Grammaires de graphes et leurs applications en théorie des langages formels

 ✂✁☎✄✝✆✟✞✠✆✟✡☛✆✌☞☎✍✏✎✒✑✔✓☛✕✖✑✗✁☎✘✚✙✜✛✣✢☎✙✗✁☎✞✒✍✤✛✥✙✗✡✦✕✌✎★✧✩ ✂✁☎✪✫✙✜✕✭✬✮✑✯✆✟✞✒✰✱✡☎✍ ✲✴✳✵✲✷✶✸ ✂✹✌✺✼✻✽✺✼✓✾ ✂✿❀✻❁✧❂✳❄❃❆❅✽✻✽✺❈❇ ❉❋❊❍●❏■▲❑◆▼€❖❘◗❚❙❱❯❳❲☛❨❈▼❳❉❋❊◆■▲❙❱❩❈❬❳❑ ❭ ❪❍❫❵❴ ❴ ❫❵❛❜❪❄❝❡❞ ❫❁✐♣✐❦♥q❛qr♠❫s❧❄❛❜t✮✉♣❞ ❝❡✉ ❢❣❝ ❤❵❪❍❫❁✐❦❥❣❝❡❞ ❧❄❥❣✈✌t❵❪❍❛❜❝ ✇✗t❵❪❍❴ ❢❣❝❡❞ ❝♠❧ ♥❜❝❡♦❣❪❍❞ ♥q❫❵✉❣❤✮❫❁❤❵❝❡❞ ❝❡♥q❞ ❖❄❙❱❯❳①②■☎③⑤④✚⑥⑧⑦✌①⑩⑨❂❶❸❷ ▼❹❶❸❺❼❻✜④✚⑥❽❺❿❾➁➀❽➂❂❶❈➃⑧❶❆❺⑤➄➅❾✭⑦➆❶✸➇✜❖❳⑨➈➃❽⑨❂❶❸③▲➉➊❊❳❬❳➉➊❊❍➋ ➉➊❶❆❺⑤➄➅❾✭⑦➆❶❆❾➍➌✝➄❼➌❍❶✝➎➏❶❸➐✂➄❿❷⑧➌❆❾➁❷✽❺➑❶❸⑨➈⑥✽➃❽❷❋⑦✚③⑤④✚❷❽❻✜❶➓➒✵❊❍➋☛❙❱❨❈❯  ✂✁☎✄✝✆✟✞✠✆✟✡☛✆♠☞☎✍✽✹✌✍q✘✖✢☎✍❜✕✖✘✖✢☎✍➔✍q✁→ ✂✁☎✪✫✙✜✕✭✬✮✑✯✆✟✞✒✰✱✡☎✍➔✍✚✆✌❇✱➣↔✄✝✆✟↕❏✬✮✍q✄➓➙❡✎✒➛q✑✯✆✟✙✗✞➜✕✖✍q✄ ✹✌✍q✁☎✁☎✍q✄✚➝✣✓☛✕✖✑✗✁☎✘✚✍ ➞✣➟★➠➢➡✂➤✖➥➧➦◆➨➫➩✂➩✝➭ ➯ ❝❡❴ ❝✌❪❍r♠❛❜❝❡❴ ❝❡✉➲❧❄❞ ➳❿➵✥➸➜➺➻➵➢➼➾➽✣➸✒➚➑➪➾➽➹➶✭➘ ➴⑤➷✖➚➑➬✒➶❆➮✾➬✒➵➢➱✃➵➢➬✒❐➢➺➻➵➢➬➹❒➻➵✫➽✣➱✃➵➢➱✦➷✝➬✒➵✫➽✃➶✝➵✥➱✃➚➑➼⑩❮✠➪✝➬➜❰❿Ï❜Ð➅➪✝➺❽➱❹➘ ẹềểễ ế ệìềễỉỉ ìềễìề ìễqĩệíịòíịệỏỉìềỉỉqễểẽ ìề ềềềéềỉ ế ế õềó ế ế õẹéọồ ổịềỗốõộóõọịờ ìềỉỡở ễ ế ởẽềễểẽỉớềề ế ế é ềìềớợ ềì ởỉỉẹ ễ ỉềềổìểỉẹỉ õềớỏùễỉ ế ỉ õẹéỗốõộùõờỉ ìề ổéềềỉệỏểệ õộùõ òểễởỏ éềỉịệõủệũỉớ ễìềỉềổệẹìễ ế ệễớỉõúụỉệềễ ẹềề ế ề ế ỉớ Û⑩➵➢➬✒❐➢➺➅➵➢➼✂õ➾➼☎➮✯➱✃➵✫➽✭Ø❸➴⑤➬✒➵➢➼➅➸✒➽❱Ï❱➱◆➴✜➽✒➚➫➵➢➪✝➬➁➵➢➸➁➱✃➵✫➽➆➴⑤➱➹➺➻➽➁Ø✖➚➑➪✝➬✭❒➻➵➢➪✝➬➆➽✒➚➑➪✝➸➜➺➻➵➢➼✦➵➢➸➁❒➻➵➢➪✝➬➆➵➢➼➾❐✫➚➑➪✝➬Ơ➴⑤Ĩ❿➵➢➱✃➵➢➼➅➸ ➮☎➸✒➚➑➪✝➸✗❒❂➘ ➺Ị➼➾➽➜➸Ơ➴⑤➼➅➸❱Ú ➺ ➯ ✈❡❞❳♦♣❴ ✈ Ý❽➵☎➸➜➬Ơ➴✫×❼➴⑤➺Ị❒❏➽✒➵☎Ø✝❒í➴➑❐✫➵➹➶➾➴⑤➼➾➽✱❒➻➵✣❐❱➴➑➶✂➬✒➵➹➶✝➵☎❒❂➘ Ù➢➸➜➪➾➶✝➵➹➶✝➵✫➽✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽↔➺Ị➼✂õ➾➼✝➺➻➽↔➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✫➽☛Ø❸➴⑤➬✱➪✝➼▲Ø✝➬✒➚⑤å ❐✫➵✫➽✒➽➜➪➾➽✜õ➾➼✝➺❂Ú❸Þ✌➸✒➚➑➪✝➸➏Ø✝➬✒➚➫❐✫➵✫➽✒➽➜➪➾➽✯õ➾➼✝➺❽Ï➾➚➑➼▲➴➑➽✒➽✒➚➫❐➢➺➻➵↔➼❸➴⑤➸➜➪✝➬✒➵➢❒Ị❒➻➵➢➱✃➵➢➼➅➸✱➪✝➼✾Ĩ❼➬Ơ➴⑤Ø Õ ➵✦➶✭➘ ➵➧ë✝Ù✫❐➢➪✝➸➜➺➻➚➑➼▲Ð➅➪✝➺➆➵✫➽➜➸ ❐✫➚➑➱➹Ø✖➚❼➽✒Ù✱➶✝➵➏➸✒➚➑➪✝➸✒➵✫➽✯❒➻➵✫➽✯❐✫➚➑➼✂õ➾Ĩ❼➪✝➬Ơ➴⑤➸➜➺➻➚➑➼➾➽➏➴➑❐✫❐✫➵✫➽✒➽➜➺Ị➷✝❒➻➵✫➽✜➶✝➵➢Ø✝➪✝➺➻➽✯❒í➴✦❐✫➚➑➼✂õ➾Ĩ❼➪✝➬Ơ➴⑤➸➜➺➻➚➑➼❹➺Ị➼✝➺Ị➸➜➺í➴⑤❒➻➵❼Ï✂➵➢➸✯❒➻➵✫➽✜➴⑤➬✒❐✫➽ ➬✒➵➢Ø✝➬✒Ù✫➽✒➵➢➼➅➸✒➵➢➼➅➸Ư❒➻➵✫➽✗Ù➢➸Ơ➴⑤Ø✖➵✫➽✗➶✝➵☛❐❱➴⑤❒➻❐➢➪✝❒➆➶✂➪áØ✝➬✒➚➫❐✫➵✫➽✒➽➜➪➾➽❱Ú đ➏➼➍➽❱➘ ➺Ị➼➅➸✒Ù➢➬✒➵✫➽✒➽✒➵⑩➮✵❐❱➴⑤➬Ơ➴➑❐➢➸✒Ù➢➬➜➺➻➽✒➵➢➬✥❒í➴✵➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒➵✾➶✝➵✾❐✫➵✫➽✃Ĩ❼➬Ơ➴⑤Ø Õ ỉềỉềổỏớ ểớềềỏừồề ỉềềễửềữ ế ềồ ễềỉớềớểểĩề ẽỉệìềễểéìớệểễề ểễỉ ế ứựỳỷỹễýỵỷểểẹẽểễềềểéẽểễềểễỉ ế ẽểễỉ ế ềừẽễéểéẽửềữ ế ẽỉềềễ ề r õ ế ỉẽễềỉỉẹởồẹốỗốỉờểễềìềểồ õỉớẽéểềểỏớ ế ềỉểễỉ ế ➽↔➴⑤➼➾➶✾➸ Õ ➵✦Ĩ❼➬Ơ➴⑤Ø Õ Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➬✒➽Ư➴⑤➬✒➵☛❐✫➚➑➼➾➽➜➺➻➶✝➵➢➬✒➵✫➶✭Ú ✟ Õ ➵✃Ø❸➴⑤➺Ị➬➜➺Ị➼✝Ĩ⑩❒➻➵➢➱➹➱◆➴➊Đ✩➚➑➬✦❐✫➚➑➼➅➸✒➵➧ë✂➸✠å✩Đè➬✒➵✫➵◆❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵✫➽✣➽➜➸Ơ➴⑤➸✒➵✫➽☛➸ Õ ➴⑤➸✦➸ Õ ➵➢➬✒➵✥➴⑤➬✒➵✥➴⑤❒✡✠✯➴✫❰✂➽☎➸☛✠❽➚⑩➽ Õ ➚➑➬➜➸ ➽➜➪✝➷➾➽➜➸➜➬➜➺Ị➼✝Ĩ❿➽↔❐➢❒➻➚❼➽✒➵✣➸✒➚➑Ĩ❿➵➢➸ Õ ➵➢➬↔➸ Õ ➴⑤➸☛❐❱➴⑤➼❳➷✖➵☎➬✒➵➢Ø✖➵❱➴⑤➸✒➵✫➶✭Ï✖➷✖➚➑➸ Õ ➸ Õ ➵➹➽Ơ➴⑤➱✃➵☎➼➅➪✝➱✦➷✖➵➢➬✦➚⑤Đ❽➸➜➺Ị➱✃➵✫➽❱Ï➁➴➑➽↔➚⑤Đè➸✒➵➢➼ ➴➑➽☞✠❽➵➏❒Ị➺Ị÷❿➵❼Ú✌✟ Õ ➵Ưư❜➴⑤➬➜➺Ị÷ Õ ➘ ➽✯➸ Õ ➵✫➚➑➬✒➵➢➱s➴➑➽✒➽✒➵➢➬➜➸✒➽⑧➸ Õ ➴⑤➸❽➸ Õ ➵Ư❐✫➚➑➱➹➱✦➪✝➸Ơ➴⑤➸➜➺Ị×❿➵✱➺Ị➱◆➴⑤Ĩ❿➵✱➚⑤Đ➆➵➢×❿➵➢➬➜❰✃❐✫➚➑➼➅➸✒➵➧ë✂➸✠å✩Đè➬✒➵✫➵ ❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵☛➺➻➽✜➸ Õ ➵↔❐✫➚➑➱➹➱✦➪✝➸Ơ➴⑤➸➜➺Ị×❿➵✦➺Ị➱◆➴⑤Ĩ❿➵☛➚⑤Đq➽✒➚➑➱✃➵↔➬✒➵➢Ĩ❼➪✝❒í➴⑤➬➏➽✒➵➢➸❱Ú ✍❽❰❄➸ Õ ➵áĨ❼➬Ơ➴⑤Ø Õ Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➬✒➽❱Ï✎✠❽➵➊Ø✝➬✒➵✫➽✒➵➢➼➅➸✃➸ Õ ➵➢➺Ị➬✃➼➾➵✏✠ ➶✝➵➢➱✃➚➑➼➾➽➜➸➜➬Ơ➴⑤➸➜➺➻➚➑➼➾➽❱Ú❏â➈➸➹Ĩ❼➺Ị×❿➵✫➽➹➪➾➽✃➴⑤➼❘➚➑➸ Õ ➵➢➬ Ø✖➚➑➺Ị➼➅➸➏➚⑤Đ❜×➫➺➻➵✏✠✌➴⑤➷✖➚➑➪✝➸✗➸ Õ ➵☛❐✫➚➑➼➅➸✒➵➧ë✂➸✠å✩Đè➬✒➵✫➵☛❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵✫➽Ư➴⑤➼➾➶á➸ Õ ➵↔Ø✖➵➢➬✒➽➜Ø✖➵✫❐➢➸➜➺Ị×❿➵✫➽➏➚⑤Đ❏➴☎➼➾➵✏✠✌➴⑤Ø✝Ø✝➬✒➚❿➴➑❐ Õ ➺Ị➼ ➸ Õ ➵↔❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵↔➸ Õ ➵✫➚➑➬➜❰❿Ú ✑áÿ✓✒✕✔☎ù✗✖✙✘✚û✚✂★ï➾➚➑➬➜➱◆➴⑤❒➫❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵✫➽❱Ï➑❐✫➚➑➼➅➸✒➵➧ë✂➸✠å✩Đè➬✒➵✫➵⑧❒í➴⑤➼✝Ĩ❼➪❸➴⑤Ĩ❿➵✫➽❱Ï★Ĩ❼➬Ơ➴⑤Ø Õ Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➬✒➽❱Ï⑤➺Ị➼✂õ➾➼✝➺Ị➸✒➵⑧Ĩ❼➬Ơ➴⑤Ø Õ Ï Ø❸➴⑤➺Ị➬➜➺Ị➼✝Ĩ✃❒➻➵➢➱➹➱◆➴✂Ï➾Ø✝➪✝➱➹Ø✝➺Ị➼✝Ĩ✃❒➻➵➢➱➹➱◆➴✂Ï❸ư❜➴⑤➬➜➺Ị÷ Õ ➘ ➽✗➸ Õ ➵✫➚➑➬✒➵➢➱❹Ï➾Ĩ❿➵✫➚➑➱✃➵➢➸➜➬➜➺➻❐✦❐ Õ ➴⑤➬Ơ➴➑❐➢➸✒➵➢➬➜➺➻➽➜➸➜➺➻❐❼Ú ➺Ị➺Ị➺ ✛ ❫ ♥❜❝ ✆ ❢❣❝❡❞ ❴ ❫s❧❄❛✢✜✌❪❄❝❡❞ ✣✞✤➅û✦✥★✧✩✤ ✪✫✪ ✬✮✭ û✫ú✯✖✙✰✝ý❼ú ✪✫✪✫✪ ✱✳✲✵✴ ú✯✖⑤ù✕✘✢✥➆ý❼ú✦✪❚ù ✴ ✱ ✶ Ú✶ ưq➬✒➚➑➷✝❒➻Ù➢➱◆➴⑤➸➜➺➻Ð➅➪➾➵ Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ✶ Ú✝ Û⑩➚➑➸➜➺Ị×❼➴⑤➸➜➺➻➚➑➼⑩➵➢➸✗➚➑➷✂❮➜➵✫❐➢➸➜➺ìĐ✩➽✗➶✂➪✾➽➜➸Ơ➴⑤Ĩ❿➵✵Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ✶ Ú ✷✹✸q➼➅×➫➺Ị➬✒➚➑➼✝➼➾➵➢➱✃➵➢➼➅➸↔➶✝➵↔➸➜➬Ơ➴✫×❼➴⑤➺Ị❒❣Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✝ ✶ Ú✺ ✷ ưq❒í➴⑤➼⑩➶✂➪❹➶✝➚➫❐➢➪✝➱✃➵➢➼➅➸②Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✻✽✼ ù➾ú✦✪❚ù ✴ ỷỵ ỷ ệễềớểể ✶ Ú ✶ Û⑩➚➑➸✒➽✗➵➢➸✜❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽❁Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❄✺ ✝✂Ú ✶ Ú ✝ ä➅❰✂➽➜➸✒ỉ➢➱✃➵✫➽✗➶✝➵✱➬✒Ù✫Ù✫❐➢➬➜➺Ị➸➜➪✝➬✒➵➔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✝✂Ú ✶ Ú ✷ ðƯ➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽➏➵➢➸✗➪✝➼➾➵ Õ ➺➻Ù➢➬Ơ➴⑤➬✒❐ Õ ➺➻➵☎➶✝➵✫➽✜❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✱Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ðƯ➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽➏➵➢➸✜❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽ ❅ ❆ Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ❇ ✝✂Ú ✝✂Ú ✶ ðƯ➬Ơ➴⑤Ø Õ ➵✫➽➓Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ❇ ✝✂Ú ✝✂Ú ✝ ðƯ➬Ơ➴⑤Ø Õ ➵✫➽✗➵➢➸✗❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽❣Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶✯❈ ✝✂Ú ✝✂Ú ✷ âé➽✒➚➑➱✃➚➑➬➜Ø Õ ➺➻➽➜➱✃➵✫➽✗➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽➓Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶❉✶ ✝✂Ú ✝✂Ú ệễềểễỉ ế ỷỷớỳ ỳỷỵỷỷỷ ✷✂Ú ✶ â➈➼➅➸➜➬✒➚➫➶✂➪➾❐➢➸➜➺➻➚➑➼❆Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❅ ✷✂Ú ✝ à➁➵➢➱➹➱✃➵✦➶✝➵✫➽✜Ø❸➴⑤➺Ị➬✒➵✫➽✗➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽ Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❅ ✷✂Ú ✷ à➁➵➢➱➹➱✃➵✦➶✝➵✫➽✜Ø❸➴⑤➺Ị➬✒➵✫➽✗➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽➏×➫➺í➴☎❒➻➵✫➽✜Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽Ư➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽✮Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❅ ➺Ị× ❋ ỵỷỷỷ õ ửềữ ế ĩễửềữ ế ìớểễềểễỉ ế ự ýỵỷự ỵự × ✛ ❫ ✆ ♥❜❝ ❢❣❝❡❞ ❭❦❤✮♦❣❪❄❝❡❞ ✝✂Ú ✶ ß➏➼➾➵↔Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵✦➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ú✃Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ✝ ✝✂Ú ✝ ß➏➼ Õ ❰➫Ø✖➵➢➬➜Ĩ❼➬Ơ➴⑤Ø Õ ➵ Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ✷ ✝✂Ú ✷ ß➏➼➾➵↔➬✒Ù✫Ù✫❐➢➬➜➺Ị➸➜➪✝➬✒➵✦➽✒➵➢❒➻➚➑➼á❒í➴✣Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽➏➶✝➵↔❒í➴✦õ➾Ĩ❼➪✝➬✒➵❪✝✂Ú ✶ Ú❈Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ✷ ✝✂Ú ✺ à➁➵✗Ĩ❼➬Ơ➴⑤Ø Õ ➵➏➶✝➵✫➽❏➸➜➬Ơ➴⑤➼➾➽➜➺Ị➸➜➺➻➚➑➼➾➽❽➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✗Ø❸➴⑤➬⑧❒í➴✱Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵Ư➶✝➵✜Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❽➶✝➵✜❒í➴➾Ĩ❼➪✝➬✒➵ G ✝✂Ú ✶ Ú❜Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ➶✝➵✫➽✜➬✒ỉ➢Ĩ❼❒➻➵✫➽✗Ø✖➚➑➪✝➬✜➪✝➼➾➵↔Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵ ✶ ✺ ✝✂Ú ❫ à❏➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ ✷✂Ú ✶ à➁➵✫➽ Õ ❰➫Ø✖➵➢➬Ơ➴⑤➬✒❐✫➽✗➼➾➵↔➽Ơ➴⑤➸➜➺➻➽✠Đ✩➚➑➼➅➸✗Ø❸➴➑➽✜❒í➴➹❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼➁Ú ✷✂Ú ✝ à➆➴➹➶✝Ù✫❐✫➚➑➱➹Ø✖➚❼➽➜➺Ị➸➜➺➻➚➑➼⑩➶✭➘ ➪✝➼❹➱✃➚➑➸ ✺➾Ú ✶ ß➏➼✾➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵↔❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ú⑧Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝❉✝ ✺➾Ú ✝ ß➏➼✾➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☛➽✒➵➢➱➹➺ìå❂❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ú➏Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝❉✷ ✺➾Ú ✷✹✸q➼➾➽✒➵➢➱✦➷✝❒➻➵ P z Ú✔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❫ Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❆ ➵➢➸✗❒❂➘ ➺Ị➸✒Ù➢➬Ơ➴⑤➸➜➺➻➚➑➼➁Ú✔Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú ✶ ❇ Λ(β) = {A, B, C, E, F } R Ú✭Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝✙✺ ✺➾Ú ✺ ß➏➼➾➵↔➬✒Ù✫➶✂➪➾❐➢➸➜➺➻➚➑➼⑩➶✭➘ ➪✝➼❹❐ Õ ➵➢➱➹➺Ị➼⑩➵➢➼❹➪✝➼✾➴⑤➪✝➸➜➬✒➵☛➵➢➼❹➬✒➵➢➸➜➺Ị➬Ơ➴⑤➼➅➸➏➪✝➼➾➵↔➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼➁Ú❣Ú↔Ú☛Ú↔Ú☛Ú❲✝❉❫ ✺➾Ú ❫ ß➏➼❹➱✃➵➢➱✦➷✝➬✒➵ ✺➾Ú ❅ à➁➵☛❐ Õ ➵➢➱➹➺Ò➼ ✺➾Ú ❆ à➁➵☛❐ Õ ➵➢➱➹➺Ò➼ β Bi ➶✝➵✱❒❂➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ α ∈ Ts α R Bi ➵➢➸✗➪✝➼➾➵✱Ø❸➴⑤➬➜➸➜➺➻➵ ➚➑➷✝➸✒➵➢➼➅➪▲➮☎Ø❸➴⑤➬➜➸➜➺Ò➬➏➶✝➵ Ú✥Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝❉❅ β ∈ R Bi α Ú✖Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝✓❆ Ø❸➴⑤➬✜➺Ị➼➾➽✒➵➢➬➜➸➜➺➻➚➑➼✾➶✝➵ ×➫➺ β Ú✟Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú☛Ú↔Ú☛Ú↔Ú☛Ú❲✝✓❆ ❴❛❵❝❜❯❞❝❡✌❢❪❣✄❤ ❥ ✉➲❧✵❪❄t ❦♠❧♥❦ ✐ ❢♣♦♣r➍❧❄❛❜t✮✉ q ĩỉễìởềềớởệí ế ữẽqềễễềớ ế ớểểệởìễểẹởỗìềệ r r ❇✦s➆➵➢➸ r ✶❉✶ sèê➧Ú Ü✱➵➢Ø✝➪✝➺➻➽ ✶ ❇❉t❉❫✂Ï➁Û✾➪✝❒Ò❒➻➵➢➬✦➵➢➸☎ä➫❐ Õ ➪✝Ø✝Ø r ✶ ✝✦s❽➚➑➼➅➸☎➴⑤Ø✝Ø✖➚➑➬➜➸✒Ù➹➪✝➼➾➵➹×➫➺➻➽➜➺➻➚➑➼❳Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵◆➶✝➵✫➽↔❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽ ➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽❱Ú➁ưq❒Ị➪➾➽↔➵➧ë➾➴➑❐➢➸✒➵➢➱✃➵➢➼➅➸❱Ï➁➺Ị❒➻➽↔➚➑➼➅➸☛➱✃➚➑➼➅➸➜➬✒Ù➹❒❂➘ ➺➻➶✝➵➢➼➅➸➜➺Ị➸✒Ù◆➵✈✉✭➵✫❐➢➸➜➺Ị×❿➵➹➵➢➼➅➸➜➬✒➵➹➪✝➼❄➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵◆➮◆Ø✝➺Ị❒➻➵ ➵➢➸✗➪✝➼➾➵↔Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵☎➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵✦➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽✇✂✝➸✒➚➑➪✝➸Ư➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵☎➮✣Ø✝➺Ị❒➻➵☛Ø✖➵➢➪✝➸②①➢➸➜➬✒➵↔➸➜➬Ơ➴⑤➼➾➽✠Đ✩➚➑➬➜➱✃Ù✦➵➢➼ ➪✝➼➾➵➊Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✾➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵❹➶✝➵➊Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽◆➵➢➼✝Ĩ❿➵➢➼➾➶✂➬Ơ➴⑤➼➅➸◆❒➻➵➊Ĩ❼➬Ơ➴⑤Ø Õ ➵❹➶✝➵✫➽✣➸➜➬Ơ➴⑤➼➾➽➜➺Ị➸➜➺➻➚➑➼➾➽◆➶✝➵➊❒❂➘ ➴⑤➪✝➸✒➚⑤å ➱◆➴⑤➸✒➵❼Ï➁➵➢➸↔➺Ị➼➅×❿➵➢➬✒➽✒➵➢➱✃➵➢➼➅➸☎➸✒➚➑➪✝➸✒➵✣Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵◆➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵◆➶✝➵✣Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽☛Ø✖➵➢➪✝➸③①➢➸➜➬✒➵➹➸➜➬Ơ➴⑤➼➾➽✠Đ✩➚➑➬➜➱✃Ù✫➵✃➵➢➼ ➪✝➼❳➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵➹➮✃Ø✝➺Ị❒➻➵☎➶✝➚➑➼➅➸✱❒➻➵✦Ĩ❼➬Ơ➴⑤Ø Õ ➵☎➶✝➵✫➽Ư➸➜➬Ơ➴⑤➼➾➽➜➺Ị➸➜➺➻➚➑➼➾➽↔➵✫➽➜➸Ư➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù☎Ø❸➴⑤➬Ư❒í➴✃Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵❼Ú✭à➁➵☛Đ❂➴⑤➺Ị➸ ➶✝➵✥Ø✖➚➑➪✝×❿➚➑➺Ị➬✃➶✝Ù✫❐➢➬➜➺Ị➬✒➵❼Ï❏➮✾❒❂➘ ➴⑤➺➻➶✝➵á➶✭➘ ➪✝➼➾➵✥Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵❹➶✝➵✥Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ï❜❒í➴⑩➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒➵➊Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵á➶✭➘ ➪✝➼ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☎➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵☛➶✝➵↔➱✃➚➑➸✒➽❱Ï✂➼➁➘ ➵✫➽➜➸✗Ø❸➴➑➽➏➴⑤➼➾➚➫➶✂➺Ị➼➁Ú ✍❽➺➻➵➢➼⑩➶✝➵✫➽➏➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸✒➽Ư❐➢❒í➴➑➽✒➽➜➺➻Ð➅➪➾➵✫➽Ư➽➜➪✝➬✗❒➻➵✫➽➏❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽↔➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽Ư➶✝➵➢×➫➺➻➵➢➼✝➼➾➵➢➼➅➸✱➼❸➴⑤➸➜➪✝➬✒➵➢❒➻➽Ư➽➜➺✚➚➑➼✾❒➻➵✫➽ ➴⑤➷✖➚➑➬✒➶✝➵➹×➫➺í➴➊❒➻➵✫➽☛Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽☎➶✝➵➹Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ú➆ư❜➴⑤➬☎➵➧ë✝➵➢➱➹Ø✝❒➻➵❼Ï✭❒í➴á➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤➸➜➺➻➚➑➼❈➶✝➵✫➽✦❐✫➚➑➼✂õ➾Ĩ❼➪✝➬Ơ➴⑤➸➜➺➻➚➑➼➾➽ ➴➑❐✫❐✫➵✫➽✒➽➜➺Ị➷✝❒➻➵✫➽➊➮✵Ø❸➴⑤➬➜➸➜➺Ị➬➊➶✭➘ ➪✝➼➾➵⑩❐✫➚➑➼✂õ➾Ĩ❼➪✝➬Ơ➴⑤➸➜➺➻➚➑➼✸➶✝➚➑➼✝➼➾Ù✫➵⑩➽✒➵❹➸➜➬Ơ➴➑➶✂➪✝➺Ị➸➊Ø❸➴⑤➬◆❒➻➵✾❐❱➴⑤❒➻❐➢➪✝❒↔➶✭➘ ➪✝➼➓Ø✝❒Ị➪➾➽✥Ø✖➵➢➸➜➺Ị➸ Ø✖➚➑➺Ị➼➅➸✣õ✝ë✝➵á➽➜➪✝➬✣❒í➴⑩Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵❹➶✝➵➊Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Úqà➁➵➊Đ❂➴⑤➱✃➵➢➪✂ë❍❒➻➵➢➱➹➱✃➵❹➶✝➵✫➽✣Ø❸➴⑤➺Ị➬✒➵✫➽➹➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽◆➽❱➘ Ù➢➸Ơ➴⑤➷✝❒Ị➺Ị➸ ➽➜➺Ị➱➹Ø✝❒➻➵➢➱✃➵➢➼➅➸Ư➵➢➸✗Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵➢➱✃➵➢➼➅➸Ừ❸➴⑤➬✜❒➻➵↔➷✝➺í➴⑤➺➻➽✗➶✝➵↔Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽➏➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ú ❦♠❧⑤④ ✲✴✙✯✆✟✞⑦⑥❽✑✯✆✟✞✒✙✗✁ ✍✚✆♠✙q♣⑨⑧➾✍q✘➁✆✟✞✒✪✫✄ơ☞☎✡ ✄✝✆✟✑♠⑩✗✍ ư❜➴⑤➬➆❒➻➵✫➽➁➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸✒➽➆❐➢❒í➴➑➽✒➽➜➺➻Ð➅➪➾➵✫➽❱Ï➢➼➾➚➑➪➾➽✚➴✫×❿➚➑➼➾➽✚Ð➅➪➾➵❏❐ Õ ➴➑Ð➅➪➾➵qĐ❂➴⑤➱➹➺Ị❒Ị❒➻➵❏➶✝➵q❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✚➽✒➵➢❒➻➚➑➼☛❒í➴ Õ ➺➻Ù➢➬Ơ➴⑤➬✒❐ Õ ➺➻➵ ➶✝➵✱Ý Õ ➚➑➱✃➽➜÷➫❰➹❐✫➚➑➬➜➬✒➵✫➽➜Ø✖➚➑➼➾➶✥➮✱➪✝➼➾➵✜Đ❂➴⑤➱➹➺Ị❒Ị❒➻➵➏➶✭➘ ➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽❽➚➑➪✥➶✝➵✜➱◆➴➑❐ Õ ➺Ị➼➾➵✫➽❱Ú➫à➁➵✫➽⑧➱◆➴➑❐ Õ ềệềể ự ỳỳốỵ ỉớểểềìễỗốỉ ờéỏề ềềềềềẽớểểệềệởỗốỉ ờéỏ ỉé ềỉì ềềỉềềềềẹớễềề ớểểềểéỗố ỉờỉỉỉềẽớểểễỗốỉờỉ ❒➻➵✫➽➏➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽✱➮✣Ù➢➸Ơ➴⑤➸✒➽✯õ➾➼✝➺➻➽❱Ú Û▲➴⑤➺➻➽❽❒í➴✦➱✃Ù✫❐❱➴⑤➼✝➺➻Ð➅➪➾➵✱➶✝➵✫➽✜➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽➏➮☛Ø✝➺Ị❒➻➵Ư➼➾➵Ư➶✝➚➑➼✝➼➾➵✱Ø❸➴➑➽❽❒í➴☛×➫➺➻➽➜➺➻➚➑➼➊➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒Ù✫➵↔➶✝➵✫➽❽❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽ ➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽✦❐✫➚➑➱➹➱✃➵✣❒➻➵✫➽✦➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽☎➮➊Ù➢➸Ơ➴⑤➸✒➽❱Ú✭Ü✱➚➑➼➾❐❼Ï✭➵➢➼✵➵✫➽✒➽Ơ➴✫❰➅➴⑤➼➅➸✦➶✝➵➹❐✫➚➑➼➾➽➜➸➜➬➜➪✝➺Ị➬✒➵➹❒➻➵✫➽✦➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽ ➮➹Ù➢➸Ơ➴⑤➸✒➽✗Ð➅➪✝➺✚➴➑❐✫❐✫➵➢Ø✝➸✒➵➢➼➅➸➏❒➻➵✫➽✗❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽Ư➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽✗Ø✖➚➑➪✝➬➏Ù➢➸➜➪➾➶✂➺➻➵➢➬➏➽➜➪✝➬✗❒➻➵✫➽✗❐❱➴⑤➬Ơ➴➑❐➢➸✒Ù➢➬➜➺➻➽➜➸➜➺➻Ð➅➪➾➵✫➽➏Ĩ❿Ù✫➚➑➱✃Ù➧å ➸➜➬➜➺➻Ð➅➪➾➵✫➽✚➶✝➵❏❒➻➵➢➪✝➬✚➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒➵❼Ï★➼➾➚➑➪➾➽✚➚➑➷✝➸✒➵➢➼➾➚➑➼➾➽➆❒➻➵✫➽❜➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽q➮✗Ù➢➸Ơ➴⑤➸✒➽➆➺Ị➼✂õ➾➼✝➺➻➽❱Ú★â➈❒➻➽➆➽✒➚➑➼➅➸✚➵➧ë➾➴➑❐➢➸✒➵➢➱✃➵➢➼➅➸❜❒➻➵✫➽ Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽Ứ➢➸➜➺➻Ð➅➪➾➵➢➸✒Ù✫➽✗➺Ị➼✂õ➾➼✝➺➻➽❱Ú❁✸q➸➏Ĩ❼➬♥❻➑❐✫➵☎➮✣❒í➴✣Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝➵☛Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ï✝➼➾➚➑➪➾➽Ư➴✫×❿➚➑➼➾➽➏❒➻➵✫➽➏➶✝➵✫➽✒❐➢➬➜➺ỊØ✝➸➜➺➻➚➑➼➾➽ ừểễỉ ế ềừ íễìềỉổệễỉỉễềềẹểéìớểễề ểễỉ ế ềễệớểểệềểé ỡẹễểệỉềềễệ ửềữ Õ Ĩ❼➬♥❻➑❐✫➵◆➴⑤➪✂ë▲Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽☎➶✝➵✣Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ú➁à➁➵➹➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸✦➚➑➷✝➸✒➵➢➼➅➪❄➼➾➚➑➪➾➽☛➶✝➚➑➼✝➼➾➵➹➪✝➼❍➴⑤➪✝➸➜➬✒➵➹Ø✖➚➑➺Ị➼➅➸ ➶✝➵☛×➫➪➾➵☎➶✝➵✫➽➏❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽↔➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽❱Ï❸❒➻➵➢➪✝➬Ư➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒➵☎Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵☎➵➢➸✱Ù➢Ĩ➅➴⑤❒➻➵➢➱✃➵➢➼➅➸✱❒➻➵✫➽➏Ø✖➵➢➬✒➽➜Ø✖➵✫❐➢➸➜➺Ị×❿➵✫➽ ➶✭➘ ➪✝➼➾➵↔➼➾➚➑➪✝×❿➵➢❒Ị❒➻➵☎➴⑤Ø✝Ø✝➬✒➚➫❐ Õ ➵↔Ø✖➚➑➪✝➬✗❒í➴☎➸ Õ Ù✫➚➑➬➜➺➻➵✦➶✝➵✱❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✜Đ✩➚➑➬➜➱✃➵➢❒Ị❒➻➵✫➽❱Ú ❦♠❧☛❽ ✺✵✁✚⑥↔✞➜✕✖✙✗✁☎✁☎✍❏✬✮✍q✁➏✆❡☞☎✍✽✆❸✕✖✑❾⑥❽✑✗✞✒✎ Ý❽➵☛➽➜➸Ơ➴⑤Ĩ❿➵↔➶✝➵➾➼✾➶✭➘ Ù➢➸➜➪➾➶✝➵✫➽Ư➴✣Ù➢➸✒Ù☛➵✈✉✭➵✫❐➢➸➜➪➾Ù↔Ø✖➵➢➼➾➶➾➴⑤➼➅➸➏➽➜➺ìë✥➱✃➚➑➺➻➽Ư➴⑤➪❹➽✒➵➢➺Ị➼❹➶✂➪❹Ĩ❼➬✒➚➑➪✝Ø✖➵☛➶✝➵✦ðƯ➬Ơ➴⑤Ø Õ ➵❼Ï Þ➏➪✝➸✒➚➑➱◆➴⑤➸✒➵❼Ï✭à➁➚➑Ĩ❼➺➻Ð➅➪➾➵➹➵➢➸❺❿✱Ù➢➬➜➺ìõ❸❐❱➴⑤➸➜➺➻➚➑➼▲åƯð✱ÞƯà➁â➜đƯị☎Ï✭➮◆❒❂➘ â➈➼➾➽➜➸➜➺Ị➸➜➪✝➸↔➶✝➵✣ã➏➵✫❐ Õ ➵➢➬✒❐ Õ ➵✃➵➢➼❳â➈➼✂Đ✩➚➑➬➜➱◆➴⑤➸➜➺➻Ð➅➪➾➵ ➵➢➸Ưä➅❰✂➽➜➸✒ỉ➢➱✃➵✫➽➏Þ➏❒➻Ù❱➴⑤➸✒➚➑➺Ị➬✒➵✫➽✜å⑧âéã➏â➜ä➫Þ✌➮✣ã➏➵➢➼✝➼➾➵✫➽❱Ï✝ï✝➬Ơ➴⑤➼➾❐✫➵❼Ú à➁➵✫➽✣➸ Õ ỉ➢➱✃➵✫➽✃➶✝➵✥➬✒➵✫❐ Õ ➵➢➬✒❐ Õ ểỉỏ ế ẽỉỉềẽ ớỉểéệìỡừỗểéỉẽểé éờqềễỗễừẽq ỉềẽỉềỉềẽểễỉ ế éẽểễỉ ế ễềờ ớểểẹềỗểềẽềểéẽởờễẹỗề ễềẽểễờíễìềễểềở ế ế ỵ ựý ✴ ú ❦♠❧➆➅ ♦ ✎✒✑✗✁ ☞☎✡ ❊ ☞☎✙↔✘✚✡✣✬✮✍q✁➏✆ à➁➵✫➽❽Ø❸➴⑤➬➜➸➜➺➻➵✫➽✜➽➜➪✝➺Ị×❼➴⑤➼➅➸✒➵✫➽✯➶✂➪✥➱✃Ù➢➱✃➚➑➺Ị➬✒➵✱➽✒➚➑➼➅➸✜➚➑➬➜Ĩ➅➴⑤➼✝➺➻➽✒Ù✫➵✫➽✯❐✫➚➑➱➹➱✃➵✱➽➜➪✝➺Ị➸❱Ú➫Ü↔➴⑤➼➾➽❽❒➻➵Ư❐ Õ ➴⑤Ø✝➺Ị➸➜➬✒➵③✝✂Ï➅➼➾➚➑➪➾➽ ➬Ơ➴⑤Ø✝Ø✖➵➢❒➻➚➑➼➾➽☛➶✝➵✫➽↔Ð➅➪➾➵➢❒➻Ð➅➪➾➵✫➽↔➼➾➚➑➸Ơ➴⑤➸➜➺➻➚➑➼➾➽☛➵➢➸☛❐✫➚➑➼➾❐✫➵➢Ø✝➸✒➽✱Đ✩➚➑➼➾➶➾➴⑤➱✃➵➢➼➅➸Ơ➴⑤➪✂ë✵➶➾➴⑤➼➾➽↔❒í➴◆➸ Õ Ù✫➚➑➬➜➺➻➵✃➶✝➵✫➽✱❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽ Đ✩➚➑➬➜➱✃➵➢❒➻➽❱Ï➅➵➢➸⑧➶✝➵✫➽⑧Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽❽➶✝➵✗Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ú✁✸q➼✥➽➜➪✝➺Ị➸✒➵❼Ï❿❒➻➵✗❒➻➵➢➱➹➱✃➵➏➶✝➵✗Ø❸➴⑤➺Ị➬✒➵✫➽⑧➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽✯➵✫➽➜➸⑧➶✝Ù➢➱✃➚➑➼➅➸➜➬✒Ù ×➫➺í➴❄❒➻➵✫➽✥Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽❹➶✝➵⑩Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽á➶➾➴⑤➼➾➽➊❒➻➵▲❐ ế ỉềỉì ửềữ ế ỉ ế ỉềqừẽ ế ỉềớềỉỉềì ➶✂➪❹➸➜➬Ơ➴✫×❼➴⑤➺Ị❒❂Ú ✑✏ ❴❛❵❝❜❯❞❝❡✌❢❪❣✄❤ ✄ ❝❡❴ ❴ ❝ ✒ ❢❣❝ ❢❣❝ ❤❵❪❍❫❁✐❦❥❣❝❡❞ ➅❪❧♥❦  ✂✁➏✆❸✕✖✙↔☞☎✡☎✘➁✆✟✞✒✙✗✁ ✔✓ ❫❁❪❍❛ ❥ ☎ ❛q❫ ♥❜❝❡❞ ❤❵❪❍❫❵❴ ❴ ❫❵❛❜❪❄❝❡❞ Ý❽➚➑➱➹➱✃➵➹❒➻➵➹❒➻➵➢➱➹➱✃➵✃➶✝➵✫➽↔Ø❸➴⑤➺Ị➬✒➵✫➽↔➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽❱Ï➁❒➻➵✣❒➻➵➢➱➹➱✃➵◆➶✝➵➹ư❜➴⑤➬➜➺Ị÷ Õ ➼➾➚➑➪➾➽✦➶✝➚➑➼✝➼➾➵➹➪✝➼➾➵➹❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼ ➼➾Ù✫❐✫➵✫➽✒➽Ơ➴⑤➺Ị➬✒➵❹Ø✖➚➑➪✝➬✃❒í➴❳➶✂➺➻➽➜➸➜➬➜➺Ị➷✝➪✝➸➜➺➻➚➑➼ ➶✝➵✫➽✃❒➻➵➢➸➜➸➜➬✒➵✫➽◆➶✝➵✫➽✃➱✃➚➑➸✒➽✥➶✭➘ ➪✝➼➓❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵⑩➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵❼Ú⑧à➁➵❹❒➻➵➢➱➹➱✃➵ ➶✝➵↔ư❜➴⑤➬➜➺Ị÷ Õ ềềệỉ r sõềỉ ỗìề r sốờẽ ỉỉééễẽỉỉ ế ỉqỉệỗìề r sq r sốờĩ ế ➴⑤Ø✝➺Ị➸➜➬✒➵❼Ï✖➼➾➚➑➪➾➽✱Ø✝➬✒Ù✫➽✒➵➢➼➅➸✒➚➑➼➾➽↔➪✝➼➾➵✣➶✝Ù➢➱✃➚➑➼➾➽➜➸➜➬Ơ➴⑤➸➜➺➻➚➑➼✵Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵➹➶✂➪▲❒➻➵➢➱➹➱✃➵ ➶✝➵☛ư❜➴⑤➬➜➺Ị÷ Õ Ú✟Ý❽➵➢➸➜➸✒➵☛➶✝Ù➢➱✃➚➑➼➾➽➜➸➜➬Ơ➴⑤➸➜➺➻➚➑➼▲➴➹Ù➢➸✒Ù✱Ø✝➪✝➷✝❒Ị➺➻Ù✫➵✦➶➾➴⑤➼➾➽ r ❫✙s➈Ú ➅❪❧⑤④ ✆ ✍❏✬✔✬✮✍✤☞☎✍ ✖✕ ửẽỉỉééỉẹễởớ ế ừềềềềẽỡồềềềẽể ớừề ềểễềì ớểểỗìềỉởỉ r s r sốờ òìớẹ {0 + k1 + + kn αn |k1 , , kn ∈ N} ➚❘à ➽✒➚➑➼➅➸⑧❒➻➵✫➽⑧Ù➢❒➻Ù➢➱✃➵➢➼➅➸✯➶✝➵ Ï❿➵✫➽➜➸⑧➶✂➺Ò➸⑧➪✝➼✥➽✒➚➑➪➾➽✠å➈➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵③➙ ➳❂➫❱➻⑦➡❘➳❂➞➟➛❏➶✝➵ α0 , , αn Nm ỗ ỏừềềề í Nm qễỡẹỉ + Nm ò ẽqềềềỉ ễềĩỉềẽềẹềểổ r t✦s➯✂✝❒í➴☎Đ❂➴⑤➱➹➺Ị❒Ị❒➻➵✦➶✝➵✫➽➏➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵✫➽Ư➽✒➵➢➱➹➺ìå ❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵☛➶✝➵ Nm ➵➢➸✜Đ✩➵➢➬➜➱✃Ù✫➵↔Ø❸➴⑤➬✜➪✝➼✝➺➻➚➑➼➁Ï➾➺Ị➼➅➸✒➵➢➬✒➽✒➵✫❐➢➸➜➺➻➚➑➼⑩➵➢➸✗❐✫➚➑➱➹Ø✝❒➻Ù➢➱✃➵➢➼➅➸Ơ➴⑤➸➜➺➻➚➑➼➁Ú ✝ ✶ ❃ ❶Û✻❹❋ ÿ✌✧❀✧✵ÿ●✘✚ÿ●€✚✰▲✖❘✪❂❙❚▼ ✻✗✻ Y X úäû❂üäý▲✺➾Ú ✶ ê ß➏➼❹➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☛❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ú ✸q➸Ơ➴⑤➼➅➸◆➶✝➚➑➼✝➼➾Ù✥➪✝➼➓➴⑤❒ỊØ Õ ➴⑤➷✖➵➢➸ ➶➾➴⑤➼➾➽ ❐✫➚➑➱➹➱✃➵☛➽➜➪✝➺Ò➸③✂ Nm ΣT = {a1 , , am } Ï❜➼➾➚➑➪➾➽➹➶✝Ù➧õ➾➼✝➺➻➽✒➽✒➚➑➼➾➽✣❒❂➘ ➴⑤Ø✝Ø✝❒Ò➺➻❐❱➴⑤➸➜➺➻➚➑➼ ψ ➶✝➵ Σ∗T ψ(w) = (|w|a1 , , |w|am ) ➚❘à |w|ai ➶✝Ù✫➽➜➺ỊĨ❼➼➾➵↔➼➾➚➑➱✦➷✝➬✒➵✦➶✭➘ ➚➫❐✫❐➢➪✝➬➜➬✒➵➢➼➾❐✫➵✫➽➏➶✂➪✾❐❱➴⑤➬Ơ➴➑❐➢➸✒ỉ➢➬✒➵ đ➏➼✾➶✂➺Ị➸✗Ð➅➪➾➵ ψ(w) ư❜➴⑤➬➏➵➧ë✝➵➢➱➹Ø✝❒➻➵❼Ï✟➴✫×❿➵✫❐ ä➫➚➑➺➻➵➢➼➅➸ ➵✫➽➜➸✜❒❂➘ ➺Ị➱◆➴⑤Ĩ❿➵☛➶✝➵☛ư❜➴⑤➬➜➺Ị÷ Õ ➶✝➵ ΣT = {a, b, c} Ï❸➚➑➼⑩➴➴✂ w Ú ➶➾➴⑤➼➾➽✜❒➻➵↔➱✃➚➑➸ ψ(abacac) = (3, 1, 2) w Ú Ú ➶✝➵➢➪✂ë➊➱✃➚➑➸✒➽➏Ð➅➪➾➵➢❒➻❐✫➚➑➼➾Ð➅➪➾➵✫➽❱Ï✝➼➾➚➑➪➾➽➏➴✫×❿➚➑➼➾➽ x, y ∈ Σ∗T ψ(x.y) = ψ(x) + ψ(y) = ψ(y) + ψ(x) = ψ(y.x) Þ➏➺Ị➼➾➽➜➺ ψ ➵✫➽➜➸✜➪✝➼á➱✃➚➑➬➜Ø Õ ➺➻➽➜➱✃➵✦➶✝➵ Σ∗T à❏➘ ➺Ị➱◆➴⑤Ĩ❿➵✦➶✝➵↔ư❜➴⑤➬➜➺Ị÷ Õ ➶✝➵✱➸✒➚➑➪✝➸✗❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵ ➶➾➴⑤➼➾➽ Nm Ú L ⊆ Σ∗T ➵✫➽➜➸✗➶✝Ù➧õ➾➼✝➺➻➵↔Ø❸➴⑤➬✗➪✝➼✝➺➻➚➑➼❀✂ ψ(L) = {ψ(x)|x ∈ L} Ý❽➚➑➱➹➱✃➵▲❒í➴❄➬Ơ➴⑤➸➜➺➻➚➑➼❸➴⑤❒Ị➺Ị➸✒Ù❳➵✫➽➜➸➊Ø✝➬✒Ù✫➽✒➵➢➬➜×❿Ù✫➵▲Ø❸➴⑤➬➊➱✃➚➑➬➜Ø Õ ➺➻➽➜➱✃➵❼Ï✜➚➑➼♠➴ ❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵↔➬Ơ➴⑤➸➜➺➻➚➑➼✝➼➾➵➢❒ L Ú ư❜➴⑤➬Ư➵➧ë✝➵➢➱➹Ø✝❒➻➵❼Ï✝❒➻➵✱❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵ L = {an b2n+1 |n ≥ 0} ➽➜➪✝➬ {a, b} ψ(L) ➬Ô➴⑤➸➜➺➻➚➑➼✝➼➾➵➢❒↔Ø✖➚➑➪✝➬➊➸✒➚➑➪✝➸ ➴✣❒❂➘ ➺Ị➱◆➴⑤Ĩ❿➵☛➶✝➵☛ư❜➴⑤➬➜➺Ị÷ Õ ψ(L) = {(0, 1) + k.(1, 2)|k 0} ự ỷỳỳự ỵỵỷỷỷ Y X ỳọỷỹọý òỡồềềề éỡồềềềỗốềềềờq ớểểềểé r ✶ ✷✙s➈Ú ✙✝✠✟ ✛✚ ✢✜ ✣✡ ✟ ✥✤ ✧✦ ✩★ ❋ ÿ✌✧❀✧✵ÿ ✻ ➛✈➦✄➦✮➛✄➵✁➛ q➡❘➞✈➳ ✯➤ ✓ã ✛✚ ✢✜ q (L) ỗ ó Þ➏➪✝➸➜➬✒➵➢➱✃➵➢➼➅➸✜➶✂➺Ị➸❱Ï➫➽✒➚➑➺Ị➸ G N2 Ú➫Ý❽➵➢➸➜➸✒➵✜Ø✝➬✒➚➑Ø✝➬➜➺➻Ù➢➸✒Ù➏➽✒➵✯Ĩ❿Ù➢➼➾Ù➢➬Ơ➴⑤❒Ị➺➻➽✒➵ ➵✁➛✇➜➆➨❘➾❖➜☞➙✡➡❘➫✌➭✓➡✯➭✁➛✄➡❘➙ ➭✁➻✯➥✈➞✈➳➝Ú✏➾❁➛ ➵✫➽➜➸⑧➪✝➼➾➵➏Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✱➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✱Ð➅➪✝➺✟➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒➵➏❒➻➵➏❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵ ➵✫➽➜➸❽❒❂➘ ➺Ị➱◆➴⑤Ĩ❿➵↔❐✫➚➑➱➹➱✦➪✝➸Ơ➴⑤➸➜➺Ị×❿➵☛➶✝➵ L Ú✂Ü✱➚➑➼➾❐❼Ï ✸q➼❹Ø✝❒Ị➪➾➽❱Ï✂❒í➴➹➶✝➵✫➽✒❐➢➬➜➺ỊØ✝➸➜➺➻➚➑➼✾❐❱➴⑤➼➾➚➑➼✝➺➻Ð➅➪➾➵✦➶✝➵ ψ(L) Q ➵✫➽➜➸✯➪✝➼á➽✒➚➑➪➾➽✠å➈➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵✱➽✒Ù➢➱➹➺ìå❂❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵ ➶➾➴⑤➼➾➽✗❒í➴✦Đ✩➚➑➬➜➱✃➵■✂ L Q ➵➢➸ ➶➾➴⑤➼➾➽ L ➛♥➠✏➜ ψ(L) Nm Q = Q1 ∪ Q2 ∪ ∪ Qn ➚❘à Qj = {x|x = αj + n1 βj1 + n2 βj2 + + nkj βjkj , ni ∈ N} Ø✖➵➢➪✝➸✠å☛①➢➸➜➬✒➵↔➸➜➬✒➚➑➪✝×❿Ù✫➵☛Ø❸➴⑤➬✜➪✝➼⑩➴⑤❒ỊĨ❿➚➑➬➜➺Ị➸ Õ ➱✃➵✦➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵✦➶✝➵ ✻✽➛❏✬✮✙✗✁☎✄✝✆❸✕✖✑✯✆✟✞✒✙✗✁ ➅❪❧☛❽ ☞☎✍ị⑩✜✕✖✑✜✛✣✢☎✍q✄ ☞☎✡€✎✒✍❏✬✔✬✮✍✔☞☎✍ G Ú ✖✕ ♦ ✑✜✕✖✞ ↔✢ ⑥↔✞✒✑ ✎✒✍q✄ ⑩✜✕✖✑➏✬✔✬✮✑✗✞➜✕✖✍q✄ à❏➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☎➶✝➵✫➽➏Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵✫➽✗➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤➪✂ë✾➬✒Ù✫❐➢➬➜➺Ị➸✒➽✗Ø✖➚➑➪✝➬➏➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒➵➢➬Ư➪✝➼✾❐ Õ ➵➢➱➹➺Ị➼ ✪✬✫✮✭ ✯ ✰✲✱✩✳✵✴ ✶ ✴✸✷✺✹✼✻✽✹✿✾✬✴✔✹✿✾✬❀✵✷❂❁❄❃✸✴ ✶ ✱❅✾✼✷❂❆✛✱✩❇ ✳✵❀✩✾✬✯ ✹✬❈❂✰❉✴❋❊✺❃✽✹✬✴✽✾✬✰❉✯ ❆❂✯ ●✠✹✬✴ Λ(β) Ú ψ(L) β ➵✫➽➜➸✗➼➾➚➑➸✒Ù ự ỷỳỳự ỵỵỷỷỷ T r1 T r2 ✻ ❃ T ri β ✍ ✸ ✍ ✍ ✍ Þ Ý F0 Þ ï F1 Fi úäû❂üäý▲✺➾Ú ✷ ê ✸q➼➾➽✒➵➢➱✦➷✝❒➻➵ Ú Λ(β) = {A, B, C, E, F } à❏➘ Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵✦➶✂➪✾❐ Õ ➵➢➱➹➺Ị➼ β ➽✒➵✱➼➾➚➑➸✒➵ ß➏➼➾➵③➞➟➻⑦➵❘➾▲➺✵➜✫➳➝➨❘➫➹➶✭➘ ➪✝➼✥❐ Õ ➵➢➱➹➺Ò➼ α ➪✝➼⑩➴⑤➪✝➸➜➬✒➵☛❐ Õ ➵➢➱➹➺Ò➼ I(β) Ú ➵✫➽➜➸❏❒❂➘ ➚➑Ø✖Ù➢➬Ơ➴⑤➸➜➺➻➚➑➼➊➶✝➚➑➼➅➸❽➚➑➼✥➵➢➼✝❒➻ỉ➢×❿➵✗➪✝➼➾➵✗Ø❸➴⑤➬➜➸➜➺➻➵ βB Ø✖➚➑➪✝➬❽➚➑➷✝➸✒➵➢➼✝➺Ị➬ Ï➾❐✫➚➑➱➹➱✃➵↔➺Ị➼➾➶✂➺➻Ð➅➪➾Ù✦➮☎❒í➴☎õ➾Ĩ❼➪✝➬✒➵⑨➾ ✺ Ú➾ ✺ Ú α đ➏➼❍➶✂➺Ị➸✦Ð➅➪➾➵ ➠✯➛■➞➟➻⑦➵❘➾✌➳✫➜❽➵➢➼ Ï➆➵➢➸✦➽✒➵➹➼➾➚➑➸✒➵●✂ Ü↔➴⑤➼➾➽☛❒➻➵✃❐❱➴➑➽✦➚❘à reduire α (α , βB ) α −→ (α , βB ); βB ➼➁➘ ➵✫➽➜➸✜Ø❸➴➑➽✗Ø✖➵➢➬➜➸➜➺Ị➼➾➵➢➼➅➸❱Ï❸➚➑➼áØ✖➵➢➪✝➸✗❒❂➘ ➺ỊĨ❼➼➾➚➑➬✒➵➢➬➏➵➢➸➏Ù✫❐➢➬➜➺Ị➬✒➵☛➽➜➺Ị➱➹Ø✝❒➻➵➢➱✃➵➢➼➅➸ đ➏➼✾➶✂➺Ị➸✗Ð➅➪➾➵ ❍ ä➅➺➁➸✒➚➑➪➾➽ α ➵➢➸ ■❍ ❏❍ ➽Ơ➴⑤➸➜➺➻➽✠Đ✩➚➑➼➅➸✗➪✝➼➾➵↔❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼ ♠➶✝➚➑➼✝➼➾Ù❼Ï ✸q➼⑩Ø❸➴⑤➬➜➸➜➺➻❐➢➪✝❒Ị➺➻ỉ➢➬✒➵➢➱✃➵➢➼➅➸❱Ï✭➽➜➺ α ➵➢➸ Ø❸➴⑤➬☎➪✝➼➾➵◆Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵➊➶✝➵✃Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽ ➳❂➞✈➞➟➻⑦➵❘➾▲➺✵➜✫➳➆➥✈➙❷➛❪➠✯➛✈➙✡➨❘➫→➙➟➹ ➛✈➫▲➠✯➛✈➦✮➥✈➙❷➛ ➽✒➵➢❒➻➚➑➼ Ú❸ä➅➺Ị➼➾➚➑➼➁Ï ❂❑ F ế ề ềỉềọềẽ ọềẽềị ò reduire α −→ α F F F Ú α R ềị ỉỉ ờẽ ỗố ế ➵➢➱➹➺Ị➼➾➽✱➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✫➽ F ➵✫➽➜➸☎➶✂➺Ị➸✞➞➟➻⑦➵❘➾▲➺✵➜✫➳➆➥✈➙❷➛✞➠✯➛✈➙✡➨❘➫❯➙➟➹ ➛✈➫▲➠✯➛✈➦✮➥✈➙❷➛ F Úqä➅➺Ị➼➾➚➑➼➁Ï α ➵✫➽➜➸ ➶✝➵✯❐ Õ ➵➢➱➹➺Ò➼➾➽⑧➵✫➽➜➸q➶✂➺Ò➸ä➞➟➻⑦➵❘➾▲➺✵➜✫➳➆➥✈➙❷➛❏➽❱➘ ➺Ò❒✝❐✫➚➑➼➅➸➜➺➻➵➢➼➅➸❽➴⑤➪✣➱✃➚➑➺Ò➼➾➽❜➪✝➼✃❐ Õ ➵➢➱➹➺Ò➼➹➬✒Ù✫➶✂➪➾❐➢➸➜➺Ò➷✝❒➻➵ ➵✫➽➜➸✗➶✂➺Ò➸③➳❂➞✈➞➟➻⑦➵❘➾▲➺✵➜✫➳➆➥✈➙❷➛➢Ú ✣✥ÿ✌✧✩✰▲✖ ❚✥➆ÿ ❶ ✟➆➚➑➪✝➸☛❐ Õ ➵➢➱➹➺Ị➼✵➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✃➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù➹Ø❸➴⑤➬✱➪✝➼➾➵✣Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✃➶✝➵☎Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽ R ➵✫➽➜➸↔➶✝➵ ❒➻➚➑➼✝Ĩ❼➪➾➵➢➪✝➬✃➷✖➚➑➬➜➼➾Ù✫➵❼Ú❾✸q➼❘❐✫➚➑➼➾➽✒Ù✫Ð➅➪➾➵➢➼➾❐✫➵❼Ïq➸✒➚➑➪✝➸◆➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵á➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✾➶✝➵á❐ Õ ➵➢➱➹➺Ị➼➾➽◆➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✫➽✃Ø❸➴⑤➬ ➪✝➼➾➵↔Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✦➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽➏➵✫➽➜➸✯õ➾➼✝➺❂Ú Ü✱➚➑➬✒Ù➢➼❸➴✫×❼➴⑤➼➅➸❱Ï➾➚➑➼á➽➜➪✝Ø✝Ø✖➚❼➽✒➵✱Ð➅➪➾➵Ừ✖➚➑➪✝➬✯➸✒➚➑➪✝➸✒➵✱Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵↔➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽ R = (ΣT , ΣN , V, P ) Ï➾➚➑➼ ✘✗ ❃ ❶❷❊ ✤✌✧✵ù ✴ û✫ú✯✖✙✰✂ú✦✪❚ù ỵỵỷỷỷ F B F B B B βB B úäû❂üäý▲✺➾Ú ✺ ê ß➏➼➾➵↔➬✒Ù✫➶✂➪➾❐➢➸➜➺➻➚➑➼✾➶✭➘ ➪✝➼✾❐ Õ ➵➢➱➹➺Ị➼⑩➵➢➼❹➪✝➼✾➴⑤➪✝➸➜➬✒➵☛➵➢➼❹➬✒➵➢➸➜➺Ị➬Ơ➴⑤➼➅➸➏➪✝➼➾➵↔➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼➁Ú ➴ ΣN = {B1 , , B|ΣN | } Ú ö✚➚➑➪✝➬✱➸✒➚➑➪✝➸↔➽✒➚➑➪➾➽✠å➈➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ ❒➻➵✫➽➏❐ Õ ➵➢➱➹➺Ị➼➾➽ ➬✒Ù✫Ù✫❐➢➬➜➺Ị➬✒➵■✂ α ΣN ➶✝➵ ΣN Ï✟➚➑➼▲❐✫➚➑➼➾➽➜➺➻➶✝ỉ➢➬✒➵☎❒➻➵✦Ĩ❼➬Ơ➴⑤Ø Õ ➵ T rN Ð➅➪✝➺✚➼➾➵☎❐✫➚➑➼➅➸➜➺➻➵➢➼➅➸☛Ð➅➪➾➵ Ð➅➪✝➺➆➽Ơ➴⑤➸➜➺➻➽✠Đ✩➚➑➼➅➸✗❒í➴➹❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼⑩Ð➅➪➁➘ ➺Ị❒➁Ø✝➬✒➵➢➼➾➶❹➸✒➚➑➪➾➽✗❒➻➵✫➽✜➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤➪✂ë⑩➶➾➴⑤➼➾➽ Λ(α) = ΣN à➁➵↔❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵↔➬✒➵✫❐✫➚➑➼✝➼➅➪✾Ø❸➴⑤➬ T rN ➵✫➽➜➸✜➼➾➚➑➸✒Ù LN Ú❸đ➏➼⑩➴➴✂ L= ưq×➫➺➻➶✝➵➢➱➹➱✃➵➢➼➅➸❱Ï✟➽➜➺✭❒❂➘ ➴★ë✂➺➻➚➑➱✃➵ Ï LN N N A N LN ìị L= LN ΣN ⊆ΣN ,A∈ΣN ✸q➼✾❐✫➚➑➼➾➽✒Ù✫Ð➅➪➾➵➢➼➾❐✫➵■✂ ψ(L) = ψ(LN ) ΣN ⊆ΣN ,A∈ΣN ΣN Ø✖➚➑➪✝➬ ✘✗ ❃ ❶❷❊ ✤✌✧✵ù ✴ û✫ú✯✖✙✰✂ú✦✪❚ù ✴ ỵỵỷỷỷ í N ừẽ ỏừ ọỉểễềềẽỉìề N N Ú v1 Bi Bi v2 úäû❂üäý▲✺➾Ú ❫ ê ß➏➼á➱✃➵➢➱✦➷✝➬✒➵ ➶✝➵↔❒❂➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ Ú β Bi R Bi ư✚➚➑➪✝➬✜❐ Õ ➴➑Ð➅➪➾➵Ư➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤❒ ➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✫➽✗Ø❸➴⑤➬ å å β β R ➮☎Ø❸➴⑤➬➜➸➜➺Ị➬➏➶✝➵ Bi Bi ➵✫➽➜➸✜➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵❼Ú ÝƯ➘ ➵✫➽➜➸✠åé➮★å➈➶✂➺Ị➬✒➵❼Ï✭➸✒➚➑➪✝➸ ➚❘à R Bi ➵➢➸➏Ð➅➪✝➺➁➽Ơ➴⑤➸➜➺➻➽✠Đ✩➚➑➼➅➸✗❒➻➵✫➽✗❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼➾➽➏➽➜➪✝➺Ị×❼➴⑤➼➅➸✒➵✫➽❪✂ Bi ➼➾➵↔❐✫➚➑➼➅➸➜➺➻➵➢➼➅➸✱Ð➅➪➁➘ ➪✝➼❹➽✒➵➢➪✝❒ Ï❿➼➾➚➑➪➾➽✯➶✝Ù➧õ➾➼✝➺➻➽✒➽➜➺➻➚➑➼➾➽❽➪✝➼➊➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵Ư➼➾➚➑➸✒Ù β Bi ∈ R Bi ➶✝➵✫➽✯❐ Õ ➵➢➱➹➺Ò➼➾➽ β Bi ❐✫➚➑➱➹➱✃➵↔➪✝➼❹➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ò➼❸➴⑤❒✚Ð➅➪✝➺➁➼➁➘ ➵✫➽➜➸✜Ø❸➴➑➽✗➵➢➼➾❐✫➚➑➬✒➵↔➬✒➵➢➱➹Ø✝❒í➴➑❐✫Ù✎➂ ➴◆❒í➴➊➽➜➪✝➺Ị➸✒➵✣❐✫➚➑➬➜➬✒➵✫➽➜Ø✖➚➑➼➾➶➾➴⑤➼➅➸✒➵ u ➶✝➵✫➽↔Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵✫➽☛➵➢➼⑩Đ✩➚➑➬➜➱✃➵ u= v1 ∈ Σ∗T , v2 ∈ Σ∗T đ➏➼❹➼➾➚➑➸✒➵ ❒➻➵↔❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵■✂ L Bi v1 Bi v2 LBi = {v1 v2 |∃β ∈ RBi , I(β) = v1 Bi v2 } ịƯ➚➑➪➾➽↔➶✝Ù➧õ➾➼✝➺➻➽✒➽✒➚➑➼➾➽✱➪✝➼✵➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ A Ï✝➶✝➵☛➽✒➚➑➬➜➸✒➵↔Ð➅➪➾➵■✂ Ts ➶✝➵➹❐ Õ ➵➢➱➹➺Ị➼➾➽ å å❏➸✒➚➑➪➾➽✗❒➻➵✫➽✜➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤➪✂ë✾➽✒➚➑➼➅➸✗Ø✝➬✒Ù✫➽✒➵➢➼➅➸✒➽➏➶➾➴⑤➼➾➽ α ➵✫➽➜➸✜➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✦➽✒➵➢❒➻➚➑➼ ưq➬✒➚➑Ø✝➬➜➺➻Ù➢➸✒Ù✦➶✭➘ ➪✝➼✾❐ Õ ➵➢➱➹➺Ị➼ Ts α Ú ➶➾➴⑤➼➾➽ Ts α ➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù✫➽↔Ø❸➴⑤➬ Λ(α) R ➮◆Ø❸➴⑤➬➜➸➜➺Ị➬✦➶✝➵☎❒❂➘ ➴★ë✂➺➻➚➑➱✃➵ ỉềỏềồềé ỉỉễềỉềềủ LA ớểểỉểễỉ ế ịìềỡồẽ ịƯ➚➑➪➾➽➏➴⑤❒Ị❒➻➚➑➼➾➽✗➱✃➚➑➼➅➸➜➬✒➵➢➬ƯÐ➅➪➾➵✿✂ L Bi Ts ➵➢➸ Ú LA ➽✒➚➑➼➅➸➏➶✝➵✫➽✜❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✜õ➾➼✝➺➻➽❱Ú ψ(LN ) = (LA LB1 LB2 LB| | ) N ỗ ự ỷỳỳự ỵỵỷỷỷ ì ũệệ é ỗ (LA LB1 LB2 LB| | ) (LN ) N ỉ ỗ (LN ) (LA LB1 LB2 LB| | ) N ờỡừớỉỉỗ ẽệì LA L N ẽ ỗ (LA ) ⊆ ψ(LN ) ✸q➼❳Ø✝❒Ò➪➾➽❱Ï✖➽✒➚➑➺➻➵➢➼➅➸ v, v ∈ LBi ➵➢➸ β ➪✝➼❳❐ Õ ➵➢➱➹➺Ò➼❄➶➾➴⑤➼➾➽ I(α) = u, u ∈ LN ẽ T rN () = N ẽ ồộồề ỗ R Bi B i ∈ Σ N ê➧Ï α ➪✝➼✵❐ Õ ➵➢➱➹➺Ò➼✵➶➾➴⑤➼➾➽ T rN Bi ∈ Λ(α) Ú α β v1 A Bi Bi u2 v2 Bi u3 úäû❂üäý▲✺➾Ú ❅ ê à➁➵☛❐ Õ ➵➢➱➹➺Ò➼ ➵➢➸✜➪✝➼➾➵↔Ø❸➴⑤➬➜➸➜➺➻➵ Ú α ∈ Ts β ∈ R Bi u1 v1 A Bi Bi u3 u2 v2 úäû❂üäý▲✺➾Ú ❆ ê à➁➵☛❐ Õ ➵➢➱➹➺Ò➼ ➚➑➷✝➸✒➵➢➼➅➪▲➮☎Ø❸➴⑤➬➜➸➜➺Ò➬➏➶✝➵ Ø❸➴⑤➬✗➺Ò➼➾➽✒➵➢➬➜➸➜➺➻➚➑➼✾➶✝➵ Ú α α β v = v1 Bi v2 ➵➢➸ I(β) = ➽✒➚➑➼➅➸☛❒➻➵✫➽✦Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵✫➽✦❐✫➚➑➬➜➬✒➵✫➽➜Ø✖➚➑➼➾➶➾➴⑤➼➅➸✒➵✫➽❱Ú✚ư❜➴⑤➬☛❒í➴á➶✝Ù➧õ➾➼✝➺Ị➸➜➺➻➚➑➼❈➶✝➵ u1 ịƯ➚➑➪➾➽➏➴✫×❿➚➑➼➾➽ ➵➢➸ u = u1 u2 u3 Ú ự ỷỳỳự ỵỵỷỷỷ ĩẽỉìề ế ➵➢➱➹➺Ị➼ ❐✫➚➑➱➹➱✃➵↔➺Ị➼➾➶✂➺➻Ð➅➪➾➵☛➶➾➴⑤➼➾➽✗❒í➴✦õ➾Ĩ❼➪✝➬✒➵⑨✺➾Ú ❆➫Ú đ➏➼⑩➴⑤Ø✝Ø✖➵➢❒Ị❒➻➵ Þ➏❒➻➚➑➬✒➽ Þ➏➺Ị➼➾➽➜➺ w ❒➻➵↔➱✃➚➑➸✗➬✒➵✫❐✫➚➑➼✝➼➅➪✾Ø❸➴⑤➬✜❒➻➵☛❐ Õ ➵➢➱➹➺Ị➼ ➚➑➷✝➸✒➵➢➼➅➪❄➮◆Ø❸➴⑤➬➜➸➜➺Ò➬↔➶✝➵ α Ï α w := I(α ) α ✻ Ø❸➴⑤➬✱➺Ò➼➾➽✒➵➢➬➜➸➜➺➻➚➑➼✵➶✝➵ β Ú w = u1 v1 u2 v2 u3 Λ(α ) = Λ(α) ∪ Λ(β) = ΣN ∪ Λ(β) = ΣN Þ➏❒➻➚➑➬✒➽ α ∈ T rN Ï✝❐❼➘ ➵✫➽➜➸✠åé➮★å➈➶✂➺Ò➬✒➵ Ü✱➚➑➼➾❐❼Ï Ú w ∈ LN ψ(uv) = ψ(u1 u2 u3 v1 v2 ) = ψ(u1 v1 u2 v2 u3 ) = ψ(w) ∈ ψ(LN ) Þ➏❒➻➚➑➬✒➽ ∀u ∈ LN , v ∈ LBi , ∀Bi ∈ ΣN Ï➾➚➑➼✾➴➧✂ (uv) (LN ) ĩ ỗ (LN LBi ) ⊆ ψ(LN ), ∀Bi ∈ ΣN ✸q➼✾❐✫➚➑➼➾➽✒Ù✫Ð➅➪➾➵➢➼➾❐✫➵❼Ï ψ(LN L∗B1 LB2 LB|N | ) (LN ) ịìỗ ờẽỗ ψ(LA L∗B1 L∗B2 L∗B|Σ | ) ⊆ ψ(LN ) N ềờỡừ ềềỗ ờọ ế ềỉ ẽ u u = I(α) â➈❒✭➼➁➘ ❰á➴➹Ð➅➪➾➵↔➶✝➵➢➪✂ë➊Ø✖➚❼➽✒➽➜➺Ò➷✝➺Ò❒Ò➺Ò➸✒Ù✫➽❱Ú Ú u ➪✝➼❍➱✃➚➑➸✣Ð➅➪➾➵➢❒➻❐✫➚➑➼➾Ð➅➪➾➵➊➶➾➴⑤➼➾➽ LN Ï✚➵➢➸ α ∈ T rN ❒➻➵ ✘✗ ❃ ❶❷❊ ✤✌✧✵ù ✴ û✫ú✯✖✙✰✂ú✦✪❚ù ✴ ỵỵỷỷỷ ọề ềềẽ Ts ù ç❂✺➾Ú ❅❿ê u ∈ LA ä➫➚➑➺Ò➸ α ➵✫➽➜➸✜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ò➷✝❒➻➵✥ç β ∈ Ts ê➧Ú Ü↔➴⑤➼➾➽❏❒➻➵✗➶✝➵➢➪✂ë✂➺➻ỉ➢➱✃➵✗❐❱➴➑➽❱Ï❼➺Ị❒❸➵➧ë✂➺➻➽➜➸✒➵✗➴⑤➪✃➱✃➚➑➺Ị➼➾➽⑧➪✝➼➾➵✜➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼✥➶✝➵✯➬✒➵➢➱➹Ø✝❒í➴➑❐✫➵➢➱✃➵➢➼➅➸✒➽✜➶➾➴⑤➼➾➽ Ð➅➪➁➘ ➚➑➼ α Ø✖➵➢➪✝➸Ư➽➜➪✝Ø✝Ø✝➬➜➺Ị➱✃➵➢➬❱Ú➃✸q×➫➺➻➶✝➵➢➱➹➱✃➵➢➼➅➸❱Ï✖➚➑➼❹Ø✖➵➢➪✝➸Ư❐ Õ ➚➑➺➻➽➜➺Ị➬Ư➸✒➚➑➪➑❮➜➚➑➪✝➬✒➽➏➪✝➼➾➵☛➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼▲Ð➅➪✝➺➁➼➾➵✦❐✫➚➑➼➅➸➜➺➻➵➢➼➅➸✱Ø❸➴➑➽ ➶✭➘ ➴⑤➪✝➸➜➬✒➵Ư➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼á➶✝➵✫➶➾➴⑤➼➾➽❱Ú✝đ➏➼á➽➜➪✝Ø✝Ø✖➚❼➽✒➵➏Ð➅➪➾➵Ư❐❼➘ ➵✫➽➜➸❽❒í➴☛➬✒Ù➢Ø✖Ù➢➸➜➺Ị➸➜➺➻➚➑➼á➶✂➪✥➼➾➚➑➼✂å❂➸✒➵➢➬➜➱➹➺Ị➼❸➴⑤❒ Ø✖➵➢➪✝➸✗➽✒➵✱➬✒Ù✫➶✂➪✝➺Ị➬✒➵✦➵➢➼ ✂ (α1 , β1 ) Bi Ú➫Ü✱➚➑➼➾❐❼Ï α reduire ∃α1 ∈ T rN , β1 ∈ RBi : α −→ (α1 , β1 ) ư✚➚➑➪✝➬ α1 Ï➅➺Ị❒✟❰◆➴☎➴⑤➪➾➽✒➽➜➺✖➶✝➵➢➪✂ë✥❐❱➴➑➽❽❐✫➚➑➱➹➱✃➵ ①➢➸➜➬✒➵↔➬✒Ù✫➶✂➪✝➺Ị➸➏➵➢➼❹➪✝➼➾➵✱Ø❸➴⑤➺Ị➬✒➵ ư❜➴⑤➬✒❐✫➵ƯÐ➅➪➾➵✗❒➻➵✗➱✃➚➑➸ β p ∈ R B ip Ï➾➴✫×❿➵✫❐ u (α2 , β2 ) Ú α Ú➾ä➫➚➑➺Ò➸ α1 ∈ TS Ï➅➚➑➪➊➽✒➚➑➺Ị➸ ➵✫➽➜➸❏õ➾➼✝➺❂Ï❿➺Ị❒✟➵➧ë✂➺➻➽➜➸✒➵✜➪✝➼➾➵➏➽➜➪✝➺Ị➸✒➵✜õ➾➼✝➺➻➵Ư➶✝➵✫➽❏Ø❸➴⑤➺Ị➬✒➵✫➽ B ip ∈ Σ N , ≤ p ≤ k − ➸✒➵➢❒➁Ð➅➪➾➵■✂ α1 ➵✫➽➜➸⑧➬✒Ù✫➶✂➪➾❐➢➸➜➺Ò➷✝❒➻➵↔➵➢➸❽Ø✖➵➢➪✝➸ (α1 , β1 ), , (αk , βk ) Ú➅Ü✱➚➑➼➅➸ reduire αp −→ (αp+1 , βp+1 ), ≤ p ≤ k − ➵➢➸ αk ∈ T S ư❜➴⑤➬➹➶✝Ù➧õ➾➼✝➺Ị➸➜➺➻➚➑➼❆➶✝➵ ❒í➴✃Đ✩➚➑➬➜➱✃➵ R B ip Ï➆❒➻➵✃➱✃➚➑➸ up = up,1 Bip up,2 ❒❂➘ Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵☛➶✂➪✾❐ Õ ➵➢➱➹➺Ị➼ ịƯ➚➑➪➾➽➏➴✫×❿➚➑➼➾➽❪✂ Ï Ï✭➴✫×❿➵✫❐ up ❐✫➚➑➬➜➬✒➵✫➽➜Ø✖➚➑➼➾➶➾➴⑤➼➅➸✃➴⑤➪❈❐ Õ ➵➢➱➹➺Ị➼ up,1 , up,2 ∈ Σ∗T βk v := I(βk ) Ú Ï✟Ø✖➚➑➪✝➬ Ï βBip up = I(βBip ) ≤ p ≤ k−1 Ú➁ñ➏➼❳➽✒➵☎➼➾➚➑➸✒➵ u = u1,1 u2,1 uk−1,1 v.uk−1,2 u1,2 ➵➢➸ ψ(u) = ψ(u1,1 u2,1 uk−1,1 v.uk−1,2 u1,2 ) = ψ(u1,1 u1,2 uk−1,1 uk−1,2 v) = ψ(u1,1 u1,2 ) + + ψ(uk−1,1 uk−1,2 ) + ψ(uk ) Ï✚➶➾➴⑤➼➾➽ v ỉ ự ỷỳỳự ỵỵỷỷỷ ❊✗õ Û▲➴⑤➺➻➽❱Ï✂➼➾➚➑➪➾➽Ư➴✫×❿➚➑➼➾➽Ư➴⑤➪➾➽✒➽➜➺❾✂ ψ(up,1 up,2 ) ∈ ψ(LBip ) ψ(uk ) ∈ ψ(LA ) Ü✱➚➑➼➾❐❼Ï✝Ø✖➚➑➪✝➬✜➸✒➚➑➪✝➸ u ∈ LN ➼➾➚➑➪➾➽➏➴✫×❿➚➑➼➾➽ ψ(u) ∈ ψ(LA L∗B1 L∗B2 L∗B|Σ | ) N ✸q➼✾❐✫➚➑➼➾➽✒Ù✫Ð➅➪➾➵➢➼➾❐✫➵ ✸q➼✾➶✝Ù➧õ➾➼✝➺Ị➸➜➺Ị×❿➵❼Ï ψ(LN ) ⊆ ψ(LA L∗B1 L∗B2 L∗B|Σ | ) N ψ(LN ) = ψ(LA L∗B1 L∗B2 L∗B|Σ | ) N Ü✱➚➑➼➾❐❼Ï ψ(LN ) ➵✫➽➜➸✣➽✒➵➢➱➹➺ìå❂❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ú❜ịƯ➚➑➪➾➽☎Ø✖➚➑➪✝×❿➚➑➼➾➽☎Ĩ❿Ù➢➼➾Ù➢➬Ơ➴⑤❒Ị➺➻➽✒➵➢➬✃➮❹➸✒➚➑➪➾➽☎❒➻➵✫➽ ➽✒➵➢➱➹➺ìå❂❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵✫➽❱Ú ψ(LN ) Ð➅➪✝➺✯➽✒➚➑➼➅➸ ịƯ➚➑➪➾➽➏➴✫×❿➚➑➼➾➽✗❒➻➵↔➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸❪✂ ψ(L) = (LN ) N N ,SN ỡồềềề ễửềữ ế ìớểễềệểễỉ ế ➵✫➽➏➵✫➽➜➸✗❐✫➚➑➱➹Ø✝❒➻ỉ➢➸✒➵❼Ú ▼▲ ❴❛❵❝❜❯❞❝❡✌❢❪❣✄❤ ◆ t✮✉♣r♠♥q♦♣❞❳❛❜t✮✉ Ý❽➵☎➱✃Ù➢➱✃➚➑➺Ị➬✒➵✣➶✝➵✦õ➾➼❳➶✭➘ Ù➢➸➜➪➾➶✝➵✫➽✱Ø✝➬✒Ù✫➽✒➵➢➼➅➸✒➵➹Ð➅➪➾➵➢❒➻Ð➅➪➾➵✫➽✱❐✫➚➑➼➅➸➜➬➜➺Ị➷✝➪✝➸➜➺➻➚➑➼➾➽✦➴⑤➪❳➶✝➚➑➱◆➴⑤➺Ị➼➾➵➹➶✝➵✦❒í➴◆➸ Õ Ù✫➚➑➬➜➺➻➵ ➶✝➵✫➽✣❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽➹Đ✩➚➑➬➜➱✃➵➢❒➻➽❱Ú✢✸q➼❘➪✝➸➜➺Ị❒Ị➺➻➽Ơ➴⑤➼➅➸➹❒➻➵✫➽➹Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽✃➶✝➵➊Ĩ❼➬Ơ➴⑤Ø ế ẽqìỏ ễéểéệỏớểểềểéỏớìểễỉ ế íễểéqỉềềễửềữ ế ỉổễỉỉễềềệệẹểéìớểễềểễỉ ế ➶✝➵✫➽✱➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸✒➽✱➷✝➺➻➵➢➼❳❐✫➚➑➼✝➼➅➪➾➽☛➽➜➪✝➬✱❒➻➵✫➽Ư❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✦➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽❱Ú✭à➁➵☎➬✒Ù✫➽➜➪✝❒Ị➸Ơ➴⑤➸☛➚➑➷✝➸✒➵➢➼➅➪❳➼➾➚➑➪➾➽↔➶✝➚➑➼✝➼➾➵✣➪✝➼ ➴⑤➪✝➸➜➬✒➵➹Ø✖➚➑➺Ị➼➅➸✦➶✝➵✣×➫➪➾➵➹➶✝➵✫➽↔❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽☎➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽❱Ï✭❒➻➵➢➪✝➬☛➽➜➸➜➬➜➪➾❐➢➸➜➪✝➬✒➵➹Ĩ❿Ù✫➚➑➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵◆➵➢➸☛Ù➢Ĩ➅➴⑤❒➻➵➢➱✃➵➢➼➅➸✦❒➻➵✫➽ Ø✖➵➢➬✒➽➜Ø✖➵✫❐➢➸➜➺Ị×❿➵✫➽✗➶✭➘ ➪✝➼➾➵↔➼➾➚➑➪✝×❿➵➢❒Ị❒➻➵☎➴⑤Ø✝Ø✝➬✒➚➫❐ Õ ➵☛Ø✖➚➑➪✝➬✜❒í➴✣➸ Õ Ù✫➚➑➬➜➺➻➵☛➶✝➵✱❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✗Đ✩➚➑➬➜➱✃➵➢❒Ị❒➻➵✫➽❱Ú ịƯ➚➑➪➾➽✜Ø✖➚➑➪✝➬➜➬✒➚➑➼➾➽➏➵➢➼➾➽➜➪✝➺Ị➸✒➵↔➪✝➸➜➺Ị❒Ị➺➻➽✒➵➢➬✜❒➻➵✫➽✗Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵✫➽➏➶✝➵↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽✗Ø✖➚➑➪✝➬✜➬✒Ù✫➽✒➚➑➪➾➶✂➬✒➵↔Ø❸➴⑤➬✗Ø✖➚➑➺Ị➼➅➸✜õ✝ë✝➵ ➶✝➵✫➽á➴⑤➪✝➸➜➬✒➵✫➽✥Ø✝➬✒➚➑➷✝❒➻ỉ➢➱✃➵✫➽➊Ð➅➪✝➺✱➽✒➚➑➼➅➸✥Ø✝❒Ị➪➾➽➊❐✫➚➑➱➹Ø✝❒Ị➺➻Ð➅➪➾Ù✫➽➊❐✫➚➑➱➹➱✃➵⑩❒➻➵✾Ø✝➬✒➚➑➷✝❒➻ỉ➢➱✃➵▲➶✝➵✾❒❂➘ ➴➑❐✫❐✫➵✫➽✒➽➜➺Ị➷✝➺Ị❒Ị➺Ị➸✒Ù▲➵➢➸ ❒➻➵◆Ø✝➬✒➚➑➷✝❒➻ỉ➢➱✃➵➊➶✝➵◆❒❂➘ ➴⑤➱✦➷✝➺ỊĨ❼➪▲➁✩➸✒Ù❹➽➜➪✝➬✦❒➻➵✫➽☎❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵✫➽✃➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵✫➽❱Ú★✸q➼❈Ø✝❒Ị➪➾➽❱Ï✚➚➑➼❍Ø✖➚➑➪✝➬➜➬Ơ➴❹➸➜➬Ơ➴⑤➺Ị➸✒➵➢➬✣Ĩ❿Ù✫➚⑤å ➱✃Ù➢➸➜➬➜➺➻Ð➅➪➾➵➢➱✃➵➢➼➅➸✦❒í➴✥➬✒Ù✫➽✒➚➑❒Ị➪✝➸➜➺➻➚➑➼❄➶✂➪ Ø✝➺Ị❒➻➵❼Ú µ å➈❐❱➴⑤❒➻❐➢➪✝❒qØ✖➚➑➪✝➬↔❒➻➵✫➽↔Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽☛➶✝➵✫➽↔➸➜➬Ơ➴⑤➼➾➽➜➺Ị➸➜➺➻➚➑➼➾➽☛➶✝➵✫➽✦➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽☎➮ ✷ ✶ ❖ ❛ ✆ ♥q❛❜t❵❤❵❪❍❫❁✐❦❥♣❛❜❝ ◗€ ◗❘ ❙✚ r sịẽ ềữẽịõểỡẹềẽ ồỡỡ q ẽóõíọ ã➏➵➢Ø✖➚➑➬➜➸Ưä➫➵➢➬➜➺➻➵✫➽❱Ï✗✝ ❈❉❈❖✶ Ú ❯❚ r ✝✦s☎➳➾Ú Û❍Ú➾Þ➏➪✝➸✒➵➢➷✖➵➢➬➜➸❱Ï ❚➤▲➻⑦➨❘➞✈➳➆➛✇➵✁➛♥➠③➙✡➡❘➫✌➭✓➡✯➭✁➛♥➠✿➛✏➜➯➵✁➛♥➠✇➡❘➾❖➜➆➨❘➦■➡❉➜☛➛♥➠➢Ï➾Û▲➴➑➽✒➽✒➚➑➼➁Ï ✶ ❇❉❇✙✺➾Ú r sĩíẽỵọỡ ẽ ế íỉọẽ ỉỉ ồtẽ ✶ ❇❉❇❉✝✂Ú ❲☞ ❨❳ r ✺❘s☎Ü✣Ú❸Ý✯➴⑤➪➾❐❱➴⑤❒❂Ï ✗➾✌➞❪➵✁➛♥➠✚➭❘➞⑦➡♥➢✗➤▲➛♥➠❪➳❂➫✯➼❾➫❁➳Û➠✚➞➟➻➝➭❘➾✌➙ ➳➆➛✈➞♥➠➢Ï ✱➴⑤➷✝➺Ị➸Ơ➴⑤➸➜➺➻➚➑➼⑩➮➹➶✂➺Ị➬➜➺ỊĨ❿➵➢➬➏➶✝➵✫➽✜➬✒➵✫❐ Õ ➵➢➬✒❐ Õ ➵✫➽❱Ï ✶ ❇❉❇❉t✂Ú ❩❳ ✟ r ❫✦s☎Ü✣Ú✯Ý✯➴⑤➪➾❐❱➴⑤❒❂Ï✯Ü✣Ú ✟↔Ú ➏➺➻➵➢➪➁Ï ❬✚ ✢✜ ➛◗➙❷➛✈➦✄➦✮➛Þ➵✁➛ q➡❘➞✈➳ ✯➤➄➲✯➳➝➡❀➙❷➛♥➠➴➭❘➞⑦➡❘➦✄➦■➡❘➳❂➞➟➛♥➠❹➵✁➛➴➭❘➞⑦➡♥➢✗➤▲➛♥➠➢Ï✯Þ✜➶✝➶✝➵➢➼✂å ➶✂➪✝➱✔Ý❽➚➑➼➅➸➜➬➜➺Ị➷✝➪✝➸➜➺➻➚➑➼➾➽✱➚⑤Đq➸ Õ ➵⑨✺❼➸ Õ õõíẹíỉọồ óõù ẽỉỉ tẽọớõẹòềìễềẽ r sũí ế ữẽỵọịỡẽõẹíẽ ỉỉ ẽ ❇❉❫❉❇✂Ú ✖❭ ✵❱ ✮❳ ❫❘ ✢✜ r ❆✯s☎ị☎Ú➾Ü✱➵➢➬✒➽ Õ ➚✯✠✜➺Ị➸ ❿Ï✖➳➾Ú ư✚Ú✟➳❿➚➑➪❸➴⑤➼✝➼❸➴⑤➪➾➶✭Ï❚â♠➛ ✎➞✈➳✫➜☛➛③➠✈å✙➠✏➜☛➛✈➦✇➠➢Ï ✱➴⑤➼➾➶✂➷✖➚➫➚➑÷á➚⑤Đ☞✟ Õ ➵✫➚➑➬✒➵➢➸➜➺➻❐❱➴⑤❒❏Ý❽➚➑➱➹Ø✝➪✝➸✒➵➢➬ ä➫❐➢➺➻➵➢➼➾❐✫➵❼Ï▲❿❏➚➑❒❏✍✱Ï✂Ø✝Ø➁Ú ✝✙✺✁✷★å⑤✷❉✝ ❈ Ï✟➵✫➶✂➺Ị➸✒➵✫➶á➷➅❰➊➳➾Ú ❿⑧➴⑤➼➁Ú❸à➁➵✫➵➢➪✁✠❽➵➢➼➁Ï➃✸q❒➻➽✒➵➢×➫➺➻➵➢➬❱Ï ✶ ❇❉❫❉❇✂Ú ✼❪ r t✦s➹ä✟Ú✭ðƯ➺Ị➼➾➽➜➷✝➪✝➬➜Ĩ➾Ï❱✸✗Ú➁ä➅Ø❸➴⑤➼✝➺➻➵➢➬❱Ï ②➨❘➾✌➫➃➵✁➛⑦➵ ②➙ ➭✓➨❘➙★➙ ➳ ❉➛✄➙✡➡❘➫✌➭❘➾▲➡✯➭✁➛♥➠➢Ï✕✟➁➬Ơ➴⑤➼➾➽❱Ú✖Þ➏➱✃➵➢➬❱Ú✟Û▲➴⑤➸ Õ Ú➁ä➫➚➫❐❼Ú ✶❉✶ ✷✂Ï Ø✝Ø➁Ú ✷❉✷❉✷★å⑤✷❉❅❉❫✂Ï ✶ ❇❉❅✙✺➾Ú ❴❳ ❴❳ ❴❳ ❨❵ ❯❛ r ❇✦s☎Û❍Ú ✱➴⑤➬➜➬➜➺➻➽✒➚➑➼➁Ï ♥➫✗➜✫➞⑦➨✯➵❘➾▲➺✵➜✫➳➝➨❘➫❹➜➆➨♠➶✵➨❘➞✈➦■➡❘➙✕➙✡➡❘➫✌➭❘➾▲➡✯➭✁➛✇➜❂➤▲➛⑦➨❘➞✈å❼Ï➾Þ✜➶✝➶✂➺➻➽✒➚➑➼áå ✵➵✫➽➜❒➻➵➢❰❿Ï ✶ ❇✓❆❘t✂Ú ❴❜ ❝❭ ❞✚ ✢✜ ❣❵ ❋❛ ❤❚ r ✶✯❈ s☎Û❍Ú Ư➚➑Ø✝÷➫➺Ị➼➾➽❱Ï✝Ü✣Ú ➏➚ ❱➵➢➼➁Ï q➡❘➞✈➳ ✯➤✎➹ ➠③➜❂➤▲➛⑦➨❘➞➟➛✈➦ ❢❡   ➳❂➫❹➺➟➨❘➦✄➦✄➾❖➜➆➡❉➜✫➳❂➲❘➛ ẽửqõ íẹểềíỉọỗốõíọ ờẽõửqẽỉỉ ẽ r s ệỉẹốẽòềềẽ ịồ ịỏồ ẽ ➙✡➡❘➫✌➭❘➾▲➡✯➭✁➛♥➠ r ✶ ✝✦s☎Ü✣Ú➑Û✾➪✝❒Ị❒➻➵➢➬❱Ï❼ư✚Ú➅ä➫❐ Õ ➪✝Ø✝Ø➁Ï ❚➤▲➛q➜❂➤▲➛⑦➨❘➞✈å✄➨ì➶②➛✈➫➃➵✙➠ ➢➃➾✁➠♥➤❖➵✓➨ ✎➫➧➡❘➾❖➜➆➨❘➦■➡❉➜➆➡ ✟➏Ý✜ä➧✷✓❆➫Ï✂Ø✝Ø➁Ú ồỡẽ t ẽ ỗỡẽ ✺✐ ✌❥ ❬ ✲ ❬ ❋❾✲ ✞➸ ✣ ✬ € r sóửềữ ế ẽỵọỗ ẽịệíỉ ế ềẽ ỗờỉỉ t ẽ ❩❦ ❧✚ ✢✜ ✛✚ r ✶ ✺❘s☎Ü✣Ú à❏Ú✝ưq➺Ị❒Ị❒Ị➺Ị➼✝Ĩ➾Ï ✎➨❘➦✄➦✄➾❖➜➆➡❉➜✫➳❂➲❘➛⑨➞➟➛➝➭❘➾✌➙✡➡❘➞✿➛⑦Ú✏➾▲➡❉➜✫➳➝➨❘➫▲➠✇➡❘➫➃➵ q➡❘➞✈➳ ẽ ế ọẽỗờ ồẽ r ✶ ❫✦s➹ÝÖÚ➾ã➏➵➢➪✝➸✒➵➢➼❸➴⑤➪➾➵➢➬❱Ï ✚➠➆➢❁➛⑦➺✵➜❂➠❪➦■➡❉➜❂➤▲➻✈➦■➡❉➜✫➳➝Ú✏➾❁➛♥➠✇➵✁➛♥➠③➞➟➻♥➠✯➛⑦➡❘➾❉➽◗➵✁➛ ♠➻✏➜✫➞✈➳èÏ➾Û▲➴➑➽✒➽✒➚➑➼➁Ï ✶ ❇❉t❉t✂Ú ♥♠ ❥ ✉♣❢❣❝ Ù➢➸➜➺➻Ð➅➪➾➵➢➸➜➸✒➵❼Ï✗❇ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☛➶✝➵↔➸➜➬Ơ➴➑❐✫➵✫➽❱Ï ✶✯❈ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵☛➽✒➵➢➱➹➺ìå❂❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ï➃✝ ✶ ➴⑤❒ỊĨ❿Ù➢➷✝➬➜➺➻Ð➅➪➾➵❼Ï➃t ➵➧ë✂➸➜➬✒Ù➢➱➹➺Ị➸✒Ù❼Ï✗❇ ➴⑤❒ỊØ Õ ➴⑤➷✖➵➢➸✒➽❱Ï▲✺ ➴⑤➬✒❐❼Ï✗❇ Đ❂➴➑❐➢➸✒➵➢➪✝➬❱Ï❁❫ ➴⑤➪✝➸✒➚➑➱◆➴⑤➸✒➵✫➽Ư➮✣Ø✝➺Ị❒➻➵❼Ï✗t Đ✩➚➑➬➜➱✃➵✱➼➾➚➑➬➜➱◆➴⑤❒➻➵❼Ï❱❆ ➴★ë✂➺➻➚➑➱✃➵❼Ï➃❆ Đ✩➚➑➬➜➸✒➵➢➱✃➵➢➼➅➸➏❐✫➚➑➼✝➼➾➵➧ë✝➵❼Ï ✶✯❈ Đ✩➚➑➬➜➸✒➵➢➱✃➵➢➼➅➸✗➼➾➚➑➬➜➱◆➴⑤❒Ị➺➻➽Ơ➴⑤➼➅➸❱Ï✕❆ ➷✖➚➑➪➾❐➢❒➻➵❼Ï✗❇ Ĩ❿Ù➢➼➾Ù➢➬Ơ➴⑤➸✒➵➢➪✝➬✒➽✗❒Ị➺Ị➷✝➬✒➵✫➽❱Ï✗❫ ❐ Õ ➵➢➱➹➺Ị➼➁Ï➃❇ Ĩ❼➬Ơ➴⑤➱➹➱◆➴⑤➺Ị➬✒➵❼Ï❱❆ ❐➢➺Ị➬✒❐➢➪✝➺Ị➸❱Ï✗❇ Ĩ❼➬Ơ➴⑤Ø Õ ➵❼Ï✗❇ ❐✫➚⑤å➈➶✝Ù➢➸✒➵➢➬➜➱➹➺Ị➼✝➺➻➽➜➸✒➵❼Ï ✶✯❈ Ĩ❼➬Ơ➴⑤Ø Õ ➵↔➺Ị➼➅×❿➵➢➬✒➽✒➵❼Ï ✶✯❈ ❐✫➚➑➱➹Ø✖➚❼➽Ơ➴⑤➼➅➸✒➵✦❐✫➚➑➼✝➼➾➵➧ë✝➵❼Ï ✶✯❈ Õ ➚➑➬✒➽✠å➈❐✫➚➑➼➅➸✒➵➧ë✂➸✒➵❼Ï➃t ❐✫➚➑➼➾❐❱➴⑤➸✒Ù➢➼❸➴⑤➸➜➺➻➚➑➼➁Ï❱❫ ❐✫➚➑➼➅➸✒➵➧ë✂➸➜➪➾➵➢❒❂Ï➃t ➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵❼Ï➃✝✙✺ ❐✫➚➑➼➅➸✒➵➧ë✂➸➜➪➾➵➢❒Ị❒➻➵❼Ï➃t ➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✦➽✒➵➢❒➻➚➑➼á❒❂➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ ♦❍ F Ï❁✝✙✺ ➶✝Ù➢➬➜➺Ị×❼➴⑤➷✝❒➻➵❼Ï➃❆ ➺Ị➬➜➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✦➽✒➵➢❒➻➚➑➼á❒í➴➹❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼ ❽Ï✗✝✙✺ ➶✝Ù➢➬➜➺Ị×❼➴⑤➸➜➺➻➚➑➼➁Ï❱❆ ➺➻➽✒➚➑➱✃➚➑➬➜Ø Õ ➵✫➽❱Ï ✶❉✶ ➶✝Ù➢➸✒➵➢➬➜➱➹➺Ò➼✝➺➻➽➜➸✒➵❼Ï ✶✯❈ ➺➻➽✒➚➑➱✃➚➑➬➜Ø Õ ➺➻➽➜➱✃➵❼Ï ✶❉✶ ➶✝➵➢Ĩ❼➬✒Ù❼Ï ✶✯❈ ❒í➴⑤➼✝Ĩ➅➴⑤Ĩ❿➵❼Ï▲✺➾Ï✗t✂Ï ✶✯❈ ➶✝➵➢Ĩ❼➬✒Ù☛➵➢➼➅➸➜➬Ơ➴⑤➼➅➸❱Ï ✶✯❈ à➁➵➢➱➹➱✃➵☛➶✝➵☛ư❜➴⑤➬➜➺Ị÷ Õ Ï✗✝❉✷ ➶✝➵➢Ĩ❼➬✒Ù☛➽✒➚➑➬➜➸Ơ➴⑤➼➅➸❱Ï ✶✯❈ à➁➵➢➱➹➱✃➵☛➶✝➵✫➽✜Ø❸➴⑤➺Ị➬✒➵✫➽✗➺Ị➸✒Ù➢➬Ơ➴⑤➼➅➸✒➵✫➽❱Ï ✶ ❅ ➶✝➵✫➽➜➸➜➺Ị➼❸➴⑤➸➜➺➻➚➑➼➁Ï➃❇ ❒➻➵➢➸➜➸➜➬✒➵❼Ï▲✺ ➵➢➼✝Ĩ❿➵➢➼➾➶✂➬✒Ù❼Ï➃t ❒Ị➺Ị➷✝➬✒➵❼Ï✗❫ ➵➢➼✝➬Ơ➴➑❐➢➺Ị➼➾Ù❼Ï ✶✯❈ ❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵❼Ï✗✝ ✶ ✷✙✺ ♣✗ rq ✲✵✼ ➧❸ ❊➃❳ ❒Ị➺Ị➼➾Ù❱➴⑤➺Ị➬✒➵✦➮✣Ĩ➅➴⑤➪➾❐ Õ ➵❼Ï➃❇ ➸➜➬Ơ➴➑❐✫➵➧å➈Ù✫Ð➅➪✝➺Ị×❼➴⑤❒➻➵➢➼➅➸✒➵✫➽❱Ï ✶✯❈ ➸➜➬Ơ➴➑❐✫➵✫➽❱Ï ✶✯❈ ➱✃➚➑➼➾➚❘➁❂➶✝➵❼Ï➃❫ ➸➈❰➫Ø✖➵ ❈ Ï❁t ➱✃➚➑➬➜Ø Õ ➺➻➽➜➱✃➵✦➶✝➵✱Ĩ❼➬Ơ➴⑤Ø Õ ➵✫➽❱Ï ✶❉✶ ➸➈❰➫Ø✖➵ ✶ Ï❁t ➱✃➚➑➸✗×➫➺➻➶✝➵❼Ï❖✺ ➸➈❰➫Ø✖➵③✝✂Ï❁t ➱✃➚➑➸✒➽❱Ï▲✺ ➸➈❰➫Ø✖➵③✷✂Ï❁❇ ➼➾➚➑➼❹➬✒➵✫➽➜➸➜➬✒➵➢➺Ị➼➅➸✒➵❼Ï➃t ➚➑➬➜➺ỊĨ❼➺Ị➼➾➵❼Ï✗❇ Ø✝➬✒Ù➧õ✝ë✝➵❼Ï✗❫ ➬✒Ù✫Ù✫❐➢➬➜➺Ị➸➜➪✝➬✒➵❼Ï➃❅ ➬✒Ù✫❐➢➪✝➬✒➽➜➺Ị×❿➵➢➱✃➵➢➼➅➸✱Ù➢➼➅➪✝➱✃Ù➢➬Ơ➴⑤➷✝❒➻➵✫➽❱Ï➃t ➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵❼Ï➃✝✙✺ ➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✦➽✒➵➢❒➻➚➑➼á❒❂➘ ➵➢➼➾➽✒➵➢➱✦➷✝❒➻➵ ■❍ F Ï✗✝✙✺ ➬✒Ù✫➶✂➪➾❐➢➸➜➺Ị➷✝❒➻➵✦➽✒➵➢❒➻➚➑➼á❒í➴➹❐✫➚➑➼➾➶✂➺Ị➸➜➺➻➚➑➼ ❽Ï❁✝✙✺ ➬✒Ù✫➶✂➪➾❐➢➸➜➺➻➚➑➼➁Ï➃✝✙✺ ➬✒Ù➢Ĩ❼➪✝❒Ị➺➻ỉ➢➬✒➵❼Ï➃❇ ➬✒Ù➢Ĩ❼➪✝❒Ị➺➻➵➢➬❱Ï➃❇ ➬Ơ➴➑❐➢➺Ị➼➾➵❼Ï➃❆➫Ï ✶✯❈ ➬Ơ➴⑤➸➜➺➻➚➑➼✝➼➾➵➢❒❂Ï➃❇ ➬✒➵✫➽➜➸➜➬➜➺➻❐➢➸➜➺➻➚➑➼➁Ï➃❇ ➽✒Ù✫Ð➅➪➾➵➢➼➾❐✫➵☛➶✝➵↔➶✝Ù➢➬➜➺Ị×❼➴⑤➸➜➺➻➚➑➼➁Ï❱❆ ➽✒➵✱➬✒Ù✫➶✂➪✝➺Ị➸❱Ï✗✝✙✺ ➽✒➵➢➼➾➽➜➺Ị➷✝❒➻➵☛➴⑤➪✾❐✫➚➑➼➅➸✒➵➧ë✂➸✒➵❼Ï➃t ➽✒➚➑➱➹➱✃➵➢➸✒➽❱Ï✗❇ ➽✒➚➑➱➹➱✃➵➢➸✒➽✜Đè➬✒➚➑➼➅➸➜➺➻ỉ➢➬✒➵✫➽❱Ï ✶ ❆ ➽✒➚➑➪✝➬✒❐✫➵❼Ï✗❇ ➽✒➚➑➪➾➽✠å❂Ĩ❼➬Ơ➴⑤Ø Õ ➵❼Ï✗❇ ➽➜➪❖➪➹ë✝➵❼Ï❁❫