥t❛❞❛ ❡♠ ❬❉❛♥t❛s ❡t ❛❧✳ ✷✵✵✽❪ ♣❛r❛ ✈❡r✐✜❝❛r ❢♦r♠❛❧♠❡♥t❡ ❛ ❝♦♥s✐stê♥❝✐❛ ❞♦ r❡✜♥❛♠❡♥t♦ ❡♥tr❡ ♦ ♠♦✲ ❞❡❧♦ ❛❧❣♦rít♠✐❝♦ ❡s♣❡❝✐✜❝❛❞♦ ❡ ♦ ❝ó❞✐❣♦ s✐♥t❡t✐③❛❞♦ ✭❛ss❡♠❜❧② ❣❡r❛❞♦✮✳
❯♠ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❢♦r♠❛❧ ❝♦♠ ♦ ♠ét♦❞♦ ❇ ❞❡ ✉♠ s✐st❡♠❛ s✐♠♣❧❡s ❢♦✐ r❡❛❧✐③❛❞♦ ❡♠ ❡q✉✐♣❡ ❛té ♦ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧② ❡♠ três ❞✐❢❡r❡♥t❡s ♣❧❛t❛❢♦r♠❛s✿ ❩✽✵ ✭❛✉t♦r ❞❡st❛ ❞✐ss❡r✲ t❛çã♦✮✱ ✽✵✺✶ ✭❙t❡♣❤❡♥s♦♥ ●❛❧✈ã♦✮ ❡ P■❈ ✭❉❛✈✐❞ ❉é❤❛r❜❡✮✳ ❆ ❞❡s❝r✐çã♦ ❞❡ss❡ ❡①♣❡r✐♠❡♥t♦ ❡♥❝♦♥tr❛✲s❡ ❡♠ ❬❉❛♥t❛s ❡t ❛❧✳ ✷✵✵✽❪✳
❆ ❡s♣❡❝✐✜❝❛çã♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ❛ss❡♠❜❧② ❞❛s três ❞✐❢❡r❡♥t❡s ♣❧❛t❛❢♦r♠❛s P■❈✱ ❆✽✵✺✶ ❡ ❩✽✵ ♣♦ss✉í❛♠ ❝♦♥❝❡✐t♦s ❝♦♠✉♥s✱ ♠♦t✐✈❛♥❞♦ ✉♠❛ ♣❛❞r♦♥✐③❛çã♦ ❞❡ss❡s ❝♦♥❝❡✐t♦s✳ ❆❧é♠ ❞✐ss♦✱ ❡①✐st✐❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❝♦♥❝❧✉✐r ❛ ❡s♣❡❝✐✜❝❛çã♦ ❝♦♠♣❧❡t❛ ❞❡ ✉♠❛ ♣❧❛t❛❢♦r♠❛✱ ❞❡s❡♥✲ ✈♦❧✈❡r ❡st✉❞♦s ❞❡ ❝❛s♦ ♠❛✐s ❛✈❛♥ç❛❞♦s ❡ ❛♣❧✐❝❛r ♥♦✈❛s ❡ ❞✐❢❡r❡♥t❡s té❝♥✐❝❛s ❞❡ ✈❡r✐✜❝❛çã♦✳ P❛r❛ ❡ss❛s ♥❡❝❡ss✐❞❛❞❡s✱ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❞❡s❝r❡✈❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❡s♣❡❝✐✜✲ ❝❛çã♦ ❞❡ ❞✉❛s ❜✐❜❧✐♦t❡❝❛s ♣❛r❛ ♣❛❞r♦♥✐③❛r ♦s ❝♦♥❝❡✐t♦s ❝♦♠✉♥s ❞❛s ❞✐❢❡r❡♥t❡s ♣❧❛t❛❢♦r♠❛s❀ ❛ ❝♦♥str✉çã♦ ❞♦ ♠♦❞❡❧♦ ❢♦r♠❛❧ ❞❡ ✉♠ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r ❝♦♠ ❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ t♦❞❛s ❛s ✐♥str✉çõ❡s ❡ ❛çõ❡s q✉❡ ♠♦❞✐✜❝❛♠ s❡✉ ❡st❛❞♦ ❡ ✉♠ ❡st✉❞♦ ❞❡ ❝❛s♦ s✐♠♣❧❡s ❞❡ ✉♠ s♦❢t✲ ✇❛r❡ ❡♠❜❛r❝❛❞♦ ✈❡r✐✜❝❛❞♦ ❛té ♦ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧②✳ ❆❧é♠ ❞✐ss♦✱ ❡ss❡ tr❛❜❛❧❤♦ ❞❡t❛❧❤❛ ❛s ❞✐❢❡r❡♥t❡s té❝♥✐❝❛s ❞❡ ✈❡r✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛s✱ ♦ q✉❡ ❞❡✈❡ ❝♦❧❛❜♦r❛r ❜❛st❛♥t❡ ♥♦s tr❛❜❛❧❤♦s ❢✉t✉r♦s✳ ❊♠ s✉♠❛✱ ❡ss❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ♣r♦✈❡r ♠❡✐♦s ❞❡ ✈❡r✐✜❝❛r s♦❢t✇❛r❡ ❡♠ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧② ❡ ❛♣r❡s❡♥t❛r ❛s ❡①♣❡r✐ê♥❝✐❛s ❡ té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ✐ss♦✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ❡ss❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ❛ ♠♦❞❡❧❛❣❡♠ ❇ ❞♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r ❩✽✵✱ ❛ q✉❛❧ é ✉s❛❞❛ ♣❛r❛ ❛♣❧✐❝❛r ❛ s♦❧✉çã♦ ❝✐t❛❞❛ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ t❡st❡ ❞❡ ♣r♦❞✉çã♦ ❞❡ ♣♦ç♦s ❞❡ ♣❡tró❧❡♦✳ ❉❡ss❛ ❢♦r♠❛✱ ❛s ❡①♣❡r✐ê♥❝✐❛s ♦❜t✐❞❛s ♥❡ss❛ ❛t✐✈✐❞❛❞❡ ❝♦♥tr✐❜✉✐rã♦ ✐♥❞✐r❡t❛✲ ♠❡♥t❡ ♣❛r❛ ♦ ♣r♦❥❡t♦ ❞❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❝♦♠ ♦❜❥❡t✐✈♦ ❞❡ ❛✉t♦♠❛t✐③❛r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ✈❡r✐✜❝❛❞♦ ♣r♦✈✐❞♦ ♣❡❧♦ ♠ét♦❞♦ ❛té ♦ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧②✳
✶✳✶ ▼♦t✐✈❛çã♦
✶✻
❝❛❞❛ ✈❡③ ♠❛✐s ♣r❡❝✐s❛♠❡♥t❡ ♦ ❝♦rr❡t♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦s ♣r♦❣r❛♠❛s ❡♠ s✉❛s ♣❧❛t❛❢♦r♠❛s ❞❡ ❡①❡❝✉çã♦✳ ❊ss❛ ♥❡❝❡ss✐❞❛❞❡ ♦❝♦rr❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ ♥ã♦ s❡ t❡♠ ✉♠❛ ❣❛r❛♥t✐❛ ❢♦r♠❛❧✱ ♥♦s ❝♦♠♣✐❧❛❞♦r❡s tr❛❞✐❝✐♦♥❛✐s✱ s♦❜r❡ ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛ tr❛♥s❢♦r♠❛çã♦ ❞♦ ❝ó❞✐❣♦ ❢♦♥t❡ ❡♠ r❡❧❛çã♦ ❛ s❡✉ ♣r♦❣r❛♠❛ ❛ss❡♠❜❧② ❣❡r❛❞♦✳ ❊♠ ❣❡r❛❧✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♠♣✐❧❛çã♦ ♣♦❞❡ ✐♥tr♦❞✉③✐r ❡rr♦s s✉t✐s ♥♦s ♣r♦❣r❛♠❛s ❣❡r❛❞♦s✳ ❊♥tã♦✱ ✉♠ ❞♦s ❣r❛♥❞❡s ❞❡s❛✜♦s ❞❛ ❝♦♠♣✉t❛çã♦ é ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ✈❡r✐✜❝❛❞♦r❛ ❞❡ ❝♦♠♣✐❧❛çã♦✳ ❊ss❛ ❢❡rr❛♠❡♥t❛ ✉s❛ ♠❛t❡♠át✐❝❛ ❡ ❧ó❣✐❝❛ ♣❛r❛ ✈❡r✐✜❝❛r ❢♦r♠❛❧♠❡♥t❡ ❛ ❝♦rr❡çã♦ ❞♦s ♣r♦❣r❛♠❛s q✉❡ ❡❧❛ ❝♦♠♣✐❧❛ ❬❍♦❛r❡ ✷✵✵✺❪✳ ❆ss✐♠✱ ❡ss❡ ❞❡s❛✜♦ ❡stá ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❡ss❡ tr❛❜❛❧❤♦✱ ♣♦✐s ❛s ❛t✐✈✐❞❛❞❡s ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ sã♦ ♣❛ss♦s ✐♥✐❝✐❛✐s ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ss❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❝♦♠♣✐❧❛çã♦✳
❊①✐st❡♠ ✈ár✐♦s ❡①❡♠♣❧♦s ❞❡ ❞❡s❛str❡s ❡♠ q✉❡ ♦ ✉s♦ ✐♥t❡♥s♦ ❞❛ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧ ❡r❛ t❡♦r✐❝❛♠❡♥t❡ ✐♥❞✐s♣❡♥sá✈❡❧✳ ❯♠ ❞❡❧❡s ❢♦✐ ♦ ❞♦ ❢♦❣✉❡t❡ ❆r✐❛♥❡ ✺✶ ❡♠ ✶✾✾✻ q✉❡ ❡①♣❧♦❞✐✉ ✸✼ s❡❣✉♥❞♦s ❛♣ós ♦ ❧❛♥ç❛♠❡♥t♦✳ ❊ss❡ ❢♦❣✉❡t❡ ❝❛rr❡❣❛✈❛ q✉❛tr♦ s❛té❧✐t❡s ❝✉❥♦ ❝✉st♦ ❡r❛ ❯✩ ✺✵✵ ♠✐❧❤õ❡s✳ ❖ ♣r♦❜❧❡♠❛ ❢♦✐ ♣r♦✈♦❝❛❞♦ ♣♦r ✉♠ ❡rr♦ ❞❡ ♣r♦❥❡t♦✱ ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❝♦♥✈❡rt❡r ✉♠ ♥ú♠❡r♦ ❞❡ ✻✹ ❜✐ts ❞❡ ♣♦♥t♦ ✢✉t✉❛♥t❡ ♣❛r❛ ✉♠ ✐♥t❡✐r♦ ❞❡ ✶✻ ❜✐ts✱ ♦❝♦rr❡♥❞♦ ✉♠ tr❛♥s❜♦r❞❛♠❡♥t♦✳ ■ss♦ ♣r♦✈♦❝♦✉ ❛ ❡♠✐ssã♦ ❞❡ s✐♥❛✐s ✐♥❝♦rr❡t♦s ❛♦s ♠♦t♦r❡s ❡ ✐♠♣❧✐❝♦✉ ♦ ❛❝✐♦♥❛♠❡♥t♦ ❞❛ ❛✉t♦❞❡str✉✐çã♦ ❞♦ ❢♦❣✉❡t❡✳ ➱ ✐♠♣♦rt❛♥t❡ ❞❡st❛❝❛r q✉❡ ❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ✉t✐❧✐③❛❞❛ ❡r❛ ❆❞❛✱ ✉♠❛ ❧✐♥❣✉❛❣❡♠ q✉❡ ♣♦ss✉✐ ♦s ♠❛✐s ❛❧t♦s ❝❡rt✐✜❝❛❞♦s ❞❡ s❡❣✉r❛♥ç❛✳
➱ ♠✉✐t♦ ❝♦♠✉♠ s♦❢t✇❛r❡s ❡♠❜❛r❝❛❞♦s ❞❛ ár❡❛ ❞❡ ♣❡tró❧❡♦ ❡ ❣ás ❡♥✈♦❧✈❡r❡♠ ❝♦♠♣❧❡✲ ①✐❞❛❞❡✱ r✐s❝♦s ❡ ❡①✐❣✐r ❛❧t❛ ❝♦♥✜❛♥ç❛✳ ❉❡ss❛ ❢♦r♠❛✱ ✉♠ ♠❡✐♦ ❞❡ ♦❢❡r❡❝❡r ♠❛✐♦r❡s ❣❛r❛♥t✐❛s s♦❜r❡ ♦ ❝♦rr❡t♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ss❡ t✐♣♦ ❞❡ s♦❢t✇❛r❡ é ❛♣❧✐❝❛♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ❡♠ ❬❉❛♥t❛s ❡t ❛❧✳ ✷✵✵✽❪ ❡♠ ✉♠ s✐st❡♠❛ r❡❛❧ ❞❛ ár❡❛✱ ♦ q✉❛❧ é ❛♣r❡s❡♥t❛❞♦ ♥❛ s❡çã♦ ✺✳✷✳ ❊♥✜♠✱ ❛ ❡✈♦❧✉çã♦ ❞❡ss❛ ♠❡t♦❞♦❧♦❣✐❛ ♣♦❞❡ r❡♥❞❡r ❡♠ ❧♦♥❣♦ ♣r❛③♦ ❡❧❡✈❛❞♦s ❝❡rt✐✜❝❛❞♦s ❞❡ s❡❣✉r❛♥ç❛ ❛ ❡ss❡ t✐♣♦ ❞❡ s✐st❡♠❛✳
❆ ❡①✐❣ê♥❝✐❛ ❞❡ ❝❡rt✐✜❝❛çõ❡s ❞❡ s❡❣✉r❛♥ç❛ ♥♦s ❝♦♠♣✐❧❛❞♦r❡s ♠❛✐s ♣♦♣✉❧❛r❡s✱ ❝♦♠♦ ♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ❈ ♣❛r❛ ❛ ❛rq✉✐t❡t✉r❛ ✽✵①✽✻✷✱ ♥ã♦ é ✉♠❛ ❣r❛♥❞❡ ♣r❡♦❝✉♣❛çã♦ ❞♦s ♣r♦❥❡t✐st❛s❀ ♣♦rq✉❡ ❡ss❡s ❝♦♠♣✐❧❛❞♦r❡s sã♦ ✉s❛❞♦s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛✳ ❆ss✐♠✱ s❡✉ ✉s♦ ❡♠ ♠❛ss❛ ❢❛③ ♦ ♣❛♣❡❧ ❞❡ ✉♠ ❣r❛♥❞❡ ❝♦♥❥✉♥t♦ ❞❡ t❡st❡s✳ ❆❧é♠ ❞✐ss♦✱ ❡ss❡s ❝♦♠♣✐❧❛❞♦r❡s ♥ã♦ tê♠ ❝♦♠♦ ❢♦❝♦ q✉❡stõ❡s ❞❡ ❢♦rt❡ s❡❣✉r❛♥ç❛✱ ♣♦✐s ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s ♥ã♦ sã♦ ✉s❛❞♦s ❡♠ ❛♣❧✐❝❛çõ❡s ❝rít✐❝❛s✳
✶❆r✐❛♥❡ ✺ é ✉♠ t✐♣♦ ❞❡ ❢♦❣✉❡t❡ ♣r♦❥❡t❛❞♦ ♣❛r❛ ❝♦❧♦❝❛r s❛té❧✐t❡s ❛rt✐✜❝✐❛✐s ❡♠ ór❜✐t❛s ❣❡♦❡st❛❝✐♦♥ár✐❛s
❡ ❡♥✈✐❛r ❝❛r❣❛s ♣❛r❛ ór❜✐t❛s ❞❡ ❜❛✐①❛ ❛❧t✐t✉❞❡✳
✷✽✵①✽✻ é ♥♦♠❡ ❣❡♥ér✐❝♦ ❞❛❞♦ ♣❛r❛ ❛ ❛rq✉✐t❡t✉r❛ ❞❛ ❢❛♠í❧✐❛ ❞♦s ♣r♦❝❡ss❛❞♦r❡s ❜❛s❡❛❞♦s ♥♦ ✽✵✽✻✱ ❞❛
✶✼
❖s ❝♦♠♣✐❧❛❞♦r❡s ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ✉♠ ♥✐❝❤♦ ♠❡♥♦r ❞❡ ❛♣❧✐❝❛çõ❡s ♥ã♦ ❝♦♥t❛♠ ❝♦♠ ♦s t❡st❡s ❞❡ ✉s♦ ❡♠ ❧❛r❣❛ ❡s❝❛❧❛✳ ❊ q✉❛♥❞♦ ❡ss❡s ❝♦♠♣✐❧❛❞♦r❡s sã♦ ✉t✐❧✐③❛❞♦s ♥❛ ❝♦♠♣✐✲ ❧❛çã♦ ❞❡ ♣r♦❣r❛♠❛ ❞❡ ❛♣❧✐❝❛çõ❡s ❝rít✐❝❛s s❡ ❢❛③ ❞❡ ❡①tr❡♠❛ ♥❡❝❡ss✐❞❛❞❡ q✉❡ ❡❧❡s ♦❢❡r❡ç❛♠ ❝r✐tér✐♦s ❛❞❡q✉❛❞♦s ❞❡ q✉❛❧✐❞❛❞❡✳ ❊ss❡ é ❝♦♠✉♠❡♥t❡ ♦ ❝❛s♦ ❞♦s ❝♦♠♣✐❧❛❞♦r❡s ✉t✐❧✐③❛❞♦s ♣❛r❛ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r❡s ❡ ♠✐❝r♦♣r♦❝❡ss❛❞♦r❡s ❞❡ ♣r♦♣ós✐t♦s ❡s♣❡❝✐❛✐s✳ P♦rt❛♥t♦✱ ❡ss❛s ♣❧❛t❛❢♦r♠❛s ❡stã♦ ♥♦ ❢♦❝♦ ❞❛s ♣❡sq✉✐s❛s ❞❡st❡ tr❛❜❛❧❤♦✳
❆ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ❡♠ ❬❉❛♥t❛s ❡t ❛❧✳ ✷✵✵✽❪ é ❛ ❛❞♦t❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦✳ ❊❧❛ ❛✐♥❞❛ t❡♠ ❝✉st♦s ❞❡ ❛♣❧✐❝❛çã♦ r❡❧❛t✐✈❛♠❡♥t❡ ❛❧t♦s✱ ❝♦♥t✉❞♦ ❡ss❡s ♣♦❞❡♠ r❡❞✉③✐r s✐❣♥✐✜❝❛✲ t✐✈❛♠❡♥t❡✳ ❊ss❡s ❝✉st♦s ♣♦❞❡♠ ❞✐♠✐♥✉✐r ❝♦♠ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠ ❝♦♠♣✐❧❛❞♦r ♣❛r❛ ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ❡ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s té❝♥✐❝❛s✳ P❛r❛ s❛t✐s❢❛③❡r ❡ss❛s ♥❡❝❡ss✐❞❛❞❡s ♣♦❞❡✲s❡ r❡✉t✐❧✐③❛r ❛❧❣✉♥s ❝♦♠♣♦♥❡♥t❡s ❞❡ s♦❢t✇❛r❡ ❞❡ s✉♣♦rt❡ ❛♦ ♠ét♦❞♦ ❇ ❡ t❛♠❜é♠ ❞❡✜♥✐r ✉♠❛ ❡str❛té❣✐❛ ❞❡ ♣r♦✈❛ ♠❛✐s ❡s♣❡❝í✜❝❛ ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ♥♦ ♥í✈❡❧ ❞❡ ❛ss❡♠❜❧②✱ ♦ q✉❡ ❞❡✈❡ ❞✐♠✐♥✉✐r s❡♥s✐✈❡❧♠❡♥t❡ ♦ ❝✉st♦ ❞♦ ♣r♦❝❡ss♦✳ ❊♥✜♠✱ ♣❡sq✉✐s❛s ✐♥t❡♥s✐✜❝❛❞❛s ♥❡ss❡ s❡♥t✐❞♦ ♣♦❞❡♠ r❡♥❞❡r ót✐♠♦s r❡s✉❧t❛❞♦s✳
✶✳✷ ❚r❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s
❆t✉❛❧♠❡♥t❡✱ ♦s ♠ét♦❞♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ t❡♥t❛r ❣❛r❛♥t✐r ❛ ❝♦♥s✐stê♥❝✐❛ ❞❛ tr❛♥s❢♦r✲ ♠❛çã♦ ❡♥tr❡ ✉♠ s♦❢t✇❛r❡ ❡♠ ❞❡t❡r♠✐♥❛❞❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡ ♦ ❝ó❞✐❣♦ ❛ss❡♠❜❧② ❝♦rr❡s♣♦♥❞❡♥t❡✱ ♣❛r❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣❧❛t❛❢♦r♠❛✱ sã♦ ❜❛s❡❛❞♦s ❡♠ s✐♠✉❧❛çõ❡s✱ t❡st❡s✱ ❝♦♠♣✐❧❛❞♦r❡s ❝❡rt✐✜❝❛❞♦s ❡ ✈❡r✐✜❝❛çã♦ ❢♦r♠❛❧ s♦❜r❡ ♦ ❝ó❞✐❣♦ ❣❡r❛❞♦ ✳
P❛r❛ ♦s t❡st❡s s❡r❡♠ r❡❛❧✐③❛❞♦s✱ ❝r✐❛✲s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣r♦❣r❛♠❛s ❡①❡♠♣❧♦s✱ q✉❡ ❝♦♥✲ tê♠ ❞✐✈❡rs❛s ❝♦♠❜✐♥❛çõ❡s ❞❡ s❡q✉ê♥❝✐❛s ❞❡ ✐♥str✉çõ❡s✱ ❛s q✉❛✐s ♣♦ss✐✈❡❧♠❡♥t❡ ♣❡r♠✐t❛♠ ✐❞❡♥t✐✜❝❛r ❡rr♦s✳ ❊♥tã♦✱ ❛♣ós ❛ ❝♦♠♣✐❧❛çã♦ ❞❡ss❡s ♣r♦❣r❛♠❛s✱ ❡❧❡s sã♦ ❡①❡❝✉t❛❞♦s ❡ ❡♠ s❡❣✉✐❞❛ sã♦ ❝♦♠♣❛r❛❞♦s ♦s r❡s✉❧t❛❞♦s ❡s♣❡r❛❞♦s ❝♦♠ ♦s ♦❜t✐❞♦s✳ ❈♦♠ ❡ss❛ ❛✈❛❧✐❛çã♦ é ♣♦ssí✈❡❧ ❧♦❝❛❧✐③❛r ✈ár✐♦s ♣r♦❜❧❡♠❛s✱ ♣♦ré♠ ♥ã♦ s❡ ❣❛r❛♥t❡ ❛ ❝♦❡rê♥❝✐❛ ❡♥tr❡ ♦ ♣r♦❣r❛♠❛ ❢♦♥t❡ ❡ ♦ ❝ó❞✐❣♦ s✐♥t❡t✐③❛❞♦✱ ❡ t❛♠❜é♠ ❛ ❛✉sê♥❝✐❛ ❞❡ ❡rr♦s ❞❡✿ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ ❝♦♥s✐stê♥✲ ❝✐❛ ❝♦♠ r❡❧❛çã♦ ❛♦s r❡q✉✐s✐t♦s ❞♦ s✐st❡♠❛✳
◆❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❝♦♠♣✐❧❛❞♦r❡s ❝❡rt✐✜❝❛❞♦s✱ ♦s ♣r♦❥❡t✐st❛s ❞❛ ❧✐♥❣✉❛❣❡♠ ❆❞❛✸ t✐♥❤❛♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❝r✐❛r ✉♠❛ ❧✐♥❣✉❛❣❡♠ s❡❣✉r❛ ♣❛r❛ s❡r ✉s❛❞❛ ♣❡❧♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❉❡❢❡s❛ ❆♠❡r✐❝❛♥❛✱ ❡♠ ❛♣❧✐❝❛çõ❡s ❝rít✐❝❛s ❞❡ s✐st❡♠❛s ❡♠❜❛r❝❛❞♦s✳ P❛r❛ ✐ss♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝❡rt✐✜❝❛çõ❡s✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛ss❡❣✉r❛r ❛ ❝♦♥✜❛♥ç❛ ❞♦ ❝♦♠♣✐❧❛❞♦r✳ ❊ss❛s
✸❆❞❛ é ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❝r✐❛❞❛ ❛tr❛✈és ❞❡ ✉♠ ❝♦♥❝✉rs♦ r❡❛❧✐③❛❞♦ ♣❡❧♦ ❉❡♣❛rt❛♠❡♥t♦
✶✽
❝❡rt✐✜❝❛çõ❡s ❞❡ ❝♦♠♣✐❧❛çã♦ ❝♦♥t✐♥❤❛♠ t❡st❡s ♣ró♣r✐♦s ❞❡ ❆❞❛✱ q✉❡ ❛♥t❡❝❡❞✐❛♠ ♦ ♣r✐♠❡✐r♦ ♣❛❞rã♦ ❞❡ t❡st❡ ❞❡ ✶✾✽✸ ❡ é ♣r♦❞✉t♦ ❞❡ ✶✺ ❛♥♦s ❞❡ ♣❡sq✉✐s❛ s♦❜r❡ ❛ ❝♦♥❢♦r♠✐❞❛❞❡ ❞❡ ❆❞❛✳ ❙❡❣✉♥❞♦ ❬❇✉r❦❤❛r❞t ✷✵✵✵❪✱ ♦ ❝♦♠♣✐❧❛❞♦r ❆❞❛ ✾✺ ❢♦✐ t❡st❛❞♦ ❝♦♥t✐♥✉❛♠❡♥t❡ ❡ ❞❡ ❢♦r♠❛ ♠✉✐t♦ ❡①✐❣❡♥t❡❀ ✉♠ ❞♦s ❝♦♥❥✉♥t♦s ❞❡ t❡st❡s ❝♦♥t✐♥❤❛ ♠❛✐s ❞❡ ✸✻✵✵ t❡st❡s ❞❡ ❝♦❜❡rt✉r❛✳ ❉❡ss❛ ❢♦r♠❛✱ ♦s ♣r♦❥❡t✐st❛s ❞❛ ❧✐♥❣✉❛❣❡♠ ❝♦♥❝❧✉ír❛♠ q✉❡ ♥♦s t❡st❡s ❞❡ ❝❡rt✐✜❝❛çã♦ ❞❡ ❝♦♠♣✐❧❛çã♦ ❝rít✐❝❛ ♦❜t✐✈❡r❛♠ s✉❝❡ss♦ ❬❇✉r❦❤❛r❞t ✷✵✵✵❪✳ ❈♦♠ ♦ ❞❡❝♦rr❡r ❞♦s tr❛❜❛❧❤♦s ❞❡ ❝❡rt✐✜❝❛çã♦✱ ♦ ❝♦♠♣✐❧❛❞♦r ❆❞❛ ♦❜t❡✈❡ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ❛♠❛❞✉r❡❝✐♠❡♥t♦ ♣❡r♠✐t✐♥❞♦ s✉❛ ✉t✐❧✐③❛çã♦ ❡♠ s✐st❡♠❛s ❝rít✐❝♦s✳ ◆♦ ❡♥t❛♥t♦✱ ❛♣❡s❛r ❞❡ s❡r ✉♠❛ ❜♦❛ ❡str❛té❣✐❛✱ ♣r♦❥❡t♦ ❞❡ ❝♦♠♣✐❧❛❞♦r❡s ❝♦♠♦ ❡ss❡s t❡♠ ❡♥♦r♠❡ ❝✉st♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✳
❊①✐st❡♠ ♥❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ✈ár✐♦s ♣r♦❥❡t♦s ❡ ❢❡rr❛♠❡♥t❛s ✭❊①❡♠♣❧♦s✿
❬▲❡✐♥❡♥❜❛❝❤✱ P❛✉❧ ❡ P❡tr♦✈❛ ✷✵✵✺✱ ❇❧❛③②✱ ❉❛r❣❛②❡ ❡ ▲❡r♦② ✷✵✵✻✱ ▲❡r♦② ✷✵✵✻❪✮ ✱ ♦s q✉❛✐s ❣❛r❛♥t❡♠ ❢♦r♠❛❧♠❡♥t❡ ❛ tr❛♥s❢♦r♠❛çã♦ ❞❡ ✉♠ ♣r♦❣r❛♠❛ ❡♠ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❡s♣❡❝í✜❝❛ ♣❛r❛ ❛ ❧✐♥❣✉❛❣❡♠ ❛ss❡♠❜❧② ❞❡ ❞❡t❡r♠✐♥❛❞❛ ♣❧❛t❛❢♦r♠❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❡ss❡s ♣r♦❥❡t♦s ♥ã♦ r❡❛❧✐③❛♠ ❛ ✈❡r✐✜❝❛çã♦ ❞♦s r❡q✉✐s✐t♦s ❡ ♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠♦❞❡❧♦ ❞♦ s♦❢t✇❛r❡✱ ♦ q✉❡ é ♣r♦♣♦st♦ ❡ ♠♦❞❡❧❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✳
❯♠❛ ❛❧t❡r♥❛t✐✈❛ ❝♦♠♣❧❡t❛ ❡ ♣♦ssí✈❡❧ é ❝♦♥str✉✐r ✉♠ tr❛❞✉t♦r ✈❡r✐✜❝❛❞♦ ❞♦ ❝ó❞✐❣♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❇ ♣❛r❛ ❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ❛❧❣✉♠❛s ❞❡ss❛s ❢❡rr❛♠❡♥t❛s✱ ♣♦r ❡①❡♠♣❧♦ ♦ ❝♦♠♣✐❧❛❞♦r ❈♦♠♣❈❡rt ❬▲❡r♦② ✷✵✵✻❪✳ ❉❡ss❛ ❢♦r♠❛✱ s❡r✐❛ ♣♦ssí✈❡❧ r❡❛❧✐③❛r ❛ ✈❡r✐✜❝❛çã♦ ❞♦s r❡q✉✐s✐t♦s ❡ ♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠♦❞❡❧♦ ❞♦ s♦❢t✇❛r❡ ❡♠ ❇✳ ❊ss❛ s❡r✐❛ ✉♠❛ tr❛❞✉çã♦ ❝♦♠ ✏❞✐stâ♥❝✐❛ s❡♠â♥t✐❝❛✑ ♣❡q✉❡♥❛ ❡ ♦ ♣ró♣r✐♦ ❝♦♠♣✐❧❛❞♦r ❈♦♠♣❈❡rt ❣❛r❛♥t✐r✐❛ ❛ ❝♦♥✈❡rsã♦ ❞♦ ❝ó❞✐❣♦ ❞❡ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ♣❛r❛ ♦ ❝ó❞✐❣♦ ❛ss❡♠❜❧②✳ ◆♦ ❡♥t❛♥t♦✱ ♣❛r❛ ❛✉t♦♠❛t✐③❛r ❡ss❛ tr❛❞✉çã♦✱ é ♥❡❝❡ssár✐❛ ❛ ❢♦r♠❛❧✐③❛çã♦ ❞❛ s❡♠â♥t✐❝❛ ♦♣❡r❛❝✐♦♥❛❧ ❞❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❇ ❡♠ ❈♦q ❬❇❡rt♦t ✷✵✵✹❪ ❡ ♣r♦✈❛r ❛s r❡❣r❛s ❞❡ tr❛❞✉çã♦ ❡♥tr❡ ❛s ❧✐♥❣✉❛❣❡♥s✳
✶✾
✷ ▼ét♦❞♦ ❇
P❛r❛ ✉♠❛ ❜♦❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡st❡ tr❛❜❛❧❤♦✱ ❡st❡ ❝❛♣ít✉❧♦ ✐♥tr♦❞✉③ ♦s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ❞♦ ♠ét♦❞♦ ❇✳ ❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛✿ ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s ❡♥✈♦❧✈✐❞❛s✱ ♦s ❞✐✈❡rs♦s ♠ó❞✉❧♦s ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❡ ♦s s❡✉s ❡❧❡♠❡♥t♦s✱ ❛s r❡❣r❛s ❞❡ s✉❜st✐t✉✐çã♦ ❡ ❛s ❝♦♥str✉çõ❡s ❞❛s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛✳
❇ é ✉♠ ♠ét♦❞♦ ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ♠♦❞✉❧❛r✱ ♥♦ q✉❛❧ ❝❛❞❛ ♠ó❞✉❧♦ ❡s♣❡❝✐✜❝❛ ✉♠ ♦❜❥❡t♦ ❞❡ s♦❢t✇❛r❡ ❡♠ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♥í✈❡❧ ❞❡ ❛❜str❛çã♦✳ ❊st❡s ♥í✈❡✐s s❡❣✉❡♠ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❞♦ ♠❛✐s ❛❜str❛t♦ ♣❛r❛ ♦ ♠❛✐s ❝♦♥❝r❡t♦✿ ▼❆❈❍■◆❊✱ ❘❊❋■◆❊▼❊◆❚ ❡ ■▼P▲❊▼❊◆❚❆✲ ❚■❖◆✳ ❊ss❡s t❡r♠♦s sã♦ ❝♦♥✈❡♥❝✐♦♥❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❝♦♠♦✿ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧✱ r❡✜♥❛♠❡♥t♦ ♦✉ ♠♦❞❡❧♦ r❡✜♥❛❞♦✱ ❡ ♠♦❞❡❧♦ ❛❧❣♦rít♠✐❝♦✳ ❆ s❡❣✉✐r sã♦ ♠♦str❛❞♦s ♥❛ ❋✐❣✉r❛ ✶ ♦s ♣❛ss♦s tr❛❞✐❝✐♦♥❛❧♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♥♦ ♠ét♦❞♦ ❇✳
❋✐❣✉r❛ ✶✿ ❊t❛♣❛s ❞❡ ✈❡r✐✜❝❛çã♦ ❇ tr❛❞✐❝✐♦♥❛❧✳
✷✵
✜♥❛❧✐③❛✲s❡ ❝♦♠ ❛ ❝♦♠♣✐❧❛çã♦ ❞♦ ♣r♦❣r❛♠❛ ✜♥❛❧ ✭✻✮✳
❖ ♠♦❞❡❧♦ ❞❡ ✉♠ s✐st❡♠❛ ❛✐♥❞❛ ♣♦❞❡ s❡r ❝♦♠♣♦st♦ ❞❡ ✈ár✐♦s ♠ó❞✉❧♦s ✐♥t❡r❞❡♣❡♥❞❡♥t❡s✱ ♦✉ s❡❥❛✱ t❛♠❜é♠ s✉♣♦rt❛ ✉♠❛ ❝♦♠♣♦s✐çã♦ ❞❡ ♠♦❞❡❧♦s✳ ❚rês ❝❧á✉s✉❧❛s ❞❡ ❝♦♠♣♦s✐çã♦ s❡rã♦ ❞❡s❝r✐t❛s✳ ❆ ❝❧á✉s✉❧❛ INCLUDES ♣❡rt❡♥❝❡ à ♥♦t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❡ ♣❡r♠✐t❡ ✐♥❝❧✉✐r ✐♥stâ♥❝✐❛s ❞❡ ♦✉tr♦s ♠♦❞❡❧♦s ❢✉♥❝✐♦♥❛✐s ❬❆❜r✐❛❧ ✶✾✾✻❪✳ ❆ ❝❧á✉s✉❧❛SEES r❡❢❡r❡♥❝✐❛ ✉♠ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❡ ♣❡r♠✐t❡ ❛❝❡ss❛r s✉❛s ❝♦♥st❛♥t❡s✱ ❢✉♥çõ❡s ❡ ✈❛r✐á✈❡✐s✱ ♣♦ré♠ s❡♠ ♠♦❞✐✜❝á✲❧❛s✳ ❆ ❝❧á✉s✉❧❛ IMPORTS ♣❡r♠✐t❡ ✐♠♣♦rt❛r✱ ❡♠ ✉♠ ♠♦❞❡❧♦ ❛❧❣♦rít♠✐❝♦✱ ✉♠ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧✳
◆❛s s❡çõ❡s s❡❣✉✐♥t❡s ❞❡st❡ ❝❛♣ít✉❧♦✱ s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s r❡❧❡✲ ✈❛♥t❡s s♦❜r❡ ♦s ♥í✈❡✐s ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❇ ❡ ❛s s✉❛s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛✳
✷✳✶ ▼♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧
❯♠ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ é ✉♠❛ ♠áq✉✐♥❛ ❞❡ ❡st❛❞♦✱ ♥❛ q✉❛❧ é ❞❡s❝r✐t♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣r♦♣r✐❡❞❛❞❡s s♦❜r❡ ♦s ❡st❛❞♦s ❡ ♦♣❡r❛çõ❡s q✉❡ ♠♦❞✐✜❝❛♠ ♦ ❡st❛❞♦ ❞♦ ♠♦❞❡❧♦✳ ❖ ❝♦♥❥✉♥t♦ ❞♦s ❞❛❞♦s r❡♣r❡s❡♥t❛❞♦s ♣❡❧❛s ✈❛r✐á✈❡✐s ❝♦♥st✐t✉✐ ✉♠ ❡st❛❞♦ ❞♦ ♠♦❞❡❧♦✳ ❊ss❡s ❞❛❞♦s sã♦ ♠♦❞❡❧❛❞♦s ♣♦r ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s✱ t❛✐s ❝♦♠♦ ❝♦♥❥✉♥t♦s✱ r❡❧❛çõ❡s✱ ❢✉♥çõ❡s✱ s❡q✉ê♥❝✐❛s ❡ ár✈♦r❡s✳ ❆ ♠✉❞❛♥ç❛ ❞❡ ❡st❛❞♦ ❞❡ ✉♠ ♠♦❞❡❧♦ é r❡♣r❡s❡♥t❛❞❛ ✉♥✐❝❛♠❡♥t❡ ♣❡❧❛s ♦♣❡r❛çõ❡s✱ q✉❡ ♣♦r s✉❛ ✈❡③✱ ❢❛③❡♠ ❛ ❛❧t❡r❛çã♦ ❞♦ ✈❛❧♦r ❞❡ ❢♦r♠❛ ❛ ♣r❡s❡r✈❛r ❛ ✐♥t❡❣r✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦✳ ❆ s❡❣✉✐r é ✐❧✉str❛❞♦ ✉♠ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❞❡ ❡①❡♠♣❧♦✳
▼❆❈❍■◆❊ ❈❛✐①❛
❱❆❘■❆❇▲❊❙ s❛❧❞♦
■◆❱❆❘■❆◆❚
s❛❧❞♦ ∈ Z ∧ s❛❧❞♦ >= ✵
■◆■❚■❆▲■❙❆❚■❖◆ s❛❧❞♦ ✿❂ ✶✵✵ ❖P❊❘❆❚■❖◆❙
s❛q✉❡ ✭✈❛❧♦r s❛q✉❡✮ ❂ P❘❊
✈❛❧♦r s❛q✉❡ ∈ Z ∧ ✈❛❧♦r s❛q✉❡ ≤ s❛❧❞♦ ❚❍❊◆
s❛❧❞♦ ✿❂ s❛❧❞♦ ✲ ✈❛❧♦r s❛q✉❡ ❊◆❉
❊◆❉
✷✶
❆ ❋✐❣✉r❛ ✷ ❝♦♥té♠ ✉♠ ❡①❡♠♣❧♦ s✐♠♣❧❡s ❞❡ ❡s♣❡❝✐✜❝❛çã♦ ❞❡ ✉♠ ❝♦♥tr♦❧❡ ❞❡ ❝ré❞✐t♦ ❝♦♠ ❛ ♦♣❡r❛çã♦ s❛q✉❡✳ ❊ss❡ ♠ó❞✉❧♦ ❝♦♥té♠ ❛s ❝❧á✉s✉❧❛s ❜ás✐❝❛s ❞❛ ❝♦♠♣♦s✐çã♦ ❞❡ ✉♠ ♠♦✲ ❞❡❧♦ ❢✉♥❝✐♦♥❛❧✳ ❆ ♣r✐♠❡✐r❛ ❝❧á✉s✉❧❛ ✭MACHINE✮ ❞❡s❝r❡✈❡ ♦ ♥♦♠❡ ❞♦ ♠ó❞✉❧♦✱ ♥❡ss❡
❝❛s♦ ✏❈❛✐①❛✑✳ ❆ s❡❣✉✐♥t❡ ✭VARIABLES✮ ❛♣❡♥❛s ❞❡❝❧❛r❛ ♦ ♥♦♠❡ ❞❡ s✉❛s ✈❛r✐á✈❡✐s✳
❆ t❡r❝❡✐r❛ ✭INVARIANT✮ ❞❡t❡r♠✐♥❛ ♦s t✐♣♦s ❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❛s ✈❛r✐á✈❡✐s✳ P♦r✲
t❛♥t♦✱ ❡ss❛ ❝❧á✉s✉❧❛ r❡q✉❡r q✉❡ ❡①✐st❛♠ ✈❛❧♦r❡s ♣❛r❛ ❛ ❧✐st❛ ❞❡ ✈❛r✐á✈❡✐s ❞♦ ♠♦❞❡❧♦ ❛ ✜♠ ❞❡ q✉❡ ♦ ✭INVARIANT✮ s❡❥❛ ✈á❧✐❞♦✱ ❡♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ q✉❡ ❡❧❛ ♥ã♦ s❡❥❛ ✐♥❝♦♥s✐s✲
t❡♥t❡ ❬❙❝❤♥❡✐❞❡r ✷✵✵✶❪✳
❆ ♣ró①✐♠❛ ✭INITIALISATION✮ ❞❡✜♥❡ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ❞❛s ✈❛r✐á✈❡✐s ❞♦ ♠♦❞❡❧♦✳ ■ss♦
s✐❣♥✐✜❝❛ q✉❡ ❛ ❡①❡❝✉çã♦ ❞❛ ✐♥✐❝✐❛❧✐③❛çã♦ ❞❡✈❡ ❢❛③❡r ❝♦♠ q✉❡ ♦ ✈❛❧♦r ❞❛s ✈❛r✐á✈❡✐s s❛t✐s❢❛ç❛ ♦INVARIANT✳ ◆♦ ♠♦❞❡❧♦ ✏❈❛✐①❛✑✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ✐♥✐❝✐❛❧✐③❛çã♦ ❞❛ ✈❛r✐á✈❡❧ s❛❧❞♦ ❝♦♠
✶✵✵ ❡st❛❜❡❧❡❝❡ ♦ INVARIANT✱ ♣♦✐s ✶✵✵ ♣❡rt❡♥❝❡ ❛♦ ❝♦♥❥✉♥t♦ ❞♦s ✐♥t❡✐r♦s ♣♦s✐t✐✈♦s✳
❊ ♣♦r ✜♠✱ ❛ ❝❧á✉s✉❧❛ ✭OPERATIONS✮ ❞❡✜♥❡ ❞❡ q✉❡ ❢♦r♠❛ ❛s ♦♣❡r❛çõ❡s ♠♦❞✐✜❝❛♠
♦ ✈❛❧♦r ❞❛s ✈❛r✐á✈❡✐s✳ ❆s ♦♣❡r❛çõ❡s sã♦ ❡s♣❡❝✐✜❝❛❞❛s ❛tr❛✈és ❞❡ ❝♦♥str✉çõ❡s ❝❤❛♠❛❞❛s s✉❜st✐t✉✐çõ❡s ❣❡♥❡r❛❧✐③❛❞❛s✳ ❊♥tã♦✱ ♣❛r❛ ❣❛r❛♥t✐r q✉❡ ♦ ♠♦❞❡❧♦ ♣❡r♠❛♥❡ç❛ s❡♠♣r❡ ❡♠ ✉♠ ❡st❛❞♦ ✈á❧✐❞♦✱ ♦ ♠ét♦❞♦ ❇ ❞❡✜♥❡ r❡❣r❛s ♣❛r❛ ❝♦♥str✉çã♦ ❞❡ ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛✳ ◆❡ss❡ ❝♦♥t❡①t♦ ❛s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ sã♦ ❢ór♠✉❧❛s ❧ó❣✐❝❛s q✉❡✱ q✉❛♥❞♦ ✈á❧✐❞❛s✱ ❣❛r❛♥t❡♠ ❛ ♣❡r♠❛♥ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡♠ ❡st❛❞♦s ✈á❧✐❞♦s✳
❖ ♠ó❞✉❧♦ ❞❛ ❋✐❣✉r❛ ✷✱ ♣♦r ❡①❡♠♣❧♦✱ ❝♦♥té♠ ❛ ♦♣❡r❛çã♦ s❛q✉❡✳ P❛r❛ ❣❛r❛♥t✐r q✉❡ ❡ss❛ ♦♣❡r❛çã♦ ♥ã♦ ❧❡✈❛ ❛ ✉♠ ❡st❛❞♦ ✐♥✈á❧✐❞♦✱ ❡❧❛ é r❡str✐t❛ ❛ s❛q✉❡s ❞❡ ✈❛❧♦r❡s ♥✉♥❝❛ ♠❛✐♦r❡s q✉❡ ♦ s❛❧❞♦ ❛t✉❛❧✳ ❊ss❛ r❡str✐çã♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞❛ ♥❛ ♣ré✲❝♦♥❞✐çã♦ ❞❛ ♦♣❡r❛çã♦✳ ❆ss✐♠✱ t♦❞❛ ♦♣❡r❛çã♦ ❞❡ ♠✉❞❛♥ç❛ ❞❡ ✈❛❧♦r ❞♦s ❞❛❞♦s ❞❡✈❡ ♣r❡s❡r✈❛r ❛s ❝♦♥❞✐çõ❡s ❞❡ ✐♥t❡❣r✐❞❛❞❡ ❡st❛❜❡❧❡❝✐❞❛s ♥♦ ♠♦❞❡❧♦✱ ♥❡ss❡ ❝❛s♦✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ❡st❛❜❡❧❡❝✐❞❛s ♥♦ INVARIANT✳
P❛r❛ t❛❧✱ ❇ ♦❢❡r❡❝❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝♦♥str✉çõ❡s ❞❡ ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛✱ q✉❡ ♣♦r s✉❛ ✈❡③ sã♦ ❝♦♥str✉í❞❛s ❛tr❛✈és ❞❛s r❡❣r❛s ❞❡ s✉❜st✐t✉✐çã♦✳
❆ s❡♠â♥t✐❝❛ ❞❛s s✉❜st✐t✉✐çõ❡s é ❞❡✜♥✐❞❛ ♣❡❧♦ ❝á❧❝✉❧♦ ❞❛s s✉❜st✐t✉✐çõ❡s✱ ✉♠ s✐st❡♠❛ ❞❡ r❡❡s❝r✐t❛ ❞♦s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ s✉❜st✐t✉✐çõ❡s ❡♠ ❢ór♠✉❧❛s ❞❛ ❧ó❣✐❝❛ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ❆ ❚❛❜❡❧❛ ✶ ❛♣r❡s❡♥t❛ ♦ ♥♦♠❡ ❞❛s ♣r✐♥❝✐♣❛✐s s✉❜st✐t✉✐çõ❡s ❣❡♥❡r❛❧✐③❛❞❛s ❡ ❛s r❡s♣❡❝t✐✈❛s r❡❣r❛s ❞❡ r❡❡s❝r✐t❛✳
◆✉♠ ♣r✐♠❡✐r♦ ♠♦♠❡♥t♦✱ é ✐♠♣♦rt❛♥t❡ ❡♥t❡♥❞❡r ❛ ♥♦t❛çã♦ ✉t✐❧✐③❛❞❛ ✭[S]P✮ ♥❛s r❡✲
❣r❛s ❞❡ s✉❜st✐t✉✐çã♦ ❣❡♥❡r❛❧✐③❛❞❛✳ ❆ ♥♦t❛çã♦ [S]P s✐❣♥✐✜❝❛ q✉❡ ✉♠❛ s✉❜st✐t✉✐çã♦ S s❡rá
❛♣❧✐❝❛❞❛ ❡♠ ✉♠❛ ❢ór♠✉❧❛ P✳ ❆ s❡❣✉✐r ❡ss❛ ♥♦t❛çã♦ s❡rá ❡①❡♠♣❧✐✜❝❛❞❛ ❡ ✐❧✉str❛❞❛ ♥❛
✷✷
◆♦♠❡ ❘❡❣r❛ ❞❡ s✉❜st✐t✉✐çã♦ SKIP ❬skip❪ Q≡Q
BEGIN [BEGINGEND]Q≡[G]Q SIMPLE [α:=β]Q ≡Q′
PRE ❬PREPTHENSEND]Q≡(P ∧[S]Q)
IF [IFPTHENS1ELSES2END]Q ≡(P ⇒[S1]Q)∧(¬P ⇒[S2]Q) CASE ❬CASEEOF EITHERe1THENS1ORe2THENS2END]Q
≡(E=e1 ⇒[S1]Q)∧(E=e2 ⇒[S2]Q) ANY [ANYxWHEREPTHENSEND]I
≡ ∀x(P ⇒[S]I)
PARALLEL [x:=E||y:=F]I ≡[x, y:=E, F]I SEQUENCING [S1 ❀ S2]Q ≡[S1][S2]Q
❚❛❜❡❧❛ ✶✿ ❘❡❣r❛s ❞❡ s✉❜st✐t✉✐çã♦ ❣❡♥❡r❛❧✐③❛❞❛✳ ❖s sí♠❜♦❧♦s ✉t✐❧✐③❛❞♦s ♥❡st❛ t❛❜❡❧❛ ❡stã♦ ❞❡✜♥✐❞♦s ❝♦♠♦✿ P✱P1✱P2✱Qsã♦ ♣r❡❞✐❝❛❞♦s❀ S✱S1✱S2 sã♦ s✉❜st✐t✉✐çõ❡s❀E ✉♠❛ ❡①♣r❡ssã♦❀ e1, e2 sã♦ ✈❛❧♦r❡s ❡ α ✉♠❛ ✈❛r✐á✈❡❧ q✉❡ é s✉❜st✐t✉í❞❛ ♣♦r ✉♠❛ ❡①♣r❡ssã♦ β✳
❆ ♣r✐♠❡✐r❛ é ❛ r❡❣r❛ ❞❛ s✉❜st✐t✉✐çã♦ SKIP✳ ❊❧❛ ♥ã♦ ♠♦❞✐✜❝❛ ♦ ❡st❛❞♦ ❞❛s ✈❛r✐á✈❡✐s✱
❝♦♥t✉❞♦ ♣♦❞❡ s❡r út✐❧ ♣❛r❛ ❡s♣❡❝✐✜❝❛r q✉❡ ❛❧❣✉♠❛ r❛♠✐✜❝❛çã♦ ❞❡IF ♥ã♦ ♠♦❞✐✜❝❛ ♦ ✈❛❧♦r
❞❛s ✈❛r✐á✈❡✐s✱ ♣♦r ❡①❡♠♣❧♦✳
❆ s❡❣✉♥❞❛ BEGIN é ✉s❛❞❛ ♣❛r❛ ❞❡✜♥✐r ♦ ❡s❝♦♣♦ ❞❡ ✉♠❛ s✉❜st✐t✉✐çã♦✱ ♦✉ s❡❥❛✱ ❢✉♥✲
❝✐♦♥❛ ❝♦♠♦ ✉♠ ✏❞❡❧✐♠✐t❛❞♦r ❞❡ ❜❧♦❝♦✑✳
❆ t❡r❝❡✐r❛ é ❛ r❡❣r❛ ❞❛ s✉❜st✐t✉✐çã♦ s✐♠♣❧❡s✳ ❖ s✐❣♥✐✜❝❛❞♦ ❞❡ss❛ r❡❣r❛ é ❛ s✉❜st✐t✉✐çã♦ ❞❡ ✉♠❛ ✈❛r✐á✈❡❧α♣♦r ✉♠❛ ❡①♣r❡ssã♦β ❡♠ ✉♠ t❡r♠♦Q✱ ❡s❝r✐t♦ ❝♦♠♦[α:=β]Q✳ ❆ss✐♠✱ s❡
α❢♦r ❧✐✈r❡ ❡♠Q❛ s✉❜st✐t✉✐çã♦ ❛❝♦♥t❡❝❡ ❡♠ t♦❞❛ ♦❝♦rrê♥❝✐❛ ❧✐✈r❡ ❞❡α♣♦rβr❡s✉❧t❛♥❞♦ ❡♠ Q′✳ ❆ ❡①♣r❡ssã♦ ✷✳✶ ✐❧✉str❛ ✉♠ ❡①❡♠♣❧♦ ✐♥t✉✐t✐✈♦ ❞♦ ❝á❧❝✉❧♦ ❞❛s s✉❜st✐t✉✐çõ❡s ❛♣❧✐❝❛♥❞♦ ❡ss❛ r❡❣r❛✳
[v :=w+v+z](w < v)≡(w < w+v+z)
✭✷✳✶✮
❆ s✉❜st✐t✉✐çã♦PREé ✉s❛❞❛ ♣❛r❛ ❡①♣r❡ss❛r ♦s r❡q✉✐s✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❡❢❡t✉❛r ✉♠❛
s✉❜st✐t✉✐çã♦✱ ♦✉ s❡❥❛✱ ♣❛r❛ ❡❢❡t✉❛rS é ♥❡❝❡ssár✐♦ ❣❛r❛♥t✐r q✉❡ P s❡❥❛ ✈á❧✐❞♦✳
❖IF é ✉♠❛ s✉❜st✐t✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡t❡r♠✐♥íst✐❝♦✳ ❊ss❛ é ✉s❛❞❛
✷✸
❝❛s♦ ❝♦♥trár✐♦✱ ❡❢❡t✉❡S2✳ ❯♠ ♦✉tr♦ ❞❡t❛❧❤❡ é q✉❡ ❛ s✉❜st✐t✉✐çã♦ELSEé ♦♣❝✐♦♥❛❧✱ ❛ss✐♠ ❝♦♠♦ ♥❛s ❧✐♥❣✉❛❣❡♥s ❞❡ ♣r♦❣r❛♠❛çã♦✳
❆ ❝♦♥str✉çã♦ CASE é t❛♠❜é♠ ✉♠❛ s✉❜st✐t✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡✲
t❡r♠✐♥íst✐❝♦✳ ◆♦ ❡♥t❛♥t♦✱ ❡❧❛ ♣♦ss✉✐ ✉♠❛ ❡①♣r❡ssã♦E ❡ ✉♠❛ ❧✐st❛ ❞❡ ✈❛❧♦r❡s ✭e1✱e2✮ ♣❛r❛
E✳ ❆ss✐♠✱ s❡ ♦ ✈❛❧♦r ❞❡ E ❢♦r ✐❣✉❛❧ ❛ e1 ❡♥tã♦ ❡❢❡t✉❡ s1✱ s❡♥ã♦ s❡ ♦ ✈❛❧♦r ❞❡ E ❢♦r ✐❣✉❛❧ ❛
e2 ❡♥tã♦ ❡❢❡t✉❡s2✳ ❊ss❛ ❝♦♥str✉çã♦ t❡♠ s❡♠â♥t✐❝❛ s✐♠✐❧❛r ❛♦ s✇✐t❝❤ ❞❛ ❧✐♥❣✉❛❣❡♠ ❈✳ ❖ANY é ✉♠❛ s✉❜st✐t✉✐çã♦ ♥ã♦ ❞❡t❡r♠✐♥íst✐❝❛✱ ❡♠ q✉❡X é ✉♠❛ ❧✐st❛ ❞❡ ✈❛r✐á✈❡✐s❀P
é ✉♠ ♣r❡❞✐❝❛❞♦ ❝♦♠ ❛ t✐♣❛❣❡♠ ❡ r❡str✐çõ❡s s♦❜r❡ ❛s ✈❛r✐á✈❡✐s ❞❡X❀ ❡S é ✉♠❛ s✉❜st✐t✉✐çã♦
s♦❜r❡ ❛s ✈❛r✐á✈❡✐s ❞❡ X✳ ❊ss❛ ❝♦♥str✉çã♦ é ♠✉✐t♦ ❝♦♠✉♠ ❡ ✉t✐❧✐③❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥♦
♣r✐♠❡✐r♦ ♥í✈❡❧ ❞❡ ♠♦❞❡❧❛❣❡♠ ❇✳
❆ s✉❜st✐t✉✐çã♦ PARALLEL é ✉♠❛ s✉❜st✐t✉✐çã♦ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✏||✑ ❡ ❝♦rr❡s♣♦♥❞❡
à ❡①❡❝✉çã♦ ❞❛s s✉❜st✐t✉✐çã♦ ❞❡ ❢♦r♠❛ ❛tô♠✐❝❛✳ ◆♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞♦ ❡①❡♠♣❧♦ ❞❛ ❚❛❜❡❧❛ ✶✱x ❡ y r❡❝❡❜❡♠ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡♠ ✉♠ ♠❡s♠♦ ✐♥st❛♥t❡✱ ♦ ✈❛❧♦r ❞❡E ❡F✳
❋✐♥❛❧♠❡♥t❡✱ ❛ SEQUENCING é ✉♠❛ s✉❜st✐t✉✐çã♦ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✏; ✑ ❡ ❝♦rr❡s✲
♣♦♥❞❡ à ❡①❡❝✉çã♦ ❡♠ s❡q✉ê♥❝✐❛ ❞❡ ✈ár✐❛s s✉❜st✐t✉✐çõ❡s✳ ■ss♦ s✐❣♥✐✜❝❛ q✉❡ ♦ ♣r❡❞✐❝❛❞♦ ♦❜t✐❞♦ ❡♠ ❬S1❀S2❪Q é ♦ ♠❡s♠♦ ♦❜t✐❞♦ ❡♠ ✭❬S1❪✭❬S2❪Q✮✮✳
❖❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧✿ ❈♦♠♦ ❥á ❞✐t♦✱ ❛s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❣❛r❛♥t❡♠ ❛ ❝♦♥s✐stê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡ ♥❡ss❡ tr❛❜❛❧❤♦ t♦❞❛s ❛s ❝♦♥str✉çõ❡s ❞❡ ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ sã♦ ❢✉♥❞❛♠❡♥t❛❞❛s ♥❛ ♥♦t❛çã♦ ❞❡ ❬❆❜r✐❛❧ ✶✾✾✻❪✳ ❆s ❡str✉t✉r❛s ❞❡ ❞♦✐s ♠♦❞❡❧♦s ❢✉♥❝✐♦♥❛✐s✱ ✉♠ ▼1 q✉❡ ✐♠♣♦rt❛ ✉♠ ♦✉tr♦ ▼✱ sã♦ ✐❧✉str❛❞❛s ♥❛ ❋✐❣✉r❛ ✸ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡st❛❜❡❧❡❝❡r ❛ ♥♦t❛çã♦✳
◆❛ ❝♦♥str✉çã♦ ❞❛s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❞❛ ❋✐❣✉r❛ ✸✱ ❛❧❣✉♠❛s ❞❛s ❡①♣r❡ssõ❡s r❡❢❡r❡♥t❡s ❛♦ ♠♦❞❡❧♦ ▼1 sã♦ ♥✉♠❡r❛❞❛s ❝♦♠ ✶ ❡ ❡ss❛ ♥✉♠❡r❛çã♦ é ❛♣r❡s❡♥t❛❞❛ ❞❡ ❢♦r♠❛ s✉❜s❝r✐t❛✳ ❊♥tr❡t❛♥t♦✱ ❛s ❡①♣r❡ssõ❡s q✉❡ ♥ã♦ ❝♦♥tê♠ ❛ ♥✉♠❡r❛çã♦ s✉❜s❝r✐t❛ ♣❡rt❡♥❝❡♠ ❛♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ▼✱ ♦ q✉❛❧ é ✐♥❝❧✉í❞♦ ♣❡❧♦ ♠♦❞❡❧♦ ▼1✳
✷✹
▼❆❈❍■◆❊ ▼1✭❳1✱①1✮ ❈❖◆❙❚❘❆■◆❚❙ ❈1
❙❊❚❙ ❇1❀ ❚1❂ ❛1✱❜1
❆❇❙❚❘❆❈❚ ❈❖◆❙❚❆◆❚❙ ❝1 P❘❖P❊❘❚■❊❙ P1 ■◆❈▲❯❉❊❙ ▼ ✭◆✱♥✮ ✭❈❖◆❈❘❊❚❊ ✮❱❆❘■❆❇▲❊❙ ✈1 ■◆❱❆❘■❆◆❚ ■1 ❆❙❙❊❘❚■❖◆❙ ❏1 ■◆■❚■❆▲■❩❆❚■❖◆ ❯1 ❖P❊❘❆❚■❖◆❙ ✉←−♦♣1✭✇1✮ ❂ P❘❊ ◗1 ❚❍❊◆ ❱1 ❊◆❉❀ ✳✳✳ ❊◆❉ ▼❆❈❍■◆❊ ▼ ✭❳✱①✮ ❈❖◆❙❚❘❆■◆❚❙ ❈ ❙❊❚❙ ❇❀ ❚ ❂ ❛✱❜ ❆❇❙❚❘❆❈❚ ❈❖◆❙❚❆◆❚❙ ❝ P❘❖P❊❘❚■❊❙ P ✭❈❖◆❈❘❊❚❊ ✮❱❆❘■❆❇▲❊❙ ✈ ■◆❱❆❘■❆◆❚ ■ ❆❙❙❊❘❚■❖◆❙ ❏ ■◆■❚■❆▲■❩❆❚■❖◆ ❯ ❖P❊❘❆❚■❖◆❙ ✳✳✳ ❊◆❉
❋✐❣✉r❛ ✸✿ ❊str✉t✉r❛ ♠♦❞✉❧❛r ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ❬❆❜r✐❛❧ ✶✾✾✻❪✳
• A1 ✲ ❡s♣❡❝✐✜❝❛ ♦ t✐♣♦ ❞♦s ❝♦♥❥✉♥t♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦✳ P♦r ❝♦♥✈❡♥çã♦✱ sã♦ ❝♦♥❥✉♥t♦s ❞❡ ✐♥t❡✐r♦s ♥ã♦ ✈❛③✐♦s✳ ❆ss✐♠✱ s❡ X é ♦ ú♥✐❝♦ ❝♦♥❥✉♥t♦ ♣❛râ♠❡tr♦ ❞♦ ♠♦❞❡❧♦✱ A1 éX ∈P1(Z)❀
• B1 ✲ ❡s♣❡❝✐✜❝❛ ♦ t✐♣♦ ❞♦s ❝♦♥❥✉♥t♦s ❞❡❝❧❛r❛❞♦s ♥❛ ❝❧á✉s✉❧❛SETS❀
• C1 ✲ ❡s♣❡❝✐✜❝❛ ❛s r❡str✐çõ❡s s♦❜r❡ ♦s ♣❛râ♠❡tr♦s✳ ➱ ❞❡✜♥✐❞♦ ♥❛ ❝❧á✉s✉❧❛
CONSTRAINTS❀
• P1 ✲ ❡s♣❡❝✐✜❝❛ ❛s r❡str✐çõ❡s s♦❜r❡ ❛s ❝♦♥st❛♥t❡s✳ ➱ ❞❡✜♥✐❞♦ ♥❛ ❝❧á✉s✉❧❛
PROPERTIES❀
• I1 ✲ ❡s♣❡❝✐✜❝❛ ❛s r❡str✐çõ❡s s♦❜r❡ ❛s ✈❛r✐á✈❡✐s ❞❡ ❡st❛❞♦✳ ➱ ❞❡✜♥✐❞♦ ♥❛ ❝❧á✉s✉❧❛
INVARIANT❀
• J1 ✲ ❡s♣❡❝✐✜❝❛ ♦s ❧❡♠❛s ❞❡✜♥✐❞♦s ♥❛ ❝❧á✉s✉❧❛ ASSERTIONS❀
• α1 ✲ ❛❜r❡✈✐❛ ❛ ❡①♣r❡ssã♦ A1∧B1 ∧C1 ∧P1❀
✷✺
❆ s❡❣✉✐r sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ♣r✐♥❝✐♣❛✐s ♦❜r✐❣❛çõ❡s ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧✳ ❆ ♣r✐♠❡✐r❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ♣r❡♦❝✉♣❛✲s❡ ❡♠ ❣❛r❛♥t✐r ❛ ❝♦rr❡çã♦ ❡♠ r❡❧❛çã♦ ❛ ✐♥❝❧✉sã♦ ❞❡ ♦✉tr♦s ♠♦❞❡❧♦s ❢✉♥❝✐♦♥❛✐s✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❋✐❣✉r❛ ✸ t❡♠♦s ❛ ✐♥❝❧✉sã♦ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ▼ ✭❳✱①✮ s❡♥❞♦ ✐♥st❛♥❝✐❛❞♦ ♥❛ ❢♦r♠❛ ▼ ✭◆✱♥✮✳ ◆❡ss❡ s❡♥t✐❞♦ ❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛ ❞❡✈❡ ✐♥st❛♥❝✐❛r ♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❝♦♠ ♦s ♣❛râ♠❡tr♦s ❡❢❡t✐✈♦s ❡ ✈❡r✐✜❝❛r s❡ s❛t✐s❢❛③ ❛s r❡str✐çõ❡s✳ ❆ ❝♦♥str✉çã♦ ❞❡ss❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛ ❝♦♠♣❧❡t❛ é r❡♣r❡s❡♥t❛❞❛ ♥❛ ❡①♣r❡ssã♦ ✷✳✷✳
α1 ⇒[X, x:=N, n](A ∧C)
✭✷✳✷✮
❆ s❡❣✉♥❞❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛ ✈❡r✐✜❝❛ s❡ ❛ ✐♥✐❝✐❛❧✐③❛çã♦ ❯1 ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ▼1 ❡ ❯ ❞♦ ♠♦❞❡❧♦ ✐♠♣♦rt❛❞♦ ▼ s❛t✐s❢❛③❡♠ ❛s r❡str✐çõ❡s ❡ ♣r♦♣r✐❡❞❛❞❡s ✐♠♣♦st❛s ❡♠ ■1 ❞❡ ▼1✳ ❊ss❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛ é ✐❧✉str❛❞❛ ♥❛ ❡①♣r❡ssã♦ ✷✳✸✳
α1 ∧B ∧P ⇒[[X, x:=N, n]U][U1]I1
✭✷✳✸✮
❊♥✜♠✱ ❛ ú❧t✐♠❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛✱ r❡♣r❡s❡♥t❛❞❛ ♥❛ ❡①♣r❡ssã♦ ✷✳✹✱ ❣❛r❛♥t❡ q✉❡ ♦ ❝♦r♣♦ ❞❡ ❝❛❞❛ ♦♣❡r❛çã♦ ♣r❡s❡r✈❛ ❛ ❝❧á✉s✉❧❛ INVARIANT✳ ◆❛ ❋✐❣✉r❛ ✹ t❡♠✲s❡ ✉♠ ❡①❡♠♣❧♦
♣rát✐❝♦ ❡ ✐♥t✉✐t✐✈♦ ❞❛ ❝♦♥str✉çã♦ ❡ r❡s♦❧✉çã♦ ❞❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛✳ ❊ss❡ ❡①❡♠♣❧♦ é ✉♠ ❞♦s ❝á❧❝✉❧♦s r❡❛❧✐③❛❞♦s ♣❛r❛ ❛ ✈❡r✐✜❝❛çã♦ ❞❛ ♦♣❡r❛çã♦ ❞♦ ♠♦❞❡❧♦ ❢✉♥❝✐♦♥❛❧ ✏❈❛✐①❛✑✳ ❖ ♣r✐♠❡✐r♦ ♣❛ss♦ ❢♦✐ ❡①♣❛♥❞✐r ♦s ❡❧❡♠❡♥t♦s ✉t✐❧✐③❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞❛ ♦❜r✐❣❛çã♦ ❞❡ ♣r♦✈❛✳ ❖ ♣❛ss♦ s❡❣✉✐♥t❡ ❢♦✐ ❛♣❧✐❝❛r ❛s r❡❣r❛s ❞❡ s✉❜st✐t✉✐çã♦ ❛té r❡s✉❧t❛r ❡♠ ✉♠ ♣r❡❞✐❝❛❞♦✳ ❊♥tã♦✱ ❡ss❡ ♣r❡❞✐❝❛❞♦ ♣♦❞❡ s❡r ♣r♦✈❛❞♦ ✈á❧✐❞♦✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ❛ ♦♣❡r❛çã♦ ♣r❡s❡r✈❛ ♦ ✐♥✈❛r✐❛♥t❡✳
α1 ∧β1 ∧B ∧P ∧[X, x:=N, n](I ∧J) ⇒[V1]I1
