Index Compression Using Byte-Aligned ANS Coding and Two-Dimensional Contexts

*OEFY$PNQSFTTJPO6TJOH#ZUF"MJHOFE"/4 $PEJOHBOE5XP%JNFOTJPOBM$POUFYU 84%.ಡΈձ $IJF)BZBTIJEB

Θͨ͠ͷ͠ΐ͏͔͍ $IJF)BZBTIJEB !DIJF ΫοΫύουɹػցֶशνʔϜ $POUSJCVUFUP"QBDIF4QBSL )BEPPQ FUD
ൃചͷ8&# %#13&44ͷ 1ZUIPOͱՊֶٕज़ܭࢉͷষ ॻ͍ͨɻ

"#453"$5 •  #MPDLCBTFEJOWFSUFEJOEFYDPNQSFTTJPOͷ࣮ݧΛߦͬͨɻ •  "TZNNFUSJD/VNFSBM4ZTUFNT "/4 ΤϯτϩϐʔίʔσΟϯ άʹରͯ͠ҎԼͷ֦ுΛߦ͏͜ͱʹΑΔվળ͕ಘΒΕͨɻ –  ͭͷू໿ύϥϝʔλʹΑΔ࣍ݩͷ৚݅ίϯςΩετʹΑͬͯɺγ
ϯϘϧͷΧςΰϥΠζΛߦ͏ɻ –  #ZUFGSJFOEMZͳϚοϐϯάΛ࢖ͬͯγϯϘϧΛ"/4ͷDPEFXPSE CVDLFUʹΘ͚Δ –  ίϯςΩετϚʔδͷϓϩηεʹΑΓɺෳ਺ͷEJTUSJCVUJPOΛͭͱ Έͳ͞ΕΔɻ •  ͜ͷख๏ʹΑΓɺJOUFSQʹΑΔΠϯσοΫεͷѹॖͷੑೳج ४఺Λ্ճͬͨɻ •  ࣮ݧ͸(#ͷHPWίʔύεͱ৽͍͠χϡʔεهࣄΛ࢖͍ɺ ΫΤϦධՁ͸ผͷCMPDLCBTFEͷख๏ͱൺֱͨ͠ɻ

*/530%6$5*0/ •  *OWFSUFE సஔ ΠϯσοΫε͸ςΩετσʔλʹର͢Δ ߴ଎ͳΫΤϦ࣮ߦͷॏཁͳߏ଄Ͱ͋Δɻ term Posting list J1IPOF
Ϗοάσʔλ Χό ϝϩϯ posting ͦΕͧΕͷυΩϡϝϯτ*%ʹରͯ͠୯ޠͷग़ݱස౓΍ϙδ γϣϯͷ৘ใ΋࣋ͭɻ ίϯύΫτͳQPTUJOHMJTUTʹ͸ɺCZUFBMJHOFEDPEFT XPSE BMJHOFEDPEFT CJOBSZQBDLFEΞϓϩʔν͕͋Δɻ

*/530%6$5*0/ •  ϋϑϚϯූ߸ԽͷΑ͏ͳΤϯτϩϐʔϕʔεͷख๏΋ఏҊ͞Ε͍ͯ ͕ͨɺҎલ͸͋·ΓސΈΒΕΔ͜ͱ͕ͳ͔ͬͨɻ೥લʹ+FSFL %VEB͕"/4ϝΧχζϜΛ։ൃͨ͜͠ͱʹΑΓɺΤϯτϩϐʔίʔ σΟϯά͕࠶ͼ஫໨͞ΕΔΑ͏ʹͳͬͨɻ •  7#ZUF 4JNQMF 1BDLFEͷख๏Λ༻͍ͯɺͦΕͧΕѹॖޮ཰͕վળ͞
Εͨɻ •  1BDLFE "/4ΞϓϩʔνͷఏҊ –  ݻఆ௕ϒϩοΫͷγϯϘϧ͕ηϨΫλʹΑͬͯಛఆ͞Εͨ֬཰෼෍ͱؔ࿈ ͯ͠ූ߸Խ͞ΕΔɻ –  1BDLFE "/4Ξϓϩʔνͷ঺հʹ͓͍ͯ͸ɺηϨΫλ͸ϒϩοΫͷ࠷্Ґ ͕ར༻͞ΕΔɻ –  QBDLFEGSBNFPGSFGFSFODF 1'03 ϝΧχζϜͷΑ͏ͳར఺͕͋Δɻ –  ΤϯτϩϐʔίʔσΟϯάͷϝϦοτ •  ΤϯτϩϐʔίʔσΟϯάͷॊೈੑʹΑΓɺࣅ௨ͬͨූ߸ͷ֬཰ٴͼූ ߸௕ͷ໘Ͱѹॖޮ཰্͕͕ͬͨɻ –  ϒϩοΫͷू໿ʹ͓͍ͯ࣍ݩͷηϨΫλ͕ར༻Ͱ͖ͨɻ •  γϯϘϧͷࣝผࢠ͔Β"/4ͷ஋΁ͱϚοϐϯάΛม͑ΔলϝϞϦͰ CZUFGSJFOEMZͳग़ྗ •  σίʔυͷࡍͷϝϞϦ࢖༻ྔΛ࡟ݮ͢ΔͨΊͷ$POUFYU.FSHJOH

#"$,(306/%ɿ*OEFY$PNQSFTTJPO ˙$PNQSFTTJPO"QQSPBDI •  طଘͷํࣜ –  ఻౷తͳख๏ɹ&MJBTDPEFT –  7#ZUF΍ͦͷมܗ –  ϫʔυϕʔεͷγϯϓϧͳΞϓϩʔν
–  *OUFSQNFDIBOJTN •  εέʔϧͨ͠ͱ͖ʹྑ͍ѹॖޮ཰͕ಘΒΕ͕ͨɺEFDPEF͕ &MJBTΑΓ஗͔ͬͨɻ

ิ଍ɿ&MJBT(BNNB https://en.wikipedia.org/wiki/Elias_gamma_coding

ิ଍ɿ7#ZUF 1 0 0 0 0 0 1 0 value
End marker 1000000110000010 整数自体を符号化するのでなく、逐次差分を符号化する方法

#"$,(306/%ɿQBDLFEDPEFT ˙1BDLFE$PEFT •  ݻఆ௕ͷQPTUJOHTʹର͢ΔQBDLFEDPEFT •  ൺֱత࠷ۙͷٕज़ •  ΩʔΞΠσΞ͸ɺϩʔΧϧͳҰ؏ੑΛར༻͢Δํ๏Ͱ͋ Δɻ • 
ݻఆ௕ʢେ఍ʣͷϒϩοΫ͝ͱͷ஋ΛͭͷϢχο τͱͯ͠ॲཧ͢Δɻ •  ྫ͑͹ɺ ͔ΒηϨΫλΛબͿ͜ͱͰɺ͋Δ஋Λ ͱ͍ͬͨॻ͖ํͰදͤΔɻ

#"$,(306/%ɿ1BUDIFE'SBNFPG3FGFSFODF 2 1 31 1 0 … 2 10 01
01 01 00 … 10 b=5 b’=2 1exception position3 •  ϒϩοΫຖʹͦͷϒϩοΫ಺ͷ਺ͷ΄ͱΜͲΛද͢͜ͱ͕Ͱ͖ΔϏοτ਺Λ ܾΊͯ Τϯίʔυ͢Δɻ •  খ͍͞Ϗοτ਺ͰදͤΔͨΊσʔλαΠζ͕খ͘͞ͳΔɻ •  1'03ͷมܗͰ͋Δ0QU1'03Ͱ͸ɺ࠷΋શମͷύοέʔδ͕͜Μͺ͘ͱʹͳ ΔΑ͏ʹηϨΫλΛબͿΑ͏ʹͳ͍ͬͯΔɻ b b’ metadata

#"$,(306/%ɿ7BSJBCMF-FOHUI#SPDLT •  Մม௕ͷϒϩοΫʹύʔςΟγϣχϯάͨ͠৔߹ͷख๏ Λ0UUBWJBOPFUBM͕ఏҊ͍ͯ͠Δɻ •  ಉҰͷσʔλ͕ग़ݱͨ͠ͱ͖ʹେ͖ͳΠϯϓοτϢχο τΛ࣋ͭηϨΫλετϨʔδΛঈ٫͢ΔΑ͏ʹγʔΫ͢ Δɻ஋͕ہॴతʹόʔετ͢Δ৔߹ʹ༗ޮͳํ๏Ͱ͋Δɻ

#"$,(306/%ɿ"TZNNFUSJD/VNFSBM 4ZTUFNTʢ"/4ʣ •  +BSFL%VEBʹΑͬͯ։ൃ͞Εͨ৽͍͠Τϯτϩϐʔූ߸ Խํࣜ •  ϋϑϚϯූ߸Խ΍ࢉज़ූ߸ͱಉ͡໾ׂΛՌͨ͢ɻ •  ग़ݱස౓ͷߴ͍γϯϘϧʹϏοτ਺ͷখ͍͞ූ߸ɺग़ݱ ස౓ͷ௿͍γϯϘϧʹϏοτ਺ͷେ͖͍ූ߸ΛׂΓ౰ͯ
Δɻ

"/4Λ༻͍ͨΠϯσοΫεѹॖͷྫ •  γϯϘϧ1 2 3͸ͦΕͧΕग़ݱ֬཰ɺɺͱ͢Δ •  ϋϑϚϯූ߸ԽͰ͸ɺ1͕̍Ϗοτɺ2ͱ3͕̎ϏοτͱͳΔɻ •  "/4ූ߸ԽͰ͸ɺ.ݸͷཁૉͷ͕1ɺ͕2ɺ͕3ʹϥϕϦϯά͞Εɺ ͦͷΞϧϑΝϕοτ্ͷه߸ͷγʔέϯε͸ɺରԠ͢ΔϑϨʔϜͷঢ়ଶ஋ͱ͠
ͯදݱ͞ΕΔɻ •  ଞͷϑϨʔϜΛ࡞Δ৔߹͸ɺଞͷॱྻ΋͘͠͸.ΑΓେ͖͍஋Λ࢖༻͢Δɻ •  ϑϨʔϜͷූ߸Խ͸ɺભҠؔ਺5 ɾ ɾ Λ༻͍ͯߦ͏ɻ5্ͷΧϥϜ͸ɺεςʔ τม਺ͰΠϯσοΫεԽ͞ΕΔɻ •  શମΛූ߸Խ͢Δ৔߹͸ɺεςʔτม਺͕େ͖͘ͳΔɻ •  σίʔυ͢Δͱ͖͸ɺɹɹɹ͕࢖ΘΕΔɻ

"/4Λ༻͍ͨΠϯσοΫεѹॖͷྫʢଓ͖ʣ •  TFRVFODF2222222222͸ݸͷεςʔτΛ ࣋ͪɺϏοτͰද͞ΕΔɻϋϑϚϯූ߸Խͩͱ ϏοτͰ͋Δɻ •  ରͯ͠ɺTRVFODF3333333333͸εςʔτ͕ ݸͱͳΓɺϏοτʹͳΔɻ •  ͜ͷख๏͸ɺ4LFXͷ͋Δσʔλʹ༗ޮͰ͋Δɻ
39364 118096 ….

"/4$PNQBSFE •  ϋϑϚϯූ߸ٴͼ"SJUINFUJDDPEJOHͱͷൺֱ –  "/4͸ཧ૝తͳූ߸Խ௕͕"SJUINFUSJDDPEJOHͱۙ͘ͳΔɻ –  ߴ͍ग़ݱස౓ͷγϯϘϧΛൃੜ͢ΔͨΊʹɺϏοτͷίʔυ͢ Βൃੜ͠ͳ͍͍ͯ͘৔߹͕͋ΔɻʢϋϑϚϯූ߸ͩͱৗʹϏο τҎ্͕ඞཁɻʣ – 
"SJUINFUSJDDPEJOHΑΓ΋͸΍͘ɺߴ౓ʹઃܭ͞ΕͨϋϑϚϯූ ߸ͷ࣮૷ʹ͍ۙεϧʔϓοτϨʔτΛग़͢͜ͱ͕Ͱ͖Δɻ –  "/4͸"SJUINFUJDDPEJOHͱҟͳΓ੩తϝΧχζϜͰ͋Γɺҟͳ ΔίϯςΩετͷ΋ͱͰγϯϘϧΛੜ੒͢Δ͜ͱ͕Ͱ͖ͳ͍ɻ ͨͩ͜͠ͷ͜ͱ͸ΠϯσοΫεѹॖʹ͸Өڹ͠ͳ͍ɻ

"/4GPS*OEFY$PNQSFTTJPO •  Ҏલͷݚڀ –  "/4Λ̏ͭͷҟͳΔΠϯσοΫεѹॖํࣜͱ૊Έ߹Θͤͨɻ –  ಛʹ7#ZUFͱ૊Έ߹ΘͤΔΞϓϩʔνΛQPTUJOHMJTUͷѹॖʹ࢖༻ ͨ͠ɻ –  σίʔυͷεϧʔϓοτ͸গ͠௿Լ͢Δ͚ͩͰɺετϨʔδΛ
͔ͳΓઅ໿Ͱ͖Δ͜ͱΛ֬ೝͨ͠ɻ •  ࠓճͷख๏ɿʮ1BDLFE "/4ʯϝΧχζϜ –  ʮͭͷύϥϝʔλʯΛ࢖͏ –  গͳ͍ϝϞϦ࢖༻ྔͷίϯύΫτͳ࣮૷ –  ίϯςΩετϚʔδ •  ͜ΕΒͷख๏ͷ༗༻ੑΛ࣮ূ͢ΔͨΊʹɺͭͷେ͖ͳ ςΩετίϨΫγϣϯΛ࢖༻ͯ͠ɺѹॖͷ༗ޮੑͱΫΤ Ϧͷεϧʔϓοτʹؔ͢Δৄࡉͳ࣮ݧ݁ՌΛఏڙ͢Δɻ

1BDLFE "/4 •  ඪ४తͳ1BDLFEBSSBOHFNFOUͰ͸ɺίϯςΩετΛಛఆ ͢ΔηϨΫλ͕֤ϒϩοΫͷූ߸Խͷௐ੔ʹར༻͞ΕΔɻ •  ූ߸Խεςοϓ͕όΠφϦίʔυΛ࢖༻͢Δ৔߹ɺηϨ Ϋλ͸ɺϒϩοΫ಺ͷ࠷େ஋Λݟग़͠ɺόΠφϦͷେ͖ ͞Λܾఆ͢Δɻ • 
࣍ʹɹɹɹɹͱͳΔΑ͏ͳୈͷ஋ɹΛٻΊΔɻैདྷͷ 1BDLFEߏ੒Ͱ͸ɺM൪໨ͷίϯςΩετΛ࢖༻ͯ͠ɹɹɹɹɹ ஋ΛؚΉϖΠϩʔυ͕ੜ੒͞ΕΔɻ

*.1307&%1"$,&%$0.13&44*0/ 1BDLFE "/4 •  1BDLFE "/4ϝΧχζϜͰ͸ɺ͜ΕΒͷ͞·͟·ͳཁૉ͕ີ ઀ʹ݁ͼ͔ͭͳ͍ɻ •  ηϨΫλ͸ϒϩοΫ಺ͷ࠷େ஋ͱ͠ɺ"/4ϑϨʔϜϓʔϧ Λࣝผ͢Δɻ
•  ֤ϑϨʔϜʹ͸ɺ૊ͷϙεςΟϯάΛॲཧ͢Δ࠷ॳͷύεத ʹ౷ܭΛ஝ੵ͠ɺ֬཰෼෍Λর߹͢ΔͨΊʹߏங͞Εͨҟ ͳΔγϯϘϧ֬཰ηοτΛؚΉɻ •  γϯϘϧͷස౓͸ਐ਺ͷόέοτʹ஝ੵ͞ΕɺͦͷΑ͏ͳ֤ όέοτ಺ͷ͢΂ͯͷγϯϘϧʢͨͱ͑͹ʣʹͳΔɻ •  ྫ͑͹ɺʜ ʜͱʜ͸౳֬཰Ͱ͋ΔͱԾఆ ͞ΕΔɻ •  ΋͕͠γʔέϯεɹͷ൪໨ͷγϯϘϧ͕ϒϩοΫͷηο τͱͯ͠ූ߸Խ͞Ε͍ͯΔͳΒ͹ɺ͸ͱಉ͡ϒϩοΫͷ γϯϘϧʹΘͨΔ࠷େਐ਺͔Βܭࢉ͞ΕͨηϨΫλ஋Ͱ͋Δɻ

5XP%JNFOUJPOBM$POUFYUT •  ίϯςΩετΛ֦ு͢Δ͜ͱͰɺηϨΫλΛ֨ೲ͢Δί ετ͸૿Ճ͢Δ͕ɺਖ਼֬ʹλʔήοτͷ֬཰෼෍Λ࢖༻ ͢Δ͜ͱ͕Ͱ͖Δ •  ίϯςΩετͷ௥Ճํ๏ͱͯ͠͸ɺҎԼ͕ڍ͛ΒΕΔ –  ̎ͷྦྷ৐ʹΑΓηϨΫλϕΫτϧΛऔಘ͢Δ – 
όέοτ͕খ͘͞ͳΔΑ͏ʹର਺ͷఈΛมߋ͢Δ •  ্ͨͩ͠ه͸྆ํڞϒϩοΫ಺ͷ࠷େ஋ʹΑܾͬͯ·ͬ ͯ͠·͏ͷͰɺΤϯτϩϐʔίʔσΟϯάͷར఺Λ׆͔ ͤͳ͍

5XP%JNFOUJPOBM$POUFYUT •  ࣍ݩͷηϨΫλΛར༻͍ͨ͠ɻ –  ୈҰ࣍ݩ͕ϒϩοΫͷ࠷େ஋ɺୈೋ࣍ݩ͕ϒϩοΫͷ࠷খ஋ͱ ͢Δɻ •  ͜ͷ্ݶ஋ΑΓେ͖͍஋ɺԼݶ஋ΑΓখ͍͞஋͸ྫ֎ͱͯ͠ ѻ͏͜ͱ͕Ͱ͖Δɻ – 
ϒϩοΫͷதԝ஋Λར༻͢Δ͜ͱ΋Ͱ͖Δɻ

5XP%JNFOUJPOBM$POUFYUT •  ࣍ݩ͔Βೋ࣍ݩͷίϯςΩετʹ੾Γସ͑ͨ৔߹ͷ༷ࢠɻ

3FEVDJOHUIF'SBNFTJ[F •  1BDLFE "/4Ͱ͸ɺσίʔυʹ࢖༻͞ΕΔςʔϒϧͷ ҡ࣋ίετ͕͔͔Δͱ͍͏σϝϦοτ͕͋Δɻ •  "/4ΛγϯϘϧͷਐ਺ͷൣғͰ࢖༻͠ɺ"/4ετϦʔ ϜͱิॿϏοτετϦʔϜΛฒྻʹॲཧ͢Δ͜ͱͰ஋Λ ࠶ߏ੒͢Δͱ͍͏खஈ͕͋Δɻ • 
͜ͷ৔߹௥ՃͷΞϥΠϝϯτʹΑΔίετ͕͔͔Δ ͜ͷͨΊɺ1'03΍0QU1'03Ͱར༻͞ΕΔྫ֎Λఆٛ͠ ͯγϯϘϧ஋ͱ"/4λʔήοτͷؒͷϚοϐϯάΛఆٛ ͢Δɻ •  ͜ΕʹΑΓѹॖͷ༗ޮੑΛߴΊΔ͜ͱ͕Ͱ͖Δɻ

1BDLFE "/4ͷσίʔυ

$POUFYU.FSHJOH •  ίϯςΩετΛ௥Ճ͢ΔͱɺηϨΫλ͕௥ՃϏοτΛඞ ཁͱ͢ΔͨΊɺίϯςΩετ͕ଟ͗͢Δͱޮ཰͕ѱ͘ͳ ΔՄೳੑ͕͋ΔɻίϯςΩετ਺͕ͷྦྷ৐Ͱ͋Δ͜ͱ Λอূ͢Δ΂͖ɻ •  ίϯςΩετͷϖΞΛϚʔδ͢Δ͜ͱͰɺ୯Ұͷίϯς Ωετʹஔ͖׵͑ΔҊɻ γϯϘϧT͕ίϯςΩετB্ͰOB
T ճൃੜ͢Δͱ͢Δͱɺ τʔλϧͷPDDVSSFODF͸ ΤϯτϩϐʔίʔσΟϯά͸ՄೳͰɺͦͷίϯςΩετ ͷτʔλϧίετ͸

&YQFSJNFOUT &YQFSJNFOUBM$POUFYU •  ࣍ݩͷηϨΫλΛར༻ͨ͠ࡍͷOFXTHBQͷ֬཰෼෍ͷ ਤ

γϯϘϧग़ݱස౓ʹجͮ͘ѹॖ༗ޮੑ

.FBTVSFE*NQSPWFNFOU

࣮ߦ࣌ؒɺϝϞϦ࢖༻ྔɺΫΤϦεϧʔϓοτ •  *OUFSQΑΓ΋ΫΤϦϨεϙϯε͕ૣ͘ɺѹॖ཰͸࠷΋ྑ ͍ͱ͍͏݁Ռ͕ಘΒΕͨɻ

$0/$-64*0/4"/%'6563&803, ˙$PODMVTJPOT •  1BDLFE "/4ϝΧχζϜʹΑΓɺͭͷҟͳΔख๏Λվળͨ͠ɻ –  ࣍ݩίϯςΩετ –  ࠷্ҐόΠτϚοϐϯά – 
ίϯςΩετϚʔδϯά •  ೥લͷ*OUFSQͷϕϯνϚʔΫʹউͬͨɻ •  1BDLFE "/4ͷ࣮૷͸0QU1'03΍&'PQUʹൺ΂ͯΫΤϦεϐʔ υʹ͓͍ͯ͸ྼ͍ͬͯΔ͕ɺ"/4ʹ͸·ͩվળͷ༨஍͕͋Δɻ •  ͢Ͱʹ΄ͱΜͲͷQPTUJOHT͕খ͍͞αΠζʹූ߸ԽͰ͖Δ͜ͱΛ֬ ೝͨ͠ɻ ˙'VUVSFXPSL •  ෳ਺ͷঢ়ଶΛฒߦͯ͠෮߸͢ΔͨΊʹ֦ு͞Εͨ෮߸Խςʔϒϧ͓ Αͼ4*.%ػߏΛ࢖༻͢Δͱɺ෮߸Խ଎౓ΛഒҎ্ʹ૿Ճͤ͞ΔՄ ೳੑ͕͋Δɻ •  Մม௕ϒϩοΫͷ࢖༻ •  ΫΤϦͷ౷ܭ৘ใΛར༻ͯ͠ҟͳΔѹॖϝΧχζϜΛมߋ͢Δ

Index Compression Using Byte-Aligned ANS Coding and Two-Dimensional Contexts

Index Compression Using Byte-Aligned ANS Coding and Two-Dimensional Contexts

chie8842

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*OEFY$PNQSFTTJPO6TJOH#ZUF"MJHOFE"/4 $PEJOHBOE5XP%JNFOTJPOBM$POUFYU 84%.ಡΈձ $IJF)BZBTIJEB

Θͨ͠ͷ͠ΐ͏͔͍ $IJF)BZBTIJEB !DIJF ΫοΫύουɹػցֶशνʔϜ $POUSJCVUFUP"QBDIF4QBSL )BEPPQ FUD

"#453"$5 •  #MPDLCBTFEJOWFSUFEJOEFYDPNQSFTTJPOͷ࣮ݧΛߦͬͨɻ •  "TZNNFUSJD/VNFSBM4ZTUFNT "/4 ΤϯτϩϐʔίʔσΟϯ άʹରͯ͠ҎԼͷ֦ுΛߦ͏͜ͱʹΑΔվળ͕ಘΒΕͨɻ –  ͭͷू໿ύϥϝʔλʹΑΔ࣍ݩͷ৚݅ίϯςΩετʹΑͬͯɺγ

/530%6$50/ •  *OWFSUFE సஔ ΠϯσοΫε͸ςΩετσʔλʹର͢Δ ߴ଎ͳΫΤϦ࣮ߦͷॏཁͳߏ଄Ͱ͋Δɻ term Posting list J1IPOF

#"$,(306/%ɿ*OEFY$PNQSFTTJPO ˙$PNQSFTTJPO"QQSPBDI •  طଘͷํࣜ –  ఻౷తͳख๏ɹ&MJBTDPEFT –  7#ZUF΍ͦͷมܗ –  ϫʔυϕʔεͷγϯϓϧͳΞϓϩʔν

ิ଍ɿ&MJBT(BNNB https://en.wikipedia.org/wiki/Elias_gamma_coding

ิ଍ɿ7#ZUF 1 0 0 0 0 0 1 0 value

#"$,(306/%ɿQBDLFEDPEFT ˙1BDLFE$PEFT •  ݻఆ௕ͷQPTUJOHTʹର͢ΔQBDLFEDPEFT •  ൺֱత࠷ۙͷٕज़ •  ΩʔΞΠσΞ͸ɺϩʔΧϧͳҰ؏ੑΛར༻͢Δํ๏Ͱ͋ Δɻ •

#"$,(306/%ɿ1BUDIFE'SBNFPG3FGFSFODF 2 1 31 1 0 … 2 10 01

#"$,(306/%ɿ"TZNNFUSJD/VNFSBM 4ZTUFNTʢ"/4ʣ •  +BSFL%VEBʹΑͬͯ։ൃ͞Εͨ৽͍͠Τϯτϩϐʔූ߸ Խํࣜ •  ϋϑϚϯූ߸Խ΍ࢉज़ූ߸ͱಉ͡໾ׂΛՌͨ͢ɻ •  ग़ݱස౓ͷߴ͍γϯϘϧʹϏοτ਺ͷখ͍͞ූ߸ɺग़ݱ ස౓ͷ௿͍γϯϘϧʹϏοτ਺ͷେ͖͍ූ߸ΛׂΓ౰ͯ

"/4Λ༻͍ͨΠϯσοΫεѹॖͷྫ •  γϯϘϧ1 2 3͸ͦΕͧΕग़ݱ֬཰ɺɺͱ͢Δ •  ϋϑϚϯූ߸ԽͰ͸ɺ1͕̍Ϗοτɺ2ͱ3͕̎ϏοτͱͳΔɻ •  "/4ූ߸ԽͰ͸ɺ.ݸͷཁૉͷ͕1ɺ͕2ɺ͕3ʹϥϕϦϯά͞Εɺ ͦͷΞϧϑΝϕοτ্ͷه߸ͷγʔέϯε͸ɺରԠ͢ΔϑϨʔϜͷঢ়ଶ஋ͱ͠

"/4Λ༻͍ͨΠϯσοΫεѹॖͷྫʢଓ͖ʣ •  TFRVFODF2222222222͸ݸͷεςʔτΛ ࣋ͪɺϏοτͰද͞ΕΔɻϋϑϚϯූ߸Խͩͱ ϏοτͰ͋Δɻ •  ରͯ͠ɺTRVFODF3333333333͸εςʔτ͕ ݸͱͳΓɺϏοτʹͳΔɻ •  ͜ͷख๏͸ɺ4LFXͷ͋Δσʔλʹ༗ޮͰ͋Δɻ

"/4$PNQBSFE •  ϋϑϚϯූ߸ٴͼ"SJUINFUJDDPEJOHͱͷൺֱ –  "/4͸ཧ૝తͳූ߸Խ௕͕"SJUINFUSJDDPEJOHͱۙ͘ͳΔɻ –  ߴ͍ग़ݱස౓ͷγϯϘϧΛൃੜ͢ΔͨΊʹɺϏοτͷίʔυ͢ Βൃੜ͠ͳ͍͍ͯ͘৔߹͕͋ΔɻʢϋϑϚϯූ߸ͩͱৗʹϏο τҎ্͕ඞཁɻʣ –

"/4GPS*OEFY$PNQSFTTJPO •  Ҏલͷݚڀ –  "/4Λ̏ͭͷҟͳΔΠϯσοΫεѹॖํࣜͱ૊Έ߹Θͤͨɻ –  ಛʹ7#ZUFͱ૊Έ߹ΘͤΔΞϓϩʔνΛQPTUJOHMJTUͷѹॖʹ࢖༻ ͨ͠ɻ –  σίʔυͷεϧʔϓοτ͸গ͠௿Լ͢Δ͚ͩͰɺετϨʔδΛ

1BDLFE "/4 •  ඪ४తͳ1BDLFEBSSBOHFNFOUͰ͸ɺίϯςΩετΛಛఆ ͢ΔηϨΫλ͕֤ϒϩοΫͷූ߸Խͷௐ੔ʹར༻͞ΕΔɻ •  ූ߸Խεςοϓ͕όΠφϦίʔυΛ࢖༻͢Δ৔߹ɺηϨ Ϋλ͸ɺϒϩοΫ಺ͷ࠷େ஋Λݟग़͠ɺόΠφϦͷେ͖ ͞Λܾఆ͢Δɻ •

.1307&%1"$,&%$0.13&440/ 1BDLFE "/4 •  1BDLFE "/4ϝΧχζϜͰ͸ɺ͜ΕΒͷ͞·͟·ͳཁૉ͕ີ ઀ʹ݁ͼ͔ͭͳ͍ɻ •  ηϨΫλ͸ϒϩοΫ಺ͷ࠷େ஋ͱ͠ɺ"/4ϑϨʔϜϓʔϧ Λࣝผ͢Δɻ

5XP%JNFOUJPOBM$POUFYUT •  ίϯςΩετΛ֦ு͢Δ͜ͱͰɺηϨΫλΛ֨ೲ͢Δί ετ͸૿Ճ͢Δ͕ɺਖ਼֬ʹλʔήοτͷ֬཰෼෍Λ࢖༻ ͢Δ͜ͱ͕Ͱ͖Δ •  ίϯςΩετͷ௥Ճํ๏ͱͯ͠͸ɺҎԼ͕ڍ͛ΒΕΔ –  ̎ͷྦྷ৐ʹΑΓηϨΫλϕΫτϧΛऔಘ͢Δ –

5XP%JNFOUJPOBM$POUFYUT •  ࣍ݩͷηϨΫλΛར༻͍ͨ͠ɻ –  ୈҰ࣍ݩ͕ϒϩοΫͷ࠷େ஋ɺୈೋ࣍ݩ͕ϒϩοΫͷ࠷খ஋ͱ ͢Δɻ •  ͜ͷ্ݶ஋ΑΓେ͖͍஋ɺԼݶ஋ΑΓখ͍͞஋͸ྫ֎ͱͯ͠ ѻ͏͜ͱ͕Ͱ͖Δɻ –

5XP%JNFOUJPOBM$POUFYUT •  ࣍ݩ͔Βೋ࣍ݩͷίϯςΩετʹ੾Γସ͑ͨ৔߹ͷ༷ࢠɻ

3FEVDJOHUIF'SBNFTJ[F •  1BDLFE "/4Ͱ͸ɺσίʔυʹ࢖༻͞ΕΔςʔϒϧͷ ҡ࣋ίετ͕͔͔Δͱ͍͏σϝϦοτ͕͋Δɻ •  "/4ΛγϯϘϧͷਐ਺ͷൣғͰ࢖༻͠ɺ"/4ετϦʔ ϜͱิॿϏοτετϦʔϜΛฒྻʹॲཧ͢Δ͜ͱͰ஋Λ ࠶ߏ੒͢Δͱ͍͏खஈ͕͋Δɻ •

1BDLFE "/4ͷσίʔυ

&YQFSJNFOUT &YQFSJNFOUBM$POUFYU •  ࣍ݩͷηϨΫλΛར༻ͨ͠ࡍͷOFXTHBQͷ֬཰෼෍ͷ ਤ

γϯϘϧग़ݱස౓ʹجͮ͘ѹॖ༗ޮੑ

.FBTVSFE*NQSPWFNFOU

࣮ߦ࣌ؒɺϝϞϦ࢖༻ྔɺΫΤϦεϧʔϓοτ •  *OUFSQΑΓ΋ΫΤϦϨεϙϯε͕ૣ͘ɺѹॖ཰͸࠷΋ྑ ͍ͱ͍͏݁Ռ͕ಘΒΕͨɻ

$0/$-64*0/4"/%'6563&803, ˙$PODMVTJPOT •  1BDLFE "/4ϝΧχζϜʹΑΓɺͭͷҟͳΔख๏Λվળͨ͠ɻ –  ࣍ݩίϯςΩετ –  ࠷্ҐόΠτϚοϐϯά –