Social interaction and argumentation in MAS

(1)

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✂✁☎✄✝✆✟✞✠✁☎✡☛✆✟✞✠☞☛✆✍✌✝✎✑✏✓✒✝✔✟✎✖✕✗✡☛☞☛✘✟✁☎✙☎☞☛✚✝✒✜✛✣✢✤✎✖✕✗✁☎✞✠✞✠✆✟✥☛✥☛✆✦✎✧✒✦✏✓✒✝✡☛✎✧✥☛☞☛✘✟✎✧✒✝✙☎☞☛✁✩★✤✞✠✡☛☞☛✪✠☞☛✙☎☞☛✁☎✥

✢✤✎✧✫✝✁☎✞✠✡☛✁☎✬✭✎✧✒✝✡☛✆✍✌✝✎✑✮✯☞☛✎✧✒✝✙☎☞☛✁✰✕✱✎✑✏✓✒✝✘✟✎✧✒✝☞☛✎✧✞✠✲☛✁✣✌✝✎✑✥☛✁✑✮✯✆✟✬✭✫✝✳✝✡☛✁☎✙☎☞☛✚✝✒

✴✤✒✝☞☛✔✟✎✧✞✵✕✗☞☛✌✝✁☎✌✜✶✤✁☎✙☎☞☛✆✟✒✝✁☎✥✷✌✝✎✧✥✹✸✺✳✝✞

★✻✔✽✼✾★✤✥☛✎✧✬❀✿❂❁❄❃❂❅✍❆✻❇✵❈❂❉✝❉✝❉✝❊●❋✯✁☎❍✝✲☛✁■❋✯✥☛✁☎✒✝✙☎✁❏❆✯❑✯▲✂▼◆✴✤❋✯✂✏✓✮✯★❖★✤❑✯P✤▲✂✶✤◗✷✏✓✶✤★

◗◆✎✧✥☛❘☛❙◆✁☎❚❱❯❲❇✠❳✻❃❂❨✝❊✠❇✠❁✝❩❄✿❂❊✠❨❄❃❂❩❄❃✝✿❂❅❄❃❂❘❬❃✽✿❂❅✽❭❪❆✻▲✂❆✠✬✭✁☎☞☛✥❬❯

{

❫◆❴☎❵✦❛❜✝❝✠❞

}

❡❢❴☎❣✐❤❥◆❦◆❣✐❤❧☎❫◆❥◆❤❜✝♠

♥♣♦✦qsr✉t✉✈✉✇✟①✰②✺③st❲④✧⑤✖④✧t✉②✺♦⑦⑥❬⑧⑨♥❏⑩❷❶❸✈✉④✭♦✦✇✟❹s②✩qs❺❼❻✰❽❸♦✦qsr✉t✉✈✉❺sr✉②❏✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉③s①➀✇✟qst✉❻✰③s❻✰♦✦❻✰qs④■✇✟①✰②✺③st✉④✖➁✻➂➃t✱❿✟✇✟③ ➄ ②❸➅✰✈✉②✺➆❏②✺❹❏✇✟④✯✇➇④✧❻✰❿✟✈✉②✺t✉⑤✭✈✉③■➆❏➈s✈✉❿✟➈❏②✺✇✟❿✟➈✣✇✟①✰②✺③sts❺s②✺❾❬❽❬❻✰❾❬♦✦④➉✈✉t✉④✯✇✟❿✟t✉✈✉➅✰✈✉t✉⑤☎➊➋❿✟❻✰❻✰❺s②✺❾❬✇✟t✉✈✉③s①■t✉❻✑✇✟❿✟➈s✈✉②✺➅✰②✤❿✟❻✰♦✦♦✦❻✰③ ①✰❻✰✇✟r✉④✧➊❲❻✰❾➇❿✟❻✰♦✦❺s②✺t✉✈✉③s①❪❽❬❻✰❾➇t✉➈s②✺♦➌➁✯➍➉➈sqs④✧➊❲②✺➅✰②✺❾❬⑤❼✇✟①✰②✺③st✯➈s✇✟④❏t✉➈s②✦✇

➄

✈✉r✉✈✉t✉⑤✜t✉❻❪❹s❻❼④✧❻✰❿✟✈✉✇✟r✯✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③s④❏➆❏✈✉t✉➈ ❻✰t✉➈s②✺❾➎✇✟①✰②✺③st✉④❼②✺④✧t✉✇ ➄ r✉✈✉④✧➈s✈✉③s①➏❹s✈✉✇✟r✉❻✰①✰qs②✺④❼➅✰✈✉✇➐④✧❻✰♦✦②❢➑s✈✉③s❹➒❻✰❽➎✇✟①✰②✺③st✉➓❬❿✟❻✰♦✦♦✦qs③s✈✉❿✟✇✟t✉✈✉❻✰③❖r✉✇✟③s①✰qs✇✟①✰②✺➊✑qs③s❹s②✺❾ ④✧❻✰♦✦②✦❿✟❻✰♦✦♦✦qs③s✈✉❿✟✇✟t✉✈✉❻✰③➔❺s❾❬❻✰t✉❻✰❿✟❻✰r→➁

➣ ②➏t✉➈s✈✉③s➑↔✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↔✈✉④➌④✧qs✈✉t✉✇

➄

r✉②➏t✉❻↕♦✦❻✰❹s②✺r✣④✧②✺➅✰②✺❾❬✇✟r✩➑s✈✉③s❹↔❻✰❽✜❹s✈✉✇✟r✉❻✰①✰qs②✺④❢✈✉③↔♦✦qsr✉t✉✈✉➓❬✇✟①✰②✺③st✉④ ④✧⑤✖④✧t✉②✺♦✦④✖➁❲➂➃t→➙☛④ ➄ ②✺✈✉③s①✩qs④✧②✺❹ ➄ ⑤✣③s❻✰➆➛✇✟④✤✇■❽❬❻✰❾❬♦➜❻✰❽✯③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③ ➄ ②✺t✉➆❏②✺②✺③✦✇✟①✰②✺③st✉④✖➁✱➝❏qs❾✻❿✟qs❾❬❾❬②✺③st❷❾❬②✺④✧②✺✇✟❾❬❿✟➈ ✇✟❿✟t✉✈✉➅✰✈✉t✉✈✉②✺④✜✇✟❾❬②➌❾❬②✺r✉✇✟t✉②✺❹➞t✉❻⑨t✉➈s②➔qs④✧②➌❻✰❽➎✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➟✈✉③➞✇✟①✰②✺③st→➙☛④➠✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③s➊➇④✧qs❿✟➈➞✇✟④➠③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③ ✇✟♦✦❻✰③s①➟④✧②✺➅✰②✺❾❬✇✟r✭❺s✇✟❾❬t✉✈✉❿✟✈✉❺s✇✟③st✉④✧➊➡❺s②✺❾❬④✧qs✇✟④✧✈✉❻✰③s➊➇✇✟❿✟➢sqs✈✉④✧✈✉t✉✈✉❻✰③➟❻✰❽➎➑s③s❻✰➆❏r✉②✺❹s①✰②❢✇✟③s❹➞❻✰t✉➈s②✺❾✩❽❬❻✰❾❬♦✦④❼❻✰❽➎④✧❻✰❿✟✈✉✇✟r ❹s✈✉✇✟r✉❻✰①✰qs②◆➁✯➤❏④✧qs✇✟r✉r✉⑤☎➊✷✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪✇✟❺s❺s②✺✇✟❾❬④❏✇✟④■✇✍♦✦②✺❿✟➈s✇✟③s✈✉④✧♦➥t✉❻❼❹s②✺✇✟r✻➆❏✈✉t✉➈❪❹s✈✉④✧✇✟①✰❾❬②✺②✺♦✦②✺③st ➄ ②✺t✉➆❏②✺②✺③ ✇✟①✰②✺③st✉④✧➊✾❽❬❻✰❾●②✺➦✰✇✟♦✦❺sr✉②✣➆❏➈s②✺③➀④✧❻✰♦✦②✣❿✟❻✰③s❽❬r✉✈✉❿✟t✷❻✰❽●✈✉③st✉②✺❾❬②✺④✧t❷✈✉④➡❺s❾❬②✺④✧②✺③st→➁✱♥❏❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③✜❿✟✇✟③ ➄ ②❏qs④✧②✺❹s➊✾③s❻✰t ❻✰③sr✉⑤❼t✉❻➔✇✟❾➃①✰qs②✜✇

➄

❻✰qst●④✧❻✰♦✦②✺t✉➈s✈✉③s①✰➊

➄

qst●t✉❻➔➑s③s❻✰➆➧♦✦❻✰❾❬②➀✇

➄

❻✰qst●❻✰t✉➈s②✺❾➡✇✟①✰②✺③st✉④✖➨➡✈✉t➉✈✉④✣②✺③s❻✰qs①✰➈❢❺s❻✰➆❏②✺❾❬❽❬qsr✉r t✉❻✦❺sr✉✇✟⑤➎✇✟③✜✈✉♦✦❺s❻✰❾❬t✉✇✟③st✂❾❬❻✰r✉②❏✈✉③➀①✰②✺③s②✺❾❬✇✟r✂④✧❻✰❿✟✈✉✇✟r✷✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③➀✈✉③➀♦✦qsr✉t✉✈✉➓❬✇✟①✰②✺③st✉④✤④✧⑤✖④✧t✉②✺♦✦④✖➁✱➩❷❻✰❾➉t✉➈s✈✉④➇❾❬②✺✇✟④✧❻✰③s➊ ✈✉t✻✈✉④■✇✟r✉④✧❻❼✈✉♦✦❺s❻✰❾❬t✉✇✟③st✯t✉❻❼❹s②✺❽❬✈✉③s②➎✇✟③❪➫➯➭❲➲✟➳s➵✻➸✟➺s➻❏➻❏➼s➳s➽✉➸✟➫s➵✉➽✉➺s➳❼➾✉➫s➳➯➭❲➼s➫➯➭❲➲✍➆❏✈✉t✉➈❪④✧❺s②✺❿✟✈✉✇✟r✻♦✦②✺④✧④✧✇✟①✰②✺④❏t✉❻❼qs④✧② ✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❢✈✉③❢④✧②✺➅✰②✺❾❬✇✟r●t✉⑤✖❺s②✺④✩❻✰❽✭❹s✈✉✇✟r✉❻✰①✰qs②✺④✖➁➡♥❏❿✟❿✟❻✰❾❬❹s✈✉③s①❢t✉❻ ➣ ✇✟r✉t✉❻✰③↕➚✉➪ ➣↕➶s➶➋➹ ❹s✈✉✇✟r✉❻✰①✰qs②✺④➎❿✟✇✟③

➄

②

❿✟r✉✇✟④✧④✧✈✉❽❬✈✉②✺❹⑨✈✉③➟➳s➲→➭❲➺s➵✉➽✉➫s➵✉➽✉➺s➳◆➊❸➆❏➈s②✺❾❬②➌t✉➈s②✺❾❬②➔✈✉④➠✇❢❿✟❻✰③s❽❬r✉✈✉❿✟t✭❻✰❽✩✈✉③st✉②✺❾❬②✺④✧t✉④✧➊➋➘✤➲✟➴✧➷✧➼s➫s➷✧➽✉➺s➳➟➆❏➈s②✺❾❬②➌t✉➈s②✺❾❬②➌✈✉④✜✇ ❿✟❻✰③s❽❬r✉✈✉❿✟t✻❻✰❽❸❻✰❺s✈✉③s✈✉❻✰③❪❻✰❾ ➄ ②✺r✉✈✉②✺❽❬④✧➊✂➽✉➳s➬s➫➯➭❲➫s➵✉➽✉➺s➳➠➆❏➈s②✺❾❬②➎t✉➈s②✺❾❬②➎✈✉④✑✇✍③s②✺②✺❹❼❽❬❻✰❾✤✇✟③❪②✺➦✰❺sr✉✇✟③s✇✟t✉✈✉❻✰③❪❻✰❾❸❺s❾❬❻✰❻✰❽✤❻✰❽ ④✧❻✰♦✦②✦❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✷➬s➲✟➾✉➽✉➮s➲✟➴✧➫s➵✉➽✉➺s➳❪➺s➴❏➸✟➺s➺s➴✐➬s➽✉➳s➫s➵✉➽✉➺s➳❪➆❏➈s②✺❾❬②✦t✉➈s②✺❾❬②✦✈✉④❏✇➀③s②✺②✺❹➔t✉❻❼❿✟❻✰❻✰❾❬❹s✈✉③s✇✟t✉②✍①✰❻✰✇✟r✉④✣✇✟③s❹ ✇✟❿✟t✉✈✉❻✰③s④✧➊✾✇✟③s❹➀❻✰③s②■④✧❺s②✺❿✟✈✉✇✟r✂➑s✈✉③s❹✍❻✰❽➉❹s✈✉✇✟r✉❻✰①✰qs②■❿✟✇✟r✉r✉②✺❹✍➲✟➴✧➽✉➷✧➵✉➽✉➸ ➄ ✇✟④✧②✺❹➀❻✰③➀❺s②✺❾❬④✧❻✰③s✇✟r✂❿✟❻✰③s❽❬r✉✈✉❿✟t✉④✖➁✱➱✯➦✰❿✟②✺❺st✷t✉➈s② r✉✇✟④✧t✷❻✰③s②✺➊❷✇✟r✉r✷t✉➈s✈✉④➡❹s✈✉✇✟r✉❻✰①✰qs②✺④➡♦✦✇✟⑤✍②✺➦✰✈✉④✧t✷✈✉③✜♦✦qsr✉t✉✈✉➓❬✇✟①✰②✺③st✉④➡④✧⑤✖④✧t✉②✺♦✦④➡✇✟④➡❺s✇✟❾❬t❲❻✰❽●④✧❻✰❿✟✈✉✇✟r✷✇✟❿✟t✉✈✉➅✰✈✉t✉✈✉②✺④➡✇✟♦✦❻✰③s① ✇✟①✰②✺③st✉④✖➁✻⑩❷❻✰♦✦②✺t✉✈✉♦✦②✺④✑③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❼✈✉♦✦❺sr✉✈✉②✺④✭❺s②✺❾❬④✧qs✇✟④✧✈✉❻✰③s➊✂④✧❻✰♦✦②✺t✉✈✉♦✦②✺④✑❺s②✺❾❬④✧qs✇✟④✧✈✉❻✰③❼❾❬②✺➢sqs✈✉②✺❾❬②✺④✭✈✉③s❹s✇✟①✰✇✟t✉✈✉❻✰③ ✇✟③s❹↔✇✟r✉r✩❻✰❽➠t✉➈s②✺♦✃❿✟✇✟③❐t✉✇✟➑s②➏❺s✇✟❾❬t✩✈✉③❒✇✟③s⑤❖❿✟❻✰❻✰❾❬❹s✈✉③s✇✟t✉✈✉❻✰③❒❺s❾❬❻✰❿✟②✺④✧④✖➁ ➣ ②⑨t✉➈s✈✉③s➑↔t✉➈s②✺④✧②➏❹s✈✉✇✟r✉❻✰①✰qs②✺④❢✇✟❾❬② t✉➈s② ➄ ✇✟④✧✈✉④❪❻✰❽✍✇✟①✰②✺③st→➙☛④❪④✧❻✰❿✟✈✉✇✟r❏✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③s➊✑✇✟③s❹❖➆❏➈s✇✟t■❹s②✺t✉②✺❾❬♦✦✈✉③s②✺④❼✈✉t✉④❪④✧❻✰❿✟✈✉✇✟r■✇ ➄ ✈✉r✉✈✉t✉✈✉②✺④✖➨➔➈s❻✰➆❮♦✦qs❿✟➈ t✉➈s②❰✇✟①✰②✺③st✩➑s③s❻✰➆❏④➌✇

➄

❻✰qst✩❻✰t✉➈s②✺❾➀✇✟①✰②✺③st✉④➌✈✉③↔❻✰❾❬❹s②✺❾✜t✉❻↕✈✉♦✦❺s❾❬❻✰➅✰②⑨✈✉t✉④

➄

②✺➈s✇✟➅✰✈✉❻✰qs❾✜✈✉③↔t✉➈s②➏④✧❻✰❿✟✈✉②✺t✉⑤✰➁Ï♥❏r✉r ❹s✈✉✇✟r✉❻✰①✰qs②✺④❸♦✦②✺③st✉✈✉❻✰③s②✺❹✦➈s②✺❾❬②✭③s②✺②✺❹✦✇■④✧t✉❾❬❻✰③s①✰➊❄➆❏②✺r✉r❄❹s②✺❽❬✈✉③s②✺❹✦❺s❾❬❻✰t✉❻✰❿✟❻✰r✉④✖➁✻➝❏qs❾✱✇✟✈✉♦♣✈✉④✹t✉❻➎②✺④✧t✉✇

➄

r✉✈✉④✧➈➎④✧②✺➅✰②✺❾❬✇✟r ♦✦②✺❿✟➈s✇✟③s✈✉④✧♦✦④■t✉❻❼❹s②✺✇✟r✯➆❏✈✉t✉➈➔✇✟r✉r✻t✉➈s✈✉④❏➑s✈✉③s❹❪❻✰❽➇✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③s④■t✉➈s❾❬❻✰qs①✰➈➔✇✟③➌✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪❽❬❻✰❾❬♦✦✇✟r✉✈✉④✧♦➌➁

∗

Ð❷Ñ→Ò❂Ó❂Ô✉ÕÖ➡×➯Ñ●ØÓ✹Ù❷Ö☎Ú●ÕÛ➃ÕÜ➯Ý✑×➯Ñ●ÞßÝ➯à☎Ñ→Û➃áÕâ☎Ó❂Ò❂ÕÖ☎Ý➯Ñ→Û✯Ù❷ÕÑ→Ý➯áãä✉ÕÒ❂Ó❂Û✱å✉Ù❷ÞßÙ❷æ

Workshop de Investigadores en Ciencias de la Computación

WICC 2002

(2)

➍➉➈s②➐❺s❾❬❻✰❿✟②✺④✧④ ➄ ⑤➞➆❏➈s✈✉❿✟➈❖✇➏①✰❾❬❻✰qs❺↕❻✰❽➀✇✟①✰②✺③st✉④❪❿✟❻✰♦✦♦✦qs③s✈✉❿✟✇✟t✉②❰t✉❻➒❻✰③s②❰✇✟③s❻✰t✉➈s②✺❾✍t✉❻➒t✉❾❬⑤➞t✉❻➒❿✟❻✰♦✦②❰t✉❻➒✇ ♦✦qst✉qs✇✟r✉r✉⑤✍✇✟❿✟❿✟②✺❺st✉✇

➄

r✉②✩✇✟①✰❾❬②✺②✺♦✦②✺③st✻❻✰③❪④✧❻✰♦✦②✩♦✦✇✟t✉t✉②✺❾✹✈✉④✑❿✟✇✟r✉r✉②✺❹➠➳s➲→➭❲➺s➵✉➽✉➫s➵✉➽✉➺s➳➏➚➣ ②✺✈✉④✧④ ➹ ➁✁➠②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❪❿✟✇✟③ ➄ ②➌qs④✧②✺❹➞t✉❻➟❾❬②✺④✧❻✰r✉➅✰②❢❿✟❻✰③s❽❬r✉✈✉❿✟t✉④➠✈✉③➞✇➐➆❏✈✉❹s②➌➅✰✇✟❾❬✈✉②✺t✉⑤⑨❻✰❽✦♦✦qsr✉t✉✈✉➓❬✇✟①✰②✺③st✉④✜❹s❻✰♦✦✇✟✈✉③s④✖➁↔➚✄✂✧➩✆☎✞✝❷⑩

➣↔➹

➁➐➍➉➈s②✺❾❬② ✇✟❾❬②✣❹s✈✉❽➃❽❬②✺❾❬②✺③st✷t✉②✺❿✟➈s③s✈✉➢sqs②✺④➡t✉❻➀❾❬②✺✇✟❿✟➈s✈✉③s①➀✇✟①✰❾❬②✺②✺♦✦②✺③st❲✈✉③➠⑧⑨♥❏⑩❷➊❷r✉✈✉➑s②❏①✰✇✟♦✦②✺➓❬t✉➈s②✺❻✰❾❬⑤➀✇✟③s❹➠②✺❿✟❻✰③s❻✰♦✦✈✉❿ ➄ ✇✟④✧②✺❹ t✉②✺❿✟➈s③s✈✉➢sqs②✺④✖➨❢④✧t✉❾❬✇✟t✉②✺①✰✈✉❿⑨③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③s➊❏✇✟qs❿✟t✉✈✉❻✰③s④✧➊❏❿✟❻✰✇✟r✉✈✉t✉✈✉❻✰③↔❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③s➊✣❿✟❻✰③st✉❾❬✇✟❿✟t✉✈✉③s①✰➊✣②✺t✉❿❐➚✄✟❏❾❬✇✟qs④✡✠☞☛

➹

➁

➍➉➈s②✭❺s❾❬❻✰❿✟②✺④✧④❸❻✰❽✻③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➎✈✉③s➅✰❻✰r✉➅✰②✺④✤♦✦✇✟➑s✈✉③s①✩❺s❾❬❻✰❺s❻✰④✧✇✟r✉④✧➊❱t✉❾❬✇✟❹s✈✉③s①✩❻✰❺st✉✈✉❻✰③s④❸✇✟③s❹✦♦✦✇✟➑s✈✉③s①✩❿✟❻✰③s❿✟②✺④✧④✧✈✉❻✰③s④ t✉❻❼❿✟qsr✉♦✦✈✉③s✇✟t✉②✺➊✷✈✉❽✤❺s❻✰④✧④✧✈➄ r✉②✺➊✷✈✉③➔✇✟③➔✇✟①✰❾❬②✺②✺♦✦②✺③st✑➚✉⑧⑨⑩ ➹ ➁

⑩❷②✺➅✰②✺❾❬✇✟r✯❾❬②✺④✧②✺✇✟❾❬❿✟➈s②✺❾❬④■✈✉③❪✇✟qst✉❻✰♦✦✇✟t✉②✺❹➔③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❪➈s✇✟➅✰②➎❺s❾❬❻✰❺s❻✰④✧②✺❹➔t✉➈s✇✟t✻✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪✈✉④✑④✧qs✈✉t✉✇

➄

r✉② t✉❻❏♦✦❻✰❹s②✺r❄③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③

➄

②✺t✉➆❏②✺②✺③✩✈✉③st✉②✺r✉r✉✈✉①✰②✺③st◆✇✟①✰②✺③st✉④■➚✉♥❏⑩ ➶s➶ ➊s⑧⑨⑩ ➹ ➁❲♥❏❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③✩❿✟✇✟③

➄

②➇❿✟❻✰③s④✧✈✉❹s②✺❾❬②✺❹ ✇✟④➇✇❏❺s❾❬❻✰❿✟②✺④✧④➇✈✉③➀➆❏➈s✈✉❿✟➈➀t✉➈s②✑❺s✇✟❾❬t✉✈✉②✺④➇⑥❬✈✉③➀t✉➈s✈✉④✤❿✟✇✟④✧②✺➊✾✇✟①✰②✺③st✉④✧❶✯②✺➦✰❿✟➈s✇✟③s①✰②❏✇✟❾➃①✰qs♦✦②✺③st✉④➇❽❬❻✰❾➉❻✰❾➉✇✟①✰✇✟✈✉③s④✧t✂④✧❻✰♦✦② ❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✷qs④✧qs✇✟r✉r✉⑤✜✈✉③➔❻✰❾❬❹s②✺❾✤t✉❻❼❺s②✺❾❬④✧qs✇✟❹s②➎②✺✇✟❿✟➈➌❻✰t✉➈s②✺❾✐➁✯♥❏③➔✇✟❾➃①✰qs♦✦②✺③st✻✈✉④❏✇✍④✧q ➄✍✌ ②✺❿✟t✉✈✉➅✰②➎②✺➦✰❺sr✉✇✟③s✇✟t✉✈✉❻✰③ ❻✰❽✤④✧❻✰♦✦②✍④✧t✉✇✟t✉②✺♦✦②✺③st

➄

②✺✈✉③s①❼✇✟r✉r✉②✺①✰②✺❹➔✈✉③❪t✉➈s②✦❺s❾❬❻✰❿✟②✺④✧④✖➁

➍➉➈s②✺❾❬②➐✇✟❾❬②➐✇➏r✉❻✰t■❻✰❽✦✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❖♦✦❻✰❹s②✺r✉④❪t✉➈s✇✟t✑➈s✇✟➅✰② ➄ ②✺②✺③➒❹s②✺➅✰②✺r✉❻✰❺s②✺❹❖✈✉③s④✧✈✉❹s②❢♥❏❾❬t✉✈✉❽❬✈✉❿✟✈✉✇✟r✑➂➃③s➓ t✉②✺r✉r✉✈✉①✰②✺③s❿✟②◆➁❢♥❏♦✦❻✰③s①➟t✉➈s②✺④✧②➌♦✦❻✰❹s②✺r✉④✧➊➡❹s✈✉❽➃❽❬②✺❾❬②✺③st✉④➠❽❬❻✰❾❬♦✦✇✟r✑④✧⑤✖④✧t✉②✺♦✦④➠❻✰❽➎❹s②✺❽❬②✺✇✟④✧✈➄ r✉②➔✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➒✇✟❾❬② ❹s②✺❽❬✈✉③s②✺❹s➊✱➆❏➈s②✺❾❬②➀✇✟❾➃①✰qs♦✦②✺③st✉④✩❽❬❻✰❾➡✇✟③s❹❢✇✟①✰✇✟✈✉③s④✧t●✇➠❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③➌✇✟❾❬②✜❺s❾❬❻✰❹sqs❿✟②✺❹❢✇✟③s❹❢②✺➅✰✇✟r✉qs✇✟t✉②✺❹➌t✉❻➌➅✰②✺❾❬✈✉❽❬⑤ t✉➈s②➐✇✟❿✟❿✟②✺❺st✉✇ ➄ ✈✉r✉✈✉t✉⑤➞❻✰❽➀t✉➈s✇✟t❏❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③❲➁↕➂➃③↕t✉➈s✈✉④➔♦✦✇✟③s③s②✺❾✓➊❏❹s②✺❽❬②✺✇✟④✧✈➄ r✉②➐✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↕✇✟r✉r✉❻✰➆❏④➌❾❬②✺✇✟➓ ④✧❻✰③s✈✉③s①➔➆❏✈✉t✉➈❢✈✉③s❿✟❻✰♦✦❺sr✉②✺t✉②✍✇✟③s❹➐qs③s❿✟②✺❾❬t✉✇✟✈✉③❢✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③❲➁➡➍➉➈s②✜❹s②✺➅✰②✺r✉❻✰❺s♦✦②✺③st●❻✰❽✭t✉➈s✈✉④✣➑s✈✉③s❹❢❻✰❽✭④✧⑤✖④✧t✉②✺♦✦④ ➈s✇✟④➀①✰❾❬❻✰➆❏③➟✈✉③⑨t✉➈s②❪r✉✇✟④✧t➇⑤✖②✺✇✟❾❬④✖➁➠➪❏②✺④✧❺s✈✉t✉②❪t✉➈s②❪➅✰✇✟❾❬✈✉②✺t✉⑤☎➊✤t✉➈s②❪♦✦✇✟✈✉③⑨✈✉❹s②✺✇➔➈s②✺❾❬②➔✈✉④➀t✉➈s✇✟t➇✇✟③s⑤➐❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③ ➆❏✈✉r✉r ➄ ②➌✇✟❿✟❿✟②✺❺st✉②✺❹➒✇✟④❼t✉❾❬qs②❢✈✉❽➎t✉➈s②✺❾❬②➌②✺➦✰✈✉④✧t✑✇✟③➒✇✟❾➃①✰qs♦✦②✺③st

A

t✉➈s✇✟t✭④✧qs❺s❺s❻✰❾❬t✑✈✉t✉➊➡✇✟③s❹➒t✉➈s✈✉④➠✇✟❾➃①✰qs♦✦②✺③st✑✈✉④ ✇✟❿✟❿✟②✺❺st✉✇ ➄ r✉②■✇✟❿✟❿✟❻✰❾❬❹s✈✉③s①✜t✉❻✍✇✟③✜✇✟③s✇✟r✉⑤✖④✧✈✉④ ➄ ②✺t✉➆❏②✺②✺③

A

✇✟③s❹✜✈✉t✉④➡❿✟❻✰qs③st✉②✺❾❬✇✟❾➃①✰qs♦✦②✺③st✉④✖➁✱➍➉➈s②✺❾❬②✺❽❬❻✰❾❬②✺➊✂✈✉③➀t✉➈s②❏④✧②✺t ❻✰❽✑✇✟❾➃①✰qs♦✦②✺③st✉④➎❻✰❽✑t✉➈s②✜④✧⑤✖④✧t✉②✺♦✦➊➉④✧❻✰♦✦②➠❻✰❽✑t✉➈s②✺♦ ➆❏✈✉r✉r

➄

②✏✎✽✇✟❿✟❿✟②✺❺st✉✇

➄

r✉②✒✑➠❻✰❾

✌

qs④✧t✉✈✉❽❬✈✉②✺❹➐✇✟❾➃①✰qs♦✦②✺③s④✧➊➉➆❏➈s✈✉r✉② ❻✰t✉➈s②✺❾❬④❏③s❻✰t✭➚✔✓✰➊☞✕✗✖✤⑩ ➶✙✘ ➊☞✝❷❻✰r➶✙✘s➹ ➁

➠❻✰t✉②✑t✉➈s✇✟t❷✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③✍✈✉④ ➄ ②✺✈✉③s①➎qs④✧②✺❹✦✇✟④✤✇❏♦✦②✺❿✟➈s✇✟③s✈✉④✧♦♣t✉❻➎✇✟❿✟➈s✈✉②✺➅✰②■③s❻✰③s♦✦❻✰③s❻✰t✉❻✰③s✈✉❿❏❾❬②✺✇✟④✧❻✰③s✈✉③s①✰➊ ④✧❻➏➆❏②❪❿✟✇✟③➞✇✟r✉④✧❻➏qs④✧②❪✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➟t✉❻➏♦✦❻✰❹s②✺r➡t✉➈s②❪✇✟①✰②✺③st→➙☛④✜✈✉③st✉②✺❾❬③s✇✟r➇❺s❾❬❻✰❿✟②✺④✧④✜❻✰❽✩❹s②✺r✉✈ ➄ ②✺❾❬✇✟t✉✈✉❻✰③s➊❸❽❬❻✰❾ ②✺➦✰✇✟♦✦❺sr✉②✦t✉❻❼❿✟➈s❻✰❻✰④✧②✍t✉➈s②✦❾❬✈✉①✰➈st✯✇✟❿✟t✉✈✉❻✰③➔t✉❻❼❺s②✺❾❬❽❬❻✰❾❬♦➌➁

➂➃③↔t✉➈s✈✉④➔❾❬②✺❺s❻✰❾❬t✉➊✩➆❏②➏➆❏✈✉r✉r❏❽❬❻✰❿✟qs④❢❻✰③❒t✉➈s②➏qs④✧②❰❻✰❽✜✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↔✇✟④❢✇⑨❽❬❻✰❾❬♦ ❻✰❽✜④✧❻✰❿✟✈✉✇✟r✣✈✉③st✉②✺❾❬✇✟❿✟➓ t✉✈✉❻✰③ ➄ ②✺t✉➆❏②✺②✺③➏✇✟①✰②✺③st✉④✖➁

➣

②❪④✧➈s❻✰➆ t✉➈s②❪♦✦❻✰④✧t➇✈✉♦✦❺s❻✰❾❬t✉✇✟③st➇✇✟④✧❺s②✺❿✟t✉④✍✈✉③⑨♦✦qsr✉t✉✈✉✇✟①✰②✺③st✉④✍④✧⑤✖④✧t✉②✺♦✦④✍✈✉③⑨➆❏➈s✈✉❿✟➈ ✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪❿✟✇✟③➌t✉✇✟➑s②✦❺sr✉✇✟❿✟②✺➊❲④✧qs❿✟➈❪✇✟④✣③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➔✇✟③s❹➔❺s②✺❾❬④✧qs✇✟④✧✈✉❻✰③❪❹s✈✉✇✟r✉❻✰①✰qs②✺④✖➁

➣

②➔➆❏✈✉r✉r ➄ ✇✟④✧②➔t✉➈s✈✉④ ➄ ❾❬✈✉②✺❽✣❹s✈✉④✧❿✟qs④✧④✧✈✉❻✰③➟✇ ➄ ❻✰qst➡④✧❻✰❿✟✈✉✇✟r✭✇✟❿✟t✉✈✉➅✰✈✉t✉✈✉②✺④✜✈✉③➟⑧⑨♥❏⑩❒❻✰③➞✇❢④✧✈✉♦✦❺sr✉②❪②✺➦✰✇✟♦✦❺sr✉②➌❹s②✺➓ ④✧❿✟❾❬✈➄ ✈✉③s①➠✇➀❿✟❻✰③s❽❬r✉✈✉❿✟t✉✈✉➅✰②✦④✧✈✉t✉qs✇✟t✉✈✉❻✰③❲➁

⑩❷qs❺s❺s❻✰④✧②➀t✉➈s②✺❾❬②➀✇✟❾❬②➀t✉➆❏❻➌✇✟①✰②✺③st✉④

A

✇✟③s❹

B

t✉❾❬⑤✖✈✉③s①➔t✉❻➔✇✟❿✟❿✟②✺④✧④✩t✉❻➌④✧❻✰♦✦②➀❺sq

➄

r✉✈✉❿➀❾❬②✺④✧❻✰qs❾❬❿✟②

R

➁➡➍➉➈s✈✉④ ❾❬②✺④✧❻✰qs❾❬❿✟②➠❿✟✇✟③ ➄ ②➠qs④✧②✺❹➐❻✰③sr✉⑤ ➄ ⑤➔❻✰③s②➠✇✟①✰②✺③st❸✇✟t✹✇❼t✉✈✉♦✦②✜✇✟③s❹ ➄ ❻✰t✉➈➐✇✟①✰②✺③st✉④➎❿✟r✉✇✟✈✉♦ ❽❬❻✰❾✑t✉➈s✇✟t✹❾❬②✺④✧❻✰qs❾❬❿✟②➠✇✟t t✉➈s②➎④✧✇✟♦✦②✦♦✦❻✰♦✦②✺③st→➁

➣ ②❼❿✟✇✟③⑨④✧②✺②❪t✉➈s✈✉④✦④✧✈✉t✉qs✇✟t✉✈✉❻✰③➏✇✟④✍✇➔❿✟❻✰③s❽❬r✉✈✉❿✟t ➄ ②✺t✉➆❏②✺②✺③

A

✇✟③s❹

B

➊ ✌ qs④✧t ➄ ②✺❿✟✇✟qs④✧②❪➆❏②❼➑s③s❻✰➆ t✉➈s✇✟t

R

❿✟✇✟③s③s❻✰t

➄

②✍qs④✧②✺❹

➄

⑤❼♦✦❻✰❾❬②✍t✉➈s✇✟③➔❻✰③s②✍✇✟①✰②✺③st✯✇✟t➉✇➀t✉✈✉♦✦②◆➁✞✖✤❻✰③s❽❬r✉✈✉❿✟t➉✈✉④❏①✰②✺③s②✺❾❬✇✟r✉r✉⑤➠❹s②✺❽❬✈✉③s②✺❹➔✇✟④✣✇✍④✧✈✉t✉qs✇✟t✉✈✉❻✰③ ✈✉③❼➆❏✈✉❿✟➈❼t✉➆❏❻✜✇✟①✰②✺③st✉④■➈s❻✰r✉❹❼❹s✈✉❽➃❽❬②✺❾❬②✺③st❲✇✟③s❹❪✈✉③s❿✟❻✰♦✦❺s✇✟t✉✈

➄

r✉②✣①✰❻✰✇✟r✉④✖➁➉➍➉➈s②✩✇✟①✰②✺③st✉④✑t✉➈s②✺③❼③s②✺②✺❹❼t✉❻➠④✧t✉✇✟❾❬t✱④✧❻✰♦✦② ➑s✈✉③s❹➞❻✰❽✍❹s✈✉✇✟r✉❻✰①✰qs②❢t✉❻➞t✉❾❬⑤➟t✉❻➟❻ ➄ t✉✇✟✈✉③❖t✉➈s✈✉④➠❾❬②✺④✧❻✰qs❾❬❿✟②◆➁➞➍➉➈s②❢❻ ➄✍✌ ②✺❿✟t✉✈✉➅✰②➐✈✉④❼t✉❻➞❾❬②✺✇✟❿✟➈❖④✧❻✰♦✦②➐❾❬②✺✇✟④✧❻✰③s✇ ➄ r✉② ④✧②✺t✉t✉r✉②✺♦✦②✺③st→➁ ➣ ②➏➆❏✈✉r✉r✣❿✟✇✟r✉r✩✇⑨➳s➲→➭❲➺s➵✉➽✉➫s➵✉➽✉➺s➳❖➬s➽✉➫s➾✉➺➯➭❲➼s➲⑨➫s➻❏➺s➳➯➭♣➫s➴✗➭❲➼s➻❏➲✟➳s➵✉➷➌t✉❻↕✇➟④✧②✺➢sqs②✺③s❿✟②➏❻✰❽✜❺s✇✟✈✉❾❬④

(Ag, Arg)

➆❏➈s②✺❾❬②

Arg

✈✉④✜t✉➈s②➔✇✟❾➃①✰qs♦✦②✺③st➡✇✟③s③s❻✰qs③s❿✟②✺❹ ➄ ⑤❰t✉➈s②➔✇✟①✰②✺③st

Ag

➁❪➍➉➈s②➌❻✰❾❬❹s②✺❾✩❻✰❽✩t✉➈s②❪❺s✇✟✈✉❾❬④ ❹s②✺③s❻✰t✉②➎t✉➈s②✦❻✰❾❬❹s②✺❾➇✈✉③❪➆❏➈s✈✉❿✟➈➔t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st✉④■✇✟❾❬②✍❺s❾❬②✺④✧②✺③st✉②✺❹❪❹sqs❾❬✈✉③s①❼t✉➈s②➎❹s✈✉✇✟r✉❻✰①✰qs②◆➁

Workshop de Investigadores en Ciencias de la Computación

WICC 2002

(3)

⑩❷qs❺s❺s❻✰④✧②✦✇✟①✰②✺③st

A

④✧t✉✇✟❾❬t✉④■t✉➈s②➎③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❲➁✯➍➉➈s②✺③

A

➆❏✈✉r✉r✻④✧➈s❻✰➆ t✉➈s②➎✇✟❾➃①✰qs♦✦②✺③st

a

₁

④✧qs❺s❺s❻✰❾❬t✉✈✉③s①➠✈✉t✉④ ❹s②✺④✧✈✉❾❬②■❻✰❽➉✇✟❿✟❿✟②✺④✧④✧✈✉③s①

R

➁✻♥❏①✰②✺③st

B

➆❏✈✉r✉r✂②✺➦✰✇✟♦✦✈✉③s②

a

₁

✇✟③s❹✜➆❏✈✉r✉r✂❺s❾❬❻✰❹sqs❿✟②❏t✉➈s②■✇✟❾➃①✰qs♦✦②✺③st

b

₁

➊❷④✧qs❺s❺s❻✰❾❬t✉✈✉③s① ✈✉t✉④➀❹s②✺④✧✈✉❾❬②❪❻✰❽✣✇✟❿✟❿✟②✺④✧✈✉③s①

R

✇✟③s❹⑨✇✟t✉t✉✇✟❿✟➑s✈✉③s①➏④✧❻✰♦✦②➔❺s✇✟❾❬t✉④✜❻✰❽

a

₁

➁❪♥❏①✰②✺③st

A

➆❏✈✉r✉r➇✇✟③s✇✟r✉✈✁✟②

b

₁

✇✟③s❹➟t✉➈s②✺③ ❺s❾❬❻✰❹sqs❿✟②

a

₂

➊❲➆❏➈s✈✉❿✟➈❪✈✉④❏✇✍③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✯✇✟t✉t✉✇✟❿✟➑s✈✉③s①

b

₁

➊❲✇✟③s❹➔④✧❻❪❻✰③❲➁

➂➃❽❸✇✟①✰②✺③st

B

❿✟✇✟③s③s❻✰t✯❺s❾❬❻✰❹sqs❿✟②✦✇✦③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✻❻✰③➔✈✉t✉④■❻✰➆❏③❪❹s②✺❽❬②✺③s④✧②➎✈✉③➔t✉➈s②➎③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❪❺s❾❬❻✰❿✟②✺④✧④✧➊ t✉➈s②✺③

B

♦✦qs④✧t✯②✺③s❹➔t✉➈s②➎❹s✈✉✇✟r✉❻✰①✰qs②✍✇✟❿✟❿✟②✺❺st✉✈✉③s①❼t✉➈s②➎✈✉③s✈✉t✉✈✉✇✟r✻❾❬②✺➢sqs②✺④✧t✯❻✰❽

A

t✉❻❼✇✟❿✟❿✟②✺④✧④

R

➁➉➩❷❻✰❾❬♦✦✇✟r✉r✉⑤☎➊✱✈✉❽✤t✉➈s② ④✧②✺➢sqs②✺③s❿✟②✜❻✰❽❏✇✟❾➃①✰qs♦✦②✺③st✉④✦❺s❾❬②✺④✧②✺③st✉②✺❹➐✈✉③❰t✉➈s②➠③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➏❹s✈✉✇✟r✉❻✰①✰qs②➠✈✉④

{

a

₁

, b

₁

, a

₂

, b

₂

, ..., a

_n

}

➊✹✇✟③s❹

B

✈✉④➎③s❻✰t❸✇

➄

r✉②➠t✉❻❢❺s❾❬❻✰❹sqs❿✟②➠✇✟③❰✇✟❾➃①✰qs♦✦②✺③st❸✇✟①✰✇✟✈✉③s④✧t

a

n

➊●t✉➈s②✺③

A

➆❏✈✉③s④✦t✉➈s②✜③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③s➊

➄

②✺❿✟✇✟qs④✧②➠✈✉t✉④➎r✉✇✟④✧t ④✧qs❺s❺s❻✰❾❬t✉✈✉③s①❢✇✟❾➃①✰qs♦✦②✺③st❸❿✟✇✟③s③s❻✰t ➄ ②❼❹s②✺❽❬②✺✇✟t✉②✺❹ ➄ ⑤

B

➁➎➍➉➈s②❼④✧②✺➢sqs②✺③s❿✟②➠❻✰❽■✇✟❾➃①✰qs♦✦②✺③st✉④✍❺s❾❬②✺④✧②✺③st✉②✺❹➐✈✉③➏t✉➈s② ❹s✈✉✇✟r✉❻✰①✰qs②❏✈✉④✭❿✟✇✟r✉r✉②✺❹➀➫s➴✗➭❲➼s➻❏➲✟➳s➵✉➫s➵✉➽✉➺s➳✍➾✉➽✉➳s➲❄➁✻➍➉➈s②✣④✧②✺t✷❻✰❽●✇✟r✉r❲✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③✜r✉✈✉③s②✺④➡t✉➈s✇✟t✷❿✟✇✟③

➄

②✣❺s❾❬❻✰❹sqs❿✟②✺❹ ④✧t✉✇✟❾❬t✉✈✉③s①❼➆❏✈✉t✉➈

a

₁

✈✉④✣❿✟✇✟r✉r✉②✺❹➌t✉➈s②➎➬s➽✉➫s➾✉➲✟➸✟➵✉➽✉➸✟➫s➾✯➵✉➴✐➲✟➲➠❻✰❽

a

₁

➁❸➂➃t➉✈✉④❏❺s❻✰④✧④✧✈

➄

r✉②✍t✉❻❪④✧✇✟⑤❼t✉➈s✇✟t➉❻✰③s②➀❻✰❽➡t✉➈s②✍①✰❻✰✇✟r✉④ ❻✰❽❏✇✟③s⑤❰✇✟①✰②✺③st➇✈✉③s➅✰❻✰r✉➅✰②✺❹➟✈✉③➏③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➟✈✉④✍t✉❻ ➄ r✉❻✰❿✟➑⑨t✉➈s②❪❻✰❺s❺s❻✰③s②✺③st→➙☛④➀❿✟✇✟❺s✇ ➄ ✈✉r✉✈✉t✉⑤❢t✉❻❰❺s❾❬❻✰❹sqs❿✟② ➄ ②✺t✉t✉②✺❾ ✇✟❾➃①✰qs♦✦②✺③st✉④✖➁✄✂❏❻✰➆❏②✺➅✰②✺❾✓➊✷✇✟③❪✇✟①✰②✺③st✻✈✉④■✇✟r✉④✧❻➠✇✟r✉r✉❻✰➆❏②✺❹❼t✉❻➠✇✟t✉t✉✇✟❿✟➑❪❻✰t✉➈s②✺❾❸✇✟❾➃①✰qs♦✦②✺③st✉④■✈✉③❼t✉➈s②✩✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③ r✉✈✉③s②✺➊✻✈✉❽➡❹s②✺④✧✈✉❾❬②✺❹s➊✯✇✟③s❹❢③s❻✰t✹③s②✺❿✟②✺④✧④✧✇✟❾❬✈✉r✉⑤❼t✉➈s②➀r✉✇✟④✧t●❻✰③s②◆➁✭➍➉➈s✈✉④✩✈✉④✩t✉➈s②➀④✧t✉✇✟❾❬t✉✈✉③s①➔❺s❻✰✈✉③st●❻✰❽✑t✉➈s②➀②✺➦✰❺sr✉❻✰❾❬✇✟t✉✈✉❻✰③ ❻✰❽✤✇➀③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪r✉✈✉③s②◆➁

➂➃③❢③s❻✰③s♦✦❻✰③s❻✰t✉❻✰③s✈✉❿➠❾❬②✺✇✟④✧❻✰③s✈✉③s①➌④✧⑤✖④✧t✉②✺♦✦④✣qs④✧✈✉③s①➔✇✟③➐✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❢❽❬❻✰❾❬♦✦✇✟r✉✈✉④✧♦✦➊✯❽❬❻✰❾✑✇✟③s⑤❪✇✟❾➃①✰qs♦✦②✺③st

a

➊❲t✉➈s②✦②✺③st✉✈✉❾❬②➎❹s✈✉✇✟r✉②✺❿✟t✉✈✉❿✟✇✟r✻t✉❾❬②✺②✦♦✦qs④✧t ➄ ②✦✇✟③s✇✟r✉✈✁✟②✺❹➔✈✉③➔❻✰❾❬❹s②✺❾✤t✉❻❪✇✟❿✟❿✟②✺❺st✯❻✰❾➇❾❬② ✌ ②✺❿✟t✯t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st

a

➁

➣

②

④✧✇✟✈✉❹ ➄ ②✺❽❬❻✰❾❬②❢t✉➈s✇✟t✭✇✟①✰②✺③st→➙☛④➠❹s②✺❽❬②✺✇✟④✧✈➄ r✉②➌❾❬②✺✇✟④✧❻✰③s✈✉③s①➟❿✟✇✟③ ➄ ②❢✇✟❿✟➈s✈✉②✺➅✰②✺❹ ➄ ⑤⑨✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❲➁➐➍➉➈s②➌♦✦✇✟✈✉③ ❹s✈✉❽❬②✺❾❬②✺③s❿✟② ➄ ②✺t✉➆❏②✺②✺③❖✇✟③❖✈✉③st✉②✺❾❬③s✇✟r■❺s❾❬❻✰❿✟②✺④✧④➔❻✰❽✍✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↕✇✟③s❹❖t✉➈s②➐qs④✧②❰❻✰❽✍✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❖✇✟④➔✇ ♦✦②✺❿✟➈s✇✟③s✈✉④✧♦ ❽❬❻✰❾✭✈✉♦✦❺sr✉②✺♦✦②✺③st✉✈✉③s①❼③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❢✈✉④✣t✉➈s✇✟t●t✉➈s②✍❽❬❻✰❾❬♦✦②✺❾✭✈✉④✣❿✟❻✰③s❿✟②✺❾❬③s②✺❹❢➆❏✈✉t✉➈➌t✉➈s②➀✇✟❿✟❿✟②✺❺st✉✇✟③s❿✟② ❻✰❽✜✇✟③s⑤❖①✰✈✉➅✰②✺③❒❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✣❹s②✺❽❬✈✉③s✈✉③s①❖✇➟❿✟❻✰♦✦❺sr✉②✺t✉②➏✇✟③s✇✟r✉⑤✖④✧✈✉④ ➄ ②✺t✉➆❏②✺②✺③↔✇✟r✉r✣t✉➈s②⑨✇✟❾➃①✰qs♦✦②✺③st✉④➌❽❬❻✰❾✜✇✟③s❹ ✇✟①✰✇✟✈✉③s④✧t❲t✉➈s✇✟t✱❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✂➆❏➈s✈✉r✉②✣t✉➈s②✣r✉✇✟t✉t✉②✺❾●✈✉④✑❻✰③sr✉⑤✍❿✟❻✰③s❿✟②✺❾❬③s②✺❹❪➆❏✈✉t✉➈➠t✉➈s②✣❾❬②✺④✧qsr✉t❲❻✰❽❸✇➎①✰✈✉➅✰②✺③❼④✧②✺➢sqs②✺③s❿✟② ❻✰❽➡✇✟❾➃①✰qs♦✦②✺③st✉④✖➁❸➍➉➈s②➀③s❻✰t✉✈✉❻✰③❢❻✰❽✆☎✟➼s➷✧➵✉➽✝✟➽✉➸✟➫s➵✉➽✉➺s➳❪➺✞✝✜➫s➴✗➭❲➼s➻❏➲✟➳s➵✉➷✣✈✉④✣❻✰③sr✉⑤❪❾❬②✺r✉✇✟t✉②✺❹➌t✉❻➔t✉➈s②✍✈✉③st✉②✺❾❬③s✇✟r➉❺s❾❬❻✰❿✟②✺④✧④ ❻✰❽✤❾❬②✺✇✟④✧❻✰③s✈✉③s①❪❻✰❽➇t✉➈s②➎✇✟①✰②✺③st→➁

➣ ➈s✇✟t➇➈s✇✟❺s❺s②✺③s④✍➆❏➈s②✺③⑨t✉➈s②✺❾❬②❼✇✟❾❬②➔♦✦❻✰❾❬②➔t✉➈s✇✟③➏t✉➆❏❻➏✇✟①✰②✺③st✉④➀✈✉③➏t✉➈s②❪❹s✈✉✇✟r✉❻✰①✰qs②✠✟❀⑩❷qs❺s❺s❻✰④✧②❪➆❏②❪➈s✇✟➅✰②

n

✇✟①✰②✺③st✉④

A

₁

, A

₂

, ..., A

n

t✉❾❬⑤✖✈✉③s①⑨t✉❻➏✇✟❿✟❿✟②✺④✧④➠t✉➈s②➔④✧✇✟♦✦②➌❾❬②✺④✧❻✰qs❾❬❿✟②

R

➁➌➱✯➅✰②✺❾❬⑤➏✇✟①✰②✺③st

A

i

❺s❾❬❻✰❹sqs❿✟②✺④➠✇✟③ ✇✟❾➃①✰qs♦✦②✺③st

a

i

④✧qs❺s❺s❻✰❾❬t✉✈✉③s①❢✈✉t✉④➎❹s②✺④✧✈✉❾❬②➠❻✰❽■✇✟❿✟❿✟②✺④✧④✧✈✉③s①

R

➁✩➱✯✇✟❿✟➈

a

i

✈✉④✦t✉➈s②✺③➐✈✉③❰❿✟❻✰③s❽❬r✉✈✉❿✟t❸➆❏✈✉t✉➈❰②✺➅✰②✺❾❬⑤

a

j

➊

(

j

6 =

i,

1 ≤

j, i

≤

n

)

➊✱④✧❻❼❻✰③sr✉⑤❼❻✰③s②✦❻✰❽➇t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st✉④❏❿✟✇✟③

➄

②✦✇✟❿✟❿✟②✺❺st✉②✺❹s➊❲④✧✇✟⑤

a

_k

✇✟③s❹➌t✉➈s②➎✇✟❿✟❿✟②✺④✧④✣t✉❻

R

✈✉④■①✰❾❬✇✟③st✉②✺❹➔❽❬❻✰❾

A

k

➁✯⑩❷❻✰♦✦②✦③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➔❺s❾❬❻✰t✉❻✰❿✟❻✰r✯✈✉④■③s②✺②✺❹s②✺❹s➊✷❽❬❻✰❾✤②✺➦✰✇✟♦✦❺sr✉②✺➊❲t✉❻❼②✺④✧t✉✇ ➄ r✉✈✉④✧➈❼t✉➈s②➎❻✰❾❬❹s②✺❾ ✈✉③❪➆❏➈s✈✉❿✟➈➔t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st✉④■✇✟❾❬②✍❺s❾❬②✺④✧②✺③st✉②✺❹❪✈✉③➔t✉➈s②➎❹s✈✉✇✟r✉❻✰①✰qs②◆➁

➣ ➈s②✺③❪③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉③s①✰➊❲✇✟①✰②✺③st✉④❏③s②✺②✺❹❪t✉❻❼❿✟➈s❻✰❻✰④✧②✍t✉➈s②

➄

②✺④✧t✻✇✟❾➃①✰qs♦✦②✺③st✯✇✟❿✟❿✟❻✰❾❬❹s✈✉③s①❪t✉❻➠✈✉t✉④❏①✰❻✰✇✟r✉④❏✇✟③s❹➔t✉➈s② ❿✟qs❾❬❾❬②✺③st➉④✧t✉✇✟t✉②✍❻✰❽➡③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❲➁✹➍➉➈s✈✉④✣❿✟✇✟③❢✇✟r✉④✧❻ ➄ ②✍❹s❻✰③s②✍t✉➈s❾❬❻✰qs①✰➈❢✈✉③st✉②✺❾❬③s✇✟r✯✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➌❺s❾❬❻✰❿✟②✺④✧④✧②✺④✖➁ ✖✤➈s❻✰❻✰④✧✈✉③s①❼t✉➈s②✦➆❏❾❬❻✰③s①❼✇✟❾➃①✰qs♦✦②✺③st✯❿✟✇✟③➌r✉②✺✇✟❹❪t✉❻❼t✉➈s②✦r✉❻✰④✧t✻❻✰❽➇t✉➈s②➎❹s② ➄ ✇✟t✉②◆➁✯➝ ➄ ➅✰✈✉❻✰qs④✧r✉⑤☎➊✷t✉➈s✈✉④■❾❬✇✟➆⑦❽❬❻✰❾❬♦➥❻✰❽ ③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➌♦✦✇✟⑤➔③s❻✰t●❺s❾❬❻✰❹sqs❿✟②➀✇☛✡✭➫s➴✐➲✟➵✉➺✌☞✂➘✤➵✉➽✉➻❏➫s➾✎✍➡✇✟①✰❾❬②✺②✺♦✦②✺③st●❽❬❻✰❾✭②✺✇✟❿✟➈❢✇✟①✰②✺③st→➁➇➂➃t➉❹s②✺❺s②✺③s❹s④✣❻✰③➐t✉➈s② ✈✉③st✉②✺r✉r✉✈✉①✰②✺③s❿✟②✦❻✰❽✭t✉➈s②➀❺s✇✟❾❬t✉✈✉❿✟✈✉❺s✇✟③st✉④✣t✉❻➔④✧②✺r✉②✺❿✟t ➄ ②✺t✉t✉②✺❾➇✇✟❾➃①✰qs♦✦②✺③st✉④✩t✉❻➔❺s❾❬②✺④✧②✺③st●t✉❻➔t✉➈s②✍❹s✈✉✇✟r✉❻✰①✰qs②◆➁➡➂➃③❢❻✰❾❬❹s②✺❾ t✉❻❪❹s❻❪t✉➈s✈✉④✧➊❲✈✉t✯✈✉④✣①✰❻✰❻✰❹❢❽❬❻✰❾➡t✉➈s②✦✇✟①✰②✺③st➉t✉❻❪➑s③s❻✰➆⑦④✧❻✰♦✦②✺t✉➈s✈✉③s①❪✇ ➄ ❻✰qst➉❻✰t✉➈s②✺❾➇✇✟①✰②✺③st✉④✧➊✱t✉➈s②✺✈✉❾✤❹s②✺④✧✈✉❾❬②✺④✧➊✱①✰❻✰✇✟r✉④ ✇✟③s❹➌✈✉③st✉②✺③st✉✈✉❻✰③s④✖➁●➍➉➈s✈✉④✣✈✉④✣➑s③s❻✰➆❏③➌✇✟④✣t✉➈s②✦➷✧➺s➸✟➽✉➫s➾✑✏✟➳s➺✓✒✤➾✉➲✟➬➯➭❲➲✜❻✰❽➡t✉➈s②✍✇✟①✰②✺③st→➁❸➍➉➈s②✍✇✟①✰②✺③st✉④✩❿✟✇✟③➌qs④✧②✍t✉➈s✈✉④ ✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③➔t✉❻❼①✰qs✈✉❹s②✦✈✉t✉④■♦✦❻✰➅✰②✺④✣✈✉③➔t✉➈s②✦❹s✈✉✇✟r✉❻✰①✰qs②◆➁

♥❏③✜✇✟①✰②✺③st❲③s②✺②✺❹s④➡✇✟❹s✈✉t✉✈✉❻✰③s✇✟r❲✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③➠✈✉③✜❻✰❾❬❹s②✺❾✹t✉❻➀④✧②✺r✉②✺❿✟t✷✇✟③➠✇✟❾➃①✰qs♦✦②✺③st❲❽❬❻✰❾●t✉➈s②✣❹s✈✉✇✟r✉❻✰①✰qs②◆➁✻➤❏④✧qs✇✟r✉r✉⑤☎➊ ✇✟❾➃①✰qs♦✦②✺③st✉④✩✈✉③❢③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➐✇✟❾❬②✜qs④✧②✺❹❢t✉❻➌✇✟❹s❹❢❻✰❾✑❾❬②✺t✉❾❬✇✟❿✟t✹✇✟③❢✈✉③st✉②✺③st✉✈✉❻✰③❢❻✰❾✭t✉❻➌❿✟➈s✇✟③s①✰②✜t✉➈s②➀❺s❾❬②✺❽❬②✺❾❬②✺③s❿✟②✺④

✔✖✕

Ý✭Ó❂â☎Ô✉Ñ→Ñ→Ú●Ñ→Ý➯ásÕÛ✄✗✽Ó❂Ô✉Ñ→áÖ✙✘✛✚sáÕÚ●Ó❂ØsÕä✂á✜➯Ñ→Ô✉Ñ➉ÕÛ✻Ý➯Ö➇Ö☎á✜➯Ñ→Ô✂Ó❂â☎Ô✉Ñ→Ñ→Ñ→Ú●Ñ→Ý➯á➋á✜➯Ó❂ás×➯Ö☎Ú●ÕÝ➯Ó❂áÑ→Û✻Õá✢

Workshop de Investigadores en Ciencias de la Computación

WICC 2002

(4)

⑩❷qs❺s❺s❻✰④✧②✦✇✟①✰②✺③st

A

④✧t✉✇✟❾❬t✉④■t✉➈s②➎③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❲➁✯➍➉➈s②✺③

A

➆❏✈✉r✉r✻④✧➈s❻✰➆ t✉➈s②➎✇✟❾➃①✰qs♦✦②✺③st

a

₁

④✧qs❺s❺s❻✰❾❬t✉✈✉③s①➠✈✉t✉④ ❹s②✺④✧✈✉❾❬②■❻✰❽➉✇✟❿✟❿✟②✺④✧④✧✈✉③s①

R

➁✻♥❏①✰②✺③st

B

➆❏✈✉r✉r✂②✺➦✰✇✟♦✦✈✉③s②

a

₁

✇✟③s❹✜➆❏✈✉r✉r✂❺s❾❬❻✰❹sqs❿✟②❏t✉➈s②■✇✟❾➃①✰qs♦✦②✺③st

b

₁

➊❷④✧qs❺s❺s❻✰❾❬t✉✈✉③s① ✈✉t✉④➀❹s②✺④✧✈✉❾❬②❪❻✰❽✣✇✟❿✟❿✟②✺④✧✈✉③s①

R

✇✟③s❹⑨✇✟t✉t✉✇✟❿✟➑s✈✉③s①➏④✧❻✰♦✦②➔❺s✇✟❾❬t✉④✜❻✰❽

a

₁

➁❪♥❏①✰②✺③st

A

➆❏✈✉r✉r➇✇✟③s✇✟r✉✈✁✟②

b

₁

✇✟③s❹➟t✉➈s②✺③ ❺s❾❬❻✰❹sqs❿✟②

a

₂

➊❲➆❏➈s✈✉❿✟➈❪✈✉④❏✇✍③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✯✇✟t✉t✉✇✟❿✟➑s✈✉③s①

b

₁

➊❲✇✟③s❹➔④✧❻❪❻✰③❲➁

➂➃❽❸✇✟①✰②✺③st

B

❿✟✇✟③s③s❻✰t✯❺s❾❬❻✰❹sqs❿✟②✦✇✦③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✻❻✰③➔✈✉t✉④■❻✰➆❏③❪❹s②✺❽❬②✺③s④✧②➎✈✉③➔t✉➈s②➎③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❪❺s❾❬❻✰❿✟②✺④✧④✧➊ t✉➈s②✺③

B

♦✦qs④✧t✯②✺③s❹➔t✉➈s②➎❹s✈✉✇✟r✉❻✰①✰qs②✍✇✟❿✟❿✟②✺❺st✉✈✉③s①❼t✉➈s②➎✈✉③s✈✉t✉✈✉✇✟r✻❾❬②✺➢sqs②✺④✧t✯❻✰❽

A

t✉❻❼✇✟❿✟❿✟②✺④✧④

R

➁➉➩❷❻✰❾❬♦✦✇✟r✉r✉⑤☎➊✱✈✉❽✤t✉➈s② ④✧②✺➢sqs②✺③s❿✟②✜❻✰❽❏✇✟❾➃①✰qs♦✦②✺③st✉④✦❺s❾❬②✺④✧②✺③st✉②✺❹➐✈✉③❰t✉➈s②➠③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➏❹s✈✉✇✟r✉❻✰①✰qs②➠✈✉④

{

a

₁

, b

₁

, a

₂

, b

₂

, ..., a

_n

}

➊✹✇✟③s❹

B

✈✉④➎③s❻✰t❸✇

➄

r✉②➠t✉❻❢❺s❾❬❻✰❹sqs❿✟②➠✇✟③❰✇✟❾➃①✰qs♦✦②✺③st❸✇✟①✰✇✟✈✉③s④✧t

a

n

➊●t✉➈s②✺③

A

➆❏✈✉③s④✦t✉➈s②✜③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③s➊

➄

②✺❿✟✇✟qs④✧②➠✈✉t✉④➎r✉✇✟④✧t ④✧qs❺s❺s❻✰❾❬t✉✈✉③s①❢✇✟❾➃①✰qs♦✦②✺③st❸❿✟✇✟③s③s❻✰t ➄ ②❼❹s②✺❽❬②✺✇✟t✉②✺❹ ➄ ⑤

B

➁➎➍➉➈s②❼④✧②✺➢sqs②✺③s❿✟②➠❻✰❽■✇✟❾➃①✰qs♦✦②✺③st✉④✍❺s❾❬②✺④✧②✺③st✉②✺❹➐✈✉③➏t✉➈s② ❹s✈✉✇✟r✉❻✰①✰qs②❏✈✉④✭❿✟✇✟r✉r✉②✺❹➀➫s➴✗➭❲➼s➻❏➲✟➳s➵✉➫s➵✉➽✉➺s➳✍➾✉➽✉➳s➲❄➁✻➍➉➈s②✣④✧②✺t✷❻✰❽●✇✟r✉r❲✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③✜r✉✈✉③s②✺④➡t✉➈s✇✟t✷❿✟✇✟③

➄

②✣❺s❾❬❻✰❹sqs❿✟②✺❹ ④✧t✉✇✟❾❬t✉✈✉③s①❼➆❏✈✉t✉➈

a

₁

✈✉④✣❿✟✇✟r✉r✉②✺❹➌t✉➈s②➎➬s➽✉➫s➾✉➲✟➸✟➵✉➽✉➸✟➫s➾✯➵✉➴✐➲✟➲➠❻✰❽

a

₁

➁❸➂➃t➉✈✉④❏❺s❻✰④✧④✧✈

➄

r✉②✍t✉❻❪④✧✇✟⑤❼t✉➈s✇✟t➉❻✰③s②➀❻✰❽➡t✉➈s②✍①✰❻✰✇✟r✉④ ❻✰❽❏✇✟③s⑤❰✇✟①✰②✺③st➇✈✉③s➅✰❻✰r✉➅✰②✺❹➟✈✉③➏③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➟✈✉④✍t✉❻ ➄ r✉❻✰❿✟➑⑨t✉➈s②❪❻✰❺s❺s❻✰③s②✺③st→➙☛④➀❿✟✇✟❺s✇ ➄ ✈✉r✉✈✉t✉⑤❢t✉❻❰❺s❾❬❻✰❹sqs❿✟② ➄ ②✺t✉t✉②✺❾ ✇✟❾➃①✰qs♦✦②✺③st✉④✖➁✄✂❏❻✰➆❏②✺➅✰②✺❾✓➊✷✇✟③❪✇✟①✰②✺③st✻✈✉④■✇✟r✉④✧❻➠✇✟r✉r✉❻✰➆❏②✺❹❼t✉❻➠✇✟t✉t✉✇✟❿✟➑❪❻✰t✉➈s②✺❾❸✇✟❾➃①✰qs♦✦②✺③st✉④■✈✉③❼t✉➈s②✩✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③ r✉✈✉③s②✺➊✻✈✉❽➡❹s②✺④✧✈✉❾❬②✺❹s➊✯✇✟③s❹❢③s❻✰t✹③s②✺❿✟②✺④✧④✧✇✟❾❬✈✉r✉⑤❼t✉➈s②➀r✉✇✟④✧t●❻✰③s②◆➁✭➍➉➈s✈✉④✩✈✉④✩t✉➈s②➀④✧t✉✇✟❾❬t✉✈✉③s①➔❺s❻✰✈✉③st●❻✰❽✑t✉➈s②➀②✺➦✰❺sr✉❻✰❾❬✇✟t✉✈✉❻✰③ ❻✰❽✤✇➀③s②✺➆ ✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❪r✉✈✉③s②◆➁

➂➃③❢③s❻✰③s♦✦❻✰③s❻✰t✉❻✰③s✈✉❿➠❾❬②✺✇✟④✧❻✰③s✈✉③s①➌④✧⑤✖④✧t✉②✺♦✦④✣qs④✧✈✉③s①➔✇✟③➐✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❢❽❬❻✰❾❬♦✦✇✟r✉✈✉④✧♦✦➊✯❽❬❻✰❾✑✇✟③s⑤❪✇✟❾➃①✰qs♦✦②✺③st

a

➊❲t✉➈s②✦②✺③st✉✈✉❾❬②➎❹s✈✉✇✟r✉②✺❿✟t✉✈✉❿✟✇✟r✻t✉❾❬②✺②✦♦✦qs④✧t ➄ ②✦✇✟③s✇✟r✉✈✁✟②✺❹➔✈✉③➔❻✰❾❬❹s②✺❾✤t✉❻❪✇✟❿✟❿✟②✺❺st✯❻✰❾➇❾❬② ✌ ②✺❿✟t✯t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st

a

➁

➣

②

④✧✇✟✈✉❹ ➄ ②✺❽❬❻✰❾❬②❢t✉➈s✇✟t✭✇✟①✰②✺③st→➙☛④➠❹s②✺❽❬②✺✇✟④✧✈➄ r✉②➌❾❬②✺✇✟④✧❻✰③s✈✉③s①➟❿✟✇✟③ ➄ ②❢✇✟❿✟➈s✈✉②✺➅✰②✺❹ ➄ ⑤⑨✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❲➁➐➍➉➈s②➌♦✦✇✟✈✉③ ❹s✈✉❽❬②✺❾❬②✺③s❿✟② ➄ ②✺t✉➆❏②✺②✺③❖✇✟③❖✈✉③st✉②✺❾❬③s✇✟r■❺s❾❬❻✰❿✟②✺④✧④➔❻✰❽✍✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↕✇✟③s❹❖t✉➈s②➐qs④✧②❰❻✰❽✍✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③❖✇✟④➔✇ ♦✦②✺❿✟➈s✇✟③s✈✉④✧♦ ❽❬❻✰❾✭✈✉♦✦❺sr✉②✺♦✦②✺③st✉✈✉③s①❼③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❢✈✉④✣t✉➈s✇✟t●t✉➈s②✍❽❬❻✰❾❬♦✦②✺❾✭✈✉④✣❿✟❻✰③s❿✟②✺❾❬③s②✺❹❢➆❏✈✉t✉➈➌t✉➈s②➀✇✟❿✟❿✟②✺❺st✉✇✟③s❿✟② ❻✰❽✜✇✟③s⑤❖①✰✈✉➅✰②✺③❒❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✣❹s②✺❽❬✈✉③s✈✉③s①❖✇➟❿✟❻✰♦✦❺sr✉②✺t✉②➏✇✟③s✇✟r✉⑤✖④✧✈✉④ ➄ ②✺t✉➆❏②✺②✺③↔✇✟r✉r✣t✉➈s②⑨✇✟❾➃①✰qs♦✦②✺③st✉④➌❽❬❻✰❾✜✇✟③s❹ ✇✟①✰✇✟✈✉③s④✧t❲t✉➈s✇✟t✱❺s❾❬❻✰❺s❻✰④✧✈✉t✉✈✉❻✰③s➊✂➆❏➈s✈✉r✉②✣t✉➈s②✣r✉✇✟t✉t✉②✺❾●✈✉④✑❻✰③sr✉⑤✍❿✟❻✰③s❿✟②✺❾❬③s②✺❹❪➆❏✈✉t✉➈➠t✉➈s②✣❾❬②✺④✧qsr✉t❲❻✰❽❸✇➎①✰✈✉➅✰②✺③❼④✧②✺➢sqs②✺③s❿✟② ❻✰❽➡✇✟❾➃①✰qs♦✦②✺③st✉④✖➁❸➍➉➈s②➀③s❻✰t✉✈✉❻✰③❢❻✰❽✆☎✟➼s➷✧➵✉➽✝✟➽✉➸✟➫s➵✉➽✉➺s➳❪➺✞✝✜➫s➴✗➭❲➼s➻❏➲✟➳s➵✉➷✣✈✉④✣❻✰③sr✉⑤❪❾❬②✺r✉✇✟t✉②✺❹➌t✉❻➔t✉➈s②✍✈✉③st✉②✺❾❬③s✇✟r➉❺s❾❬❻✰❿✟②✺④✧④ ❻✰❽✤❾❬②✺✇✟④✧❻✰③s✈✉③s①❪❻✰❽➇t✉➈s②➎✇✟①✰②✺③st→➁

➣ ➈s✇✟t➇➈s✇✟❺s❺s②✺③s④✍➆❏➈s②✺③⑨t✉➈s②✺❾❬②❼✇✟❾❬②➔♦✦❻✰❾❬②➔t✉➈s✇✟③➏t✉➆❏❻➏✇✟①✰②✺③st✉④➀✈✉③➏t✉➈s②❪❹s✈✉✇✟r✉❻✰①✰qs②✠✟❀⑩❷qs❺s❺s❻✰④✧②❪➆❏②❪➈s✇✟➅✰②

n

✇✟①✰②✺③st✉④

A

₁

, A

₂

, ..., A

n

t✉❾❬⑤✖✈✉③s①⑨t✉❻➏✇✟❿✟❿✟②✺④✧④➠t✉➈s②➔④✧✇✟♦✦②➌❾❬②✺④✧❻✰qs❾❬❿✟②

R

➁➌➱✯➅✰②✺❾❬⑤➏✇✟①✰②✺③st

A

i

❺s❾❬❻✰❹sqs❿✟②✺④➠✇✟③ ✇✟❾➃①✰qs♦✦②✺③st

a

i

④✧qs❺s❺s❻✰❾❬t✉✈✉③s①❢✈✉t✉④➎❹s②✺④✧✈✉❾❬②➠❻✰❽■✇✟❿✟❿✟②✺④✧④✧✈✉③s①

R

➁✩➱✯✇✟❿✟➈

a

i

✈✉④✦t✉➈s②✺③➐✈✉③❰❿✟❻✰③s❽❬r✉✈✉❿✟t❸➆❏✈✉t✉➈❰②✺➅✰②✺❾❬⑤

a

j

➊

(

j

6 =

i,

1 ≤

j, i

≤

n

)

➊✱④✧❻❼❻✰③sr✉⑤❼❻✰③s②✦❻✰❽➇t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st✉④❏❿✟✇✟③

➄

②✦✇✟❿✟❿✟②✺❺st✉②✺❹s➊❲④✧✇✟⑤

a

_k

✇✟③s❹➌t✉➈s②➎✇✟❿✟❿✟②✺④✧④✣t✉❻

R

✈✉④■①✰❾❬✇✟③st✉②✺❹➔❽❬❻✰❾

A

k

➁✯⑩❷❻✰♦✦②✦③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➔❺s❾❬❻✰t✉❻✰❿✟❻✰r✯✈✉④■③s②✺②✺❹s②✺❹s➊✷❽❬❻✰❾✤②✺➦✰✇✟♦✦❺sr✉②✺➊❲t✉❻❼②✺④✧t✉✇ ➄ r✉✈✉④✧➈❼t✉➈s②➎❻✰❾❬❹s②✺❾ ✈✉③❪➆❏➈s✈✉❿✟➈➔t✉➈s②✦✇✟❾➃①✰qs♦✦②✺③st✉④■✇✟❾❬②✍❺s❾❬②✺④✧②✺③st✉②✺❹❪✈✉③➔t✉➈s②➎❹s✈✉✇✟r✉❻✰①✰qs②◆➁

➣ ➈s②✺③❪③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉③s①✰➊❲✇✟①✰②✺③st✉④❏③s②✺②✺❹❪t✉❻❼❿✟➈s❻✰❻✰④✧②✍t✉➈s②

➄

②✺④✧t✻✇✟❾➃①✰qs♦✦②✺③st✯✇✟❿✟❿✟❻✰❾❬❹s✈✉③s①❪t✉❻➠✈✉t✉④❏①✰❻✰✇✟r✉④❏✇✟③s❹➔t✉➈s② ❿✟qs❾❬❾❬②✺③st➉④✧t✉✇✟t✉②✍❻✰❽➡③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❲➁✹➍➉➈s✈✉④✣❿✟✇✟③❢✇✟r✉④✧❻ ➄ ②✍❹s❻✰③s②✍t✉➈s❾❬❻✰qs①✰➈❢✈✉③st✉②✺❾❬③s✇✟r✯✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➌❺s❾❬❻✰❿✟②✺④✧④✧②✺④✖➁ ✖✤➈s❻✰❻✰④✧✈✉③s①❼t✉➈s②✦➆❏❾❬❻✰③s①❼✇✟❾➃①✰qs♦✦②✺③st✯❿✟✇✟③➌r✉②✺✇✟❹❪t✉❻❼t✉➈s②✦r✉❻✰④✧t✻❻✰❽➇t✉➈s②➎❹s② ➄ ✇✟t✉②◆➁✯➝ ➄ ➅✰✈✉❻✰qs④✧r✉⑤☎➊✷t✉➈s✈✉④■❾❬✇✟➆⑦❽❬❻✰❾❬♦➥❻✰❽ ③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➌♦✦✇✟⑤➔③s❻✰t●❺s❾❬❻✰❹sqs❿✟②➀✇☛✡✭➫s➴✐➲✟➵✉➺✌☞✂➘✤➵✉➽✉➻❏➫s➾✎✍➡✇✟①✰❾❬②✺②✺♦✦②✺③st●❽❬❻✰❾✭②✺✇✟❿✟➈❢✇✟①✰②✺③st→➁➇➂➃t➉❹s②✺❺s②✺③s❹s④✣❻✰③➐t✉➈s② ✈✉③st✉②✺r✉r✉✈✉①✰②✺③s❿✟②✦❻✰❽✭t✉➈s②➀❺s✇✟❾❬t✉✈✉❿✟✈✉❺s✇✟③st✉④✣t✉❻➔④✧②✺r✉②✺❿✟t ➄ ②✺t✉t✉②✺❾➇✇✟❾➃①✰qs♦✦②✺③st✉④✩t✉❻➔❺s❾❬②✺④✧②✺③st●t✉❻➔t✉➈s②✍❹s✈✉✇✟r✉❻✰①✰qs②◆➁➡➂➃③❢❻✰❾❬❹s②✺❾ t✉❻❪❹s❻❪t✉➈s✈✉④✧➊❲✈✉t✯✈✉④✣①✰❻✰❻✰❹❢❽❬❻✰❾➡t✉➈s②✦✇✟①✰②✺③st➉t✉❻❪➑s③s❻✰➆⑦④✧❻✰♦✦②✺t✉➈s✈✉③s①❪✇ ➄ ❻✰qst➉❻✰t✉➈s②✺❾➇✇✟①✰②✺③st✉④✧➊✱t✉➈s②✺✈✉❾✤❹s②✺④✧✈✉❾❬②✺④✧➊✱①✰❻✰✇✟r✉④ ✇✟③s❹➌✈✉③st✉②✺③st✉✈✉❻✰③s④✖➁●➍➉➈s✈✉④✣✈✉④✣➑s③s❻✰➆❏③➌✇✟④✣t✉➈s②✦➷✧➺s➸✟➽✉➫s➾✑✏✟➳s➺✓✒✤➾✉➲✟➬➯➭❲➲✜❻✰❽➡t✉➈s②✍✇✟①✰②✺③st→➁❸➍➉➈s②✍✇✟①✰②✺③st✉④✩❿✟✇✟③➌qs④✧②✍t✉➈s✈✉④ ✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③➔t✉❻❼①✰qs✈✉❹s②✦✈✉t✉④■♦✦❻✰➅✰②✺④✣✈✉③➔t✉➈s②✦❹s✈✉✇✟r✉❻✰①✰qs②◆➁

♥❏③✜✇✟①✰②✺③st❲③s②✺②✺❹s④➡✇✟❹s✈✉t✉✈✉❻✰③s✇✟r❲✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③➠✈✉③✜❻✰❾❬❹s②✺❾✹t✉❻➀④✧②✺r✉②✺❿✟t✷✇✟③➠✇✟❾➃①✰qs♦✦②✺③st❲❽❬❻✰❾●t✉➈s②✣❹s✈✉✇✟r✉❻✰①✰qs②◆➁✻➤❏④✧qs✇✟r✉r✉⑤☎➊ ✇✟❾➃①✰qs♦✦②✺③st✉④✩✈✉③❢③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③➐✇✟❾❬②✜qs④✧②✺❹❢t✉❻➌✇✟❹s❹❢❻✰❾✑❾❬②✺t✉❾❬✇✟❿✟t✹✇✟③❢✈✉③st✉②✺③st✉✈✉❻✰③❢❻✰❾✭t✉❻➌❿✟➈s✇✟③s①✰②✜t✉➈s②➀❺s❾❬②✺❽❬②✺❾❬②✺③s❿✟②✺④

✔✖✕

Ý✭Ó❂â☎Ô✉Ñ→Ñ→Ú●Ñ→Ý➯ásÕÛ✄✗✽Ó❂Ô✉Ñ→áÖ✙✘✛✚sáÕÚ●Ó❂ØsÕä✂á✜➯Ñ→Ô✉Ñ➉ÕÛ✻Ý➯Ö➇Ö☎á✜➯Ñ→Ô✂Ó❂â☎Ô✉Ñ→Ñ→Ñ→Ú●Ñ→Ý➯á➋á✜➯Ó❂ás×➯Ö☎Ú●ÕÝ➯Ó❂áÑ→Û✻Õá✢

Workshop de Investigadores en Ciencias de la Computación

WICC 2002

Página 50

Workshop de Investigadores en Ciencias de la Computación

WICC 2002

(5)

❻✰❽✤t✉➈s②✦❻✰❺s❺s❻✰③s②✺③sts➁✂✁✤✇✟④✧✈✉❿✟✇✟r✉r✉⑤☎➊❲t✉➈s②✺❾❬②✦✇✟❾❬②✍t✉➆❏❻❼t✉⑤✖❺s②✺④■❻✰❽➇✈✉③s❽❬❻✰❾❬♦✦✇✟t✉✈✉❻✰③➔t✉➈s✇✟t✯❿✟❻✰③st✉❾❬✈

➄

qst✉②✦t✉❻❼t✉➈s✈✉④■t✉✇✟④✧➑❲➨

•

➝❏❺s❺s❻✰③s②✺③st→➙☛④❏♦✦②✺③st✉✇✟r✻④✧t✉✇✟t✉②◆➁

•

♥❏❿✟t✉qs✇✟r✯④✧t✉✇✟t✉②✦❻✰❽✤t✉➈s②✦❹s✈✉✇✟r✉❻✰①✰qs②◆➁

➍➉➈s②❼✇✟❿✟t✉qs✇✟r❸④✧t✉✇✟t✉②❼❻✰❽■t✉➈s②❼❹s✈✉✇✟r✉❻✰①✰qs②❼②✺④✦①✰✈✉➅✰②✺③

➄

⑤❢t✉➈s②➠④✧②✺t❸❻✰❽❏✇✟❾➃①✰qs♦✦②✺③st✉④✦✈✉③➏t✉➈s②➠✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③➏r✉✈✉③s②◆➁ ➍➉➈s②■✇✟①✰②✺③st✂♦✦qs④✧t✂②✺➅✰✇✟r✉qs✇✟t✉②■t✉➈s②✑r✉✇✟④✧t✂✇✟❾➃①✰qs♦✦②✺③st✂✈✉③➀t✉➈s②✑❹s② ➄ ✇✟t✉②✺➊✾✇✟③s❹➀t✉❾❬⑤➎t✉❻✦❺s❾❬❻✰❹sqs❿✟②❏✇❏❿✟❻✰qs③st✉②✺❾❬✇✟❾➃①✰qs♦✦②✺③st ❽❬❻✰❾➠✈✉t→➁ ➂➃❽➠t✉➈s②⑨✇✟①✰②✺③st➎❿✟✇✟③❒③s❻✰t➎❹s❻↔t✉➈s✈✉④✧➊✩t✉➈s②✺③❒✈✉t→➙☛④❢❺s❻✰④✧④✧✈➄ r✉②➏t✉❻↔②✺➅✰✇✟r✉qs✇✟t✉②➟✇✟③❐②✺✇✟❾❬r✉✈✉②✺❾✜✇✟❾➃①✰qs♦✦②✺③st➎✈✉③ t✉➈s②❰✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③↕r✉✈✉③s②✺➊❏✇✟③s❹↕❺s❾❬❻✰❹sqs❿✟②➏✇⑨❿✟❻✰qs③st✉②✺❾❬✇✟❾➃①✰qs♦✦②✺③st✣✇✟④➌✇➏❾❬②✺❽❬qst✉✇✟t✉✈✉❻✰③↔❻✰❽➀t✉➈s②

➄

✇✟④✧✈✉④➔❻✰❽✜t✉➈s② ❹s② ➄ ✇✟t✉②✺➊ ➄ ②✺❿✟✇✟qs④✧②✩➆❏➈s✇✟t❲✈✉④✭③s❻✰t✱❾❬②✺❽❬qst✉②✺❹➠❹sqs❾❬✈✉③s①✜t✉➈s②✣③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❼❺s❾❬❻✰❿✟②✺④✧④✭✈✉④✑③s❻✰t❲③s②✺❿✟②✺④✧④✧✇✟❾❬✈✉r✉⑤✍✇✟❿✟❿✟②✺❺st✉②✺❹❲➁ ➝❏❽❏❿✟❻✰qs❾❬④✧②✺➊❸t✉➈s✈✉④✍➑s✈✉③s❹➏❻✰❽❏✇✟❿✟t✉✈✉❻✰③s④➀❹s②✺❺s②✺③s❹s④✍❻✰③⑨t✉➈s②❼✈✉③st✉②✺r✉r✉✈✉①✰②✺③s❿✟②❼❻✰❽❏t✉➈s②❼✇✟①✰②✺③st➇✇✟③s❹⑨t✉➈s②❼③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③ ❺s❾❬❻✰t✉❻✰❿✟❻✰r

➄

②✺✈✉③s①➠qs④✧②✺❹❲➁

➍➉➈s②✣✇✟①✰②✺③st✱♦✦✇✟⑤✍③s❻✰t❲➈s✇✟➅✰②✩✇➎t✉❻✰t✉✇✟r❲➑s③s❻✰➆❏r✉②✺❹s①✰②✣❻✰❽✹t✉➈s②❏❻✰❺s❺s❻✰③s②✺③st→➙☛④✭♦✦②✺③st✉✇✟r❲④✧t✉✇✟t✉②◆➁

➣

➈s✇✟t✱✈✉④➡➑s③s❻✰➆❏③ ➄ ⑤⑨t✉➈s②❢✇✟①✰②✺③st■✇ ➄ ❻✰qst■❻✰t✉➈s②✺❾✦✇✟①✰②✺③st✉④❼❹s②✺❺s②✺③s❹s④❼❻✰③❖✈✉t✉④➠➷✧➺s➸✟➽✉➫s➾✑➫s➮s➽✉➾✉➽✉➵✄✯➁➏➝ ➄ ➅✰✈✉❻✰qs④✧r✉⑤☎➊✑✈✉t✑✈✉④❪③s❻✰t✑②✺✇✟④✧⑤➟t✉❻ ✇✟❾➃①✰qs②✜➆❏✈✉t✉➈➐✇➠t✉❻✰t✉✇✟r✉r✉⑤➔qs③s➑s③s❻✰➆❏③➐✇✟①✰②✺③st✉➊

➄

②✺❿✟✇✟qs④✧②➠t✉➈s②➀qs③s❿✟②✺❾❬t✉✇✟✈✉③st✉⑤➔❻✰❽✑❿✟❻✰♦✦♦✦❻✰③➏①✰❻✰✇✟r✉④✧➊➉✈✉③st✉②✺❾❬②✺④✧t✉④✩✇✟③s❹ ➄ ②✺r✉✈✉②✺❽❬④✣♦✦✇✟➑s②✺④➎t✉➈s②➀❺s②✺❾❬④✧qs✇✟④✧✈✉❻✰③➐✈✉③❢t✉➈s②➀❹s✈✉✇✟r✉❻✰①✰qs②✜➅✰②✺❾❬⑤➔❹s✈✉❽➃❽❬✈✉❿✟qsr✉t→➨➡✇✟①✰❾❬②✺②✺♦✦②✺③st✹✈✉④✩✇✟r✉➆❏✇✟⑤✖④➎t✉➈s② ➄ ✇✟④✧✈✉④✩❻✰❽ ③s②✺①✰❻✰t✉✈✉✇✟t✉✈✉❻✰③❲➁ ☎✯②✺✇✟❾❬③s✈✉③s①❢✇ ➄ ❻✰qst✹❻✰t✉➈s②✺❾❬④➎✈✉④➎✇❼➅✰②✺❾❬⑤➌✈✉♦✦❺s❻✰❾❬t✉✇✟③st✹❿✟❻✰r✉r✉✇✟t✉②✺❾❬✇✟r✹②✺❽➃❽❬②✺❿✟t✹❻✰❽✑✇✟①✰②✺③st✉④✦✈✉③st✉②✺❾❬✇✟❿✟t✉✈✉❻✰③❲➁ ➱✯➅✰②✺❾❬⑤ ✑✟②✺③s❿✟❻✰qs③st✉②✺❾✑

➄

②✺t✉➆❏②✺②✺③➠✇✟①✰②✺③st✉④✭✈✉④✑✇✟③➠❻✰❺s❻✰❾❬t✉qs③s✈✉t✉⑤➀t✉❻✜➑s③s❻✰➆♣④✧❻✰♦✦②✺t✉➈s✈✉③s①➀✇

➄

❻✰qst✱②✺✇✟❿✟➈❼❻✰t✉➈s②✺❾✐➁✯➍➉➈s✈✉④ ❿✟✇✟③➔✇✟r✉④✧❻ ➄ ②✦❹s❻✰③s②✦t✉➈s❾❬❻✰qs①✰➈➌✇✟❾➃①✰qs♦✦②✺③st✉✇✟t✉✈✉❻✰③s➊ ➄ ②✺❿✟✇✟qs④✧②✦②✺➅✰②✺❾❬⑤❼✇✟❾➃①✰qs♦✦②✺③st✯t✉➈s✇✟t✻✇✟③➌✇✟①✰②✺③st✯❾❬②✺❿✟②✺✈✉➅✰②✺④❏❽❬❾❬❻✰♦ ✇✟③s❻✰t✉➈s②✺❾✹✇✟①✰②✺③st✱✈✉④✑✇✟③❼②✺➦✰✇✟♦✦❺sr✉②✩❻✰❽❸➆❏➈s✇✟t✱t✉➈s✈✉④✭✇✟①✰②✺③st ➄ ②✺r✉✈✉②✺➅✰②✺④✑✈✉③❲➁✻➱✯➅✰②✺❾❬⑤➀✇✟❾➃①✰qs♦✦②✺③st✱❿✟✇✟③ ➄ ②✣qs④✧②✺❹❼t✉➈s②✺③s➊ ③s❻✰t✯❻✰③sr✉⑤➠t✉❻❼❽❬✈✉③s❹➔❹s✈✉④✧✇✟①✰❾❬②✺②✺♦✦②✺③st✉④✧➊

➄

qst✻t✉❻❪❽❬✈✉③s❹❪❿✟❻✰♦✦♦✦❻✰③

➄

②✺r✉✈✉②✺❽❬④✧➊✷➆❏✈✉❿✟➈❪✈✉④❏qs④✧②✺❽❬qsr✉r✻t✉❻❼t✉➈s✈✉④■✇✟③s❹➔❽❬qst✉qs❾❬② ❹s✈✉✇✟r✉❻✰①✰qs②✺④✖➁

☎✆✞✝✠✟☛✡☛☞✌✆✠✍✏✎✑✓✒✔✖✕✘✗✚✙✛✝✠✒✗✚✜✢✏✒✤✣✠✥✧✦✩★✖✪✫☛✬☛✪✏✦☛✭✠✦☛✮✤✯✰☛✱✳✲✤✱✛✴✰☛✬☛✯✮✤✦✂✪✲✤✵☛✦☛✶✯✵☛✴✲✤✷✹✸☛✺✛✻☛✲✼✽✯✱☛✯✮✤✯✰☛✱✾✶✲✤✰☛✪✏✯✮✤✦❀✿✌✮✤✫☛✭❁★✖✺☛✶✦☛✮✤✯✫☛✱☛✦☛✴❃❂❄✎✤❅❆✏❅✩✕☛✎❈❇❃✒❉❊❆✏❅❋✏✎✗●✎✔❃❍■❅✏✣❏✕☛✎❈✍✏✒ ❍■✙▲❑✩▼☛◆☛❋✏✒✤✜❆✏❖✘✔✖✣✽P✠✔☛❆◗❁✎✗✚❅❆✏✕☛✒✤✕❙❘✞✒✤✜❆✏✙▲✔✖✒✍✩✕☛✎✍❙❚✤◆☛✗✏✣

✍

✟☛✟☛✡☛✣

☎✆✞❚❄✟☛✟☛☞✌✆✞✣❯❚✤❋✏✒✔☛❱✖✎◗❊❆✏✜❆◆✖❅✏✣❳❲✾✫☛✻☛✲✤✴✴✯✱☛✬❩❨■✲✤✬☛✫☛✶✯✦☛✶✯✫☛✱❩❬✖✪✫☛✶✫☛✮✤✫☛✴❭✹✯✱❪✦❪❫✠✯✦☛✴✲✤✮✤✶✯✮✤✦☛✴✖❴✖✪✏✦☛✭✠✲✤❵■✫☛✪✏❛✤✷❄❜❄✗✚✙❊✜✤✎✤✎✤✕✘❆✔☛❉❁❅✹✕☛✎✍❄❜❄✗❆❑✛✎✗✖❝❞✙▲✗❱✖❅❡✖✙▲▼✂✕☛✎❣❢✔☛◗❁✎✤❅❋❆❉❁✒✤✕☛✙▲✗✚✎✤❅ ✎✔✾❍❤❆✏✎✔✖✜❆✏✒✤❅✐✕☛✎❥✍✏✒❪❍■✙▲❑✩▼☛◆☛❋✏✒✤✜❆✏✙▲✔❃❦❝✾❢✤❍■❍❧✟☛✟✘♠✚✣❁❚❄✒✔❩♥✏◆✖✒✔✖♦

✍

✟☛✟☛✟☛✣ ☎♣✠✗✚✒◆✖❅✏q

✍

☞r❚❄✣☛♣✠✗✚✒◆✖❅✏✣❏s❙✺☛✶✫☛✭✠✦☛✶✲✤✻t❨■✲✤✬☛✫☛✶✯✦☛✶✯✫☛✱☛❭✉✦☛✱☛✻●❫✠✲✤✮✤✯❭✏✯✫☛✱✩❲✾✦☛❛✤✯✱☛✬☛✷t❍■✙▲◆☛✗✚❅✏✎✧✔✖✙▲❋✏✎✤❅✏✣✽✆✞✕✘◗❁✒✔✖✜✤✎✤✕✛❍■✙▲◆☛✗✚❅✏✎✉✙▲✔●✆✠✗❋❆✏✈❆✏✜❆✏✒✍✹❢✔☛❋✏✎✍✍❆❉❁✎✔✖✜✤✎✠✆✞❍❤✆✠❢✤✇q

✍

♦

❜❄✗✚✒❉❊◆✖✎✤♦❁❍❤①❄✎✤✜❡✞②❪✎▼☛◆☛③☛✍❆✏✜✤♦☛♥✏◆☛✍④✽♦ ✇ ✍☛⑤

♦ q☛q

✍

✣

☎❝❞✎❆✏❅✏❅✏☞⑥✝✠✣✤❝❞✎❆✏❅✏❅✏✣❊❲✾✺☛✴✶✯✦☛✬☛✲✤✱☛✶❭✐✸✘✿❄❭✏✶✲✤✭✠❭✏⑦■s✂❲✾✫☛✻☛✲✤✪✏✱❈s✖★✖✪✫☛✦☛✮✤⑧✉✶✫❩❫✠✯❭✏✶✪✏✯✵☛✺☛✶✲✤✻✠s❙✪✏✶✯✼✽✯✮✤✯✦☛✴☛⑨✚✱☛✶✲✤✴✴✯✬☛✲✤✱☛✮✤✲✤✷❪✝✠✣✤❝❞✎❆✏❅✏❅✏♦⑩✎✤✕✘❆❋✏✙▲✗✏✣✚❇✛❢✤❂❩❜❄✗✚✎✤❅✏❅✏✣❤❍■✒❑✩③☛✗❆✏✕✘❉❁✎✤♦ ❇❃✒✤❅✏❅✏✒✤✜❡☛◆✖❅✏❅✏✎❋✏❅✏✣

✍

✟☛✟☛✟☛✣

☎♥✏❶❄❷✖❜✧❚✤❝⑥☞✳♥✽✎✔☛✔☛❆✔☛❉❁❅✏♦✚❶✧✒✗✚✒❋❆✔✖♦❊❷❙✙▲❑✩◆✖❅✏✜❆✏✙❊♦✚❜✧✒✗✚❅✏✙▲✔✖❅✏♦⑩❚✤❆✏✎✗✗✚✒✐✒✔✖✕✹❝❞✙❊✙▲✍✏✕✘✗❆✏✕✘❉❁✎✤✣✽s❙✺☛✶✫☛✭✠✦☛✶✲✤✻❩⑧☛✦☛✬☛✬☛✴✯✱☛✬☛⑦❀❸✖✺☛✯✴✻☛✯✱☛✬❩✦☛✪✏✶✯✼✽✯✮✤✯✦☛✴❏✱☛✲✤✬☛✫☛✶✯✦☛✶✫☛✪✏❭✏✷❏❜✧✒✤✜❆✏✈❆✏✜■②■❆❑ ❢✔☛❋✏✎✗✔✖✒❋❆✏✙▲✔✖✒✍❪❍■✙▲✔✖✈✎✗✚✎✔✖✜✤✎❪✙▲✔✞✆✠✗❋❆✏✈❆✏✜❆✏✒✍❥❢✔☛❋✏✎✍✍❆❉❁✎✔✖✜✤✎✤♦ q☛q☛q☛✣

☎❇❃❚❄☞❹❇❃✙▲❋✏❅❡✖✎❉❊❺✞✒✤♦❣❂✾✒✔✖✕✉❚✤❡☛✗✚✙❊✎✤✕☛✎✗✓♦❇❃✣❁❨■✲✤✬☛✫☛✶✯✦☛✶✯✫☛✱●❵■✯✶⑧❩✦☛✪✬☛✺☛✭✠✲✤✱☛✶✦☛✶✯✫☛✱☛⑦✉⑧☛✫☛❵❧✶✫❩✦☛✪✬☛✺☛✲✩✲✼✼✽✯✮✤✯✲✤✱☛✶✴✿✖♦✖✆✞❍❤✆✠❢ q☛q

✍

✇❯❻✖✆✞❚❄❚❄❚ q☛q

✍

❜❄✗✚✙❊✜✤✎✤✎✤✕✘❆✔☛❉❁❅✏✣ ❍❤①❄✎✤✜❡❞❂❄✎✤✜❡☛✔☛❆✏✜✤✒✍❏P✠✔☛❆◗❁✎✗✚❅❆❋④✽✣ q☛q

✍

✣

☎▲✝✠❍■❚❄✟✘❼✖☞✌✆✠✍✏✎✑✓✒✔✖✕✘✗✚✙❽✝✠✒✗✚✜✢✏✒✤♦❥❍■✒✗✍✏✙❊❅✩❍❤❡✖✎✤❅❾✖✎◗❁✒✗✓♦✖✝❁◆☛❆✍✍✏✎✗❑✛✙❽❚✤❆❑✛✒✗❆✏✣❈❿❄⑧☛✲❀➀✖✫☛✴✲❀✫✼✛❫✠✯✦☛✴✲✤✮✤✶✯✮✤❭❪✯✱●❫✠✲✼✽✲✤✦☛❭✏✯✵☛✴✲❈s❙✪✬☛✺☛✭✠✲✤✱☛✶✦☛✶✯✫☛✱❞❜❄✗✚✙❊✜✤✎✤✎✤✕✘❆✔☛❉❁❅✩✙❊✈⑩❋❡✖✎

➁

❢➂⑥❢✔☛❋✏✎✗✔✖✒❋❆✏✙▲✔✖✒✍✩❍■✙▲✔✖✈✎✗✚✎✔✖✜✤✎❪✙❊✈❄❋❡✖✎✩❍❤❡☛❆✍✏✎✤✒✔❞❍■✙▲❑✩▼☛◆☛❋✏✎✗❀❚❄✜❆✏✎✔✖✜✤✎❪❚❄✙❊✜❆✏✎❋④✽✣✖❍■✙▲✔✖✜✤✎▼✖✜❆✏❖✘✔✖♦✖❍❤❡☛❆✍✏✎✤♦❊❘✞✙▲◗❊❆✏✎❑✩③☛✗✚✎✩✕☛✎

✍

✟☛✟✘❼✖✣ ☎❜✧✙▲✍✏✟✘❼✖☞✌❜✧✙❊✙▲✍✏✎✤♦❊➃✞✣❷❙✣☛➄❄✺☛❭✏✶✯✼✽✯✮✤✦☛✶✯✫☛✱✛✦☛✱☛✻✞✻☛✲✼✽✲✤✦☛✶✷✧✆✠✗❋❆✏✈❆✏✜❆✏✒✍❥❢✔☛❋✏✎✍✍❆❉❁✎✔✖✜✤✎✤♦☛➂✠✙▲✍✏✣❣➅☛✡✠❘✞✣ ▼☛▼

⑤

✡☛✡☛✇❼✖q☛✡

☎➃✠❝⑥✟☛✟☛☞✾➃✞✙▲◆☛❉❊✍✏✒✤❅✖❝❞✒✍❋✏✙▲✔✖✣✹❂✽❡✖✎✖❘✞✎❺➆➃✠❆✏✒✍✏✎✤✜❋❆✏✜✤➇❏✆➆❇❃✎❋❡✖✙❊✕❩✈✙▲✗❥❻✖◗❁✒✍◆✖✒❋❆✔☛❉✌✒✔❩✆✠✗❉❊◆☛❑✛✎✔☛❋❣◆✖❅✏✎✤✕✹❜❄◆☛✗▼✖✙❊❅✏✎❏❆✔✾✒✐✝❁❆◗❁✎✔✾❍■✒✤❅✏✎✤✣❁❬✖✪✫☛✶✫✉✸☛✫☛✮✤✯✫☛✴✫☛✬✘✿❄⑦✹s❙✱ ⑨✚✱☛✶✲✤✪✏✱☛✦☛✶✯✫☛✱☛✦☛✴❤➄❄✫☛✺☛✪✏✱☛✦☛✴❏✫✼❙⑨✚✱☛✶✲✤✪✻☛✯❭✏✮✤✯★✖✴✯✱☛✦☛✪✿✾➀✖✲✤❭✏✲✤✦☛✪✮✤⑧☛➈❙➉✏✫☛✴✷⑩➊☛➋☛➈❣➊☛➌☛➌☛➌☛✷❊★☛★⑥➍✘➎☛➏➌☛➊☛✷

➐❯➑

✜➯ÕÛ❲ÕÛ✱Ò❂Ó❂ØØÑ→×❽➒✐➓❄➔❊→❊➣❏↔❏→❊↕➙❏➛■➜✹➝✄✜➯ÕÒ ✜➇Ó❂Ò❂Ò❂Ö☎Ô✉×➯ÕÝ➯â❸áÖ❃➞■Ó❂ØáÖ☎Ý➆➟❳➠❁➡❷ÕÛ✱Ó❂Ý➯Ö☎á✜➯Ñ→Ô❀➢➯ÕÝ➯×➇Ö☎ä✾×➯ÕÓ❂ØÖ☎â❁➤➯Ñ❤➜✖×➯Õä✗ä✉Ñ→Ô✉Ñ→Ý➯á✖ä✉Ô✉Ö☎Ú⑨Ý➯Ñ→â☎Ö☎áÕ➥ Ó❂áÕÖ☎Ý ✢❽➦✽Ö☎Ú●Ñ→áÕÚ●Ñ→Û❊➜✐➝✄✜➯Ñ→Ý➡Ý➯Ñ→â☎Ö☎áÕÓ❂áÕÝ➯â❁➜➋ÕásÕÛ✻Ý➯Ñ→Ò❂Ñ→Û➃Û➃Ó❂Ô➨➧✤áÖ✄✚sÑ→Ô✉Û❊➤➯Ó❂×➯Ñ➉á✜➯Ñ●Ö✎✚ ✚sÖ☎Ý➯Ñ→Ý➯á➋ÕÝ✭Û➃Ö☎Ú●Ñ❸áÖ✎✚sÕÒ❂Û✎✢