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勉強会 #3
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titech.crypto
May 27, 2018
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勉強会 #3
titech.crypto
May 27, 2018
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Transcript
LT: νϡʔϦϯάશ OHKAWA TAKEHIKO
"MBO.BUIJFTPO5VSJOH (Wikipedia ΞϥϯɾνϡʔϦϯά) •1912 - 1954 •ΠΪϦεͷֶऀɺཧֶऀɺ҉߸ղಡऀɺίϯϐϡʔ λՊֶऀ •ίϯϐϡʔλՊֶ͓ΑͼਓೳͷͱݴΘΕΔ ɹ-
νϡʔϦϯάϚγϯ ɹ- ΤχάϚͷ҉߸ղಡ ɹ- ACE (ίϯϐϡʔλ) ɹ- νϡʔϦϯά ɹ- νϡʔϦϯάɾςετ
1 :8 8AD E c • x iw n i
d Slnarz n iHc X]V R [TbTrw x s r w xy KX X TSXP # • n j • i iw j • v6XbR X] aR X b3 Hc X]V =]R [TbT]Taa w jU n i xb P]aPRbX ] j s j n p
ɹSolidity(ϓϩάϥϛϯάݴޠ)νϡʔϦϯάશ(≒ສೳ νϡʔϦϯάϚγϯ)Ͱ͋ΔΑ͏ʹ࡞ΒΕͨͷͰɺ͍͔ͳΔؔ (ΞϧΰϦζϜ)࣮ՄೳͰɺࣗ༝͕ඇৗʹߴ͍ɻ͔͠͠ɺͦ ͷΘΓʹࣄલʹఀࢭ͢Δ͔Ͳ͏͔༧ଌෆՄೳͳͷͰɺGas ͱGaslimitΛಋೖ͢Δ͜ͱʹΑͬͯɺແݶϧʔϓʹؕͬͨΓɺཞ ༻͞Εͳ͍Α͏ʹͨ͠ɻ
νϡʔϦϯάϚγϯ ສೳνϡʔϦϯάϚγϯ ఀࢭੑ Ωʔϫʔυ
νϡʔϦϯάϚγϯ ≒ ίϯϐϡʔλϓϩάϥϜɾΞϧΰϦζϜ M = {Q, , ⌃, } 2੍ޚ෦ʹهԱͰ͖Δঢ়ଶͷू߹
ЎભҠؔ Єग़ೖྗه߸ͷू߹ ϵςʔϓه߸ͷू߹ ςʔϓ # # # # qi ςʔϓϔου ੍ޚ෦
⌃ = {0, 1} = {0, 1, B}
# # # # qi inc(x) = x + 1 ঢ়ଶભҠਤ : (Q {qfin }) ⇥ 7 ! Q ⇥ ⇥ {L, R, N} Q = {q0, qfin, q1, q2, ...} ঢ়ଶભҠؔ
= {0, 1, B} Q = {q0, qfin, q1, q2,
...} νϡʔϦϯάϚγϯ2ਐίʔυԽͰ͖Δ ঢ়ଶO ه߸N ۭനه߸#ͷΛׂΓ͚ͭΔ : (Q {qfin }) ⇥ 3 3 - 3 ɾ ɾ ɾ ೖྗ͕ࣙॻࣜॱংʹฒΜͰ͍ΔͱԾఆͯ͠ɺ Ўͷ͚ͩΛϒϩοΫɾίʔυͰهड़ "4$**ίʔυ
ɹܭࢉՄೳੑཧͷͰɺνϡʔϦϯάػցMʹೖྗxΛೖΕͨΒ༗ݶ࣌ؒͰఀࢭ͢Δ ͔ɺͱ͍͏ɻΞϥϯɾνϡʔϦϯά1936ɺఀࢭੑΛղ͘νϡʔϦϯάػց ͕ଘࡏ͠ͳ͍ࣄΛର֯ઢ๏Ͱࣔͨ͠ɻ͢ͳΘͪͦͷΑ͏ͳνϡʔϦϯάػցͷଘࡏΛ Ծఆ͢Δͱɺ͕ࣗఀࢭ͢Δͱఆͨ͠ͳΒແݶϧʔϓΛߦ͍ɺఀࢭ͠ͳ͍ͱఆ͠ ͨͳΒఀࢭ͢ΔΑ͏ͳผͷνϡʔϦϯάػց͕ߏͰ͖Δͱ͍͏ໃ६͕ಋ͔ΕΔɻ (Wikipedia) ఀࢭੑ
ఀࢭੑͷূ໌ ఆٛ1. νϡʔϦϯάϚγϯͷܭࢉ ఆٛ2. νϡʔϦϯάϚγϯͷܭࢉՄೳੑ ఆཧ1. ສೳνϡʔϦϯάϚγϯͷଘࡏఆཧ ఆཧ2. ܭࢉෆՄೳͳؔͷଘࡏఆཧ ఆཧ3.
ܭࢉෆՄೳͳؔ halt?(p, x) = ( 1 (p ͕͋Δ M ͷίʔυͰɺ͔͠ 0 (ͦͷଞͷͱ͖)
ఆٛ1: νϡʔϦϯάϚγϯͷܭࢉ ɹೖྗx(BBxBB)ʹର͢ΔMͷܭࢉ͕ɺਖ਼ৗऴྃঢ়گ(BByBB)ʹ౸ୡͨ͠߹ɺܭࢉ ͕ఀࢭͨ͠ͱ͍͍ɺͦͷ࣌ͷग़ྗyΛɺೖྗxʹର͢ΔMͷग़ྗͱ͍͏ɻͳ͓ɺೖྗx ʹର͢Δ͢Δܭࢉ͕ਖ਼ৗऴྃঢ়گʹୡ͠ͳ͍߹ʹɺMͷग़ྗະఆٛͱΈͳ ͢ɻ inc(x) = ( n
+ 1 ͷೋਐදه (x ͕ɺ͋Δ n 2 N ͷೋਐදهͷͱ͖) ະఆٛ (ͦͷଞͷͱ͖)
νϟʔνͷఏএ ɹνϡʔϦϯάػցͰهड़Ͱ͖ΔҎ্ͷܭࢉೳྗΛ࣋ͭܭࢉݪཧଘࡏ͠ͳ͍.͕ͨͬ͠ ͯɼνϡʔϦϯάػցܭࢉՄೳੑΛɼܭࢉՄೳੑͷج४ͱͯ͠͏ͷ͕ଥͰ͋Δ. ৭ʑͳํ๏ͰܭࢉՄೳੑΛఆٛ ࠶ؼతఆٛFUD ͯ݁͠ہɺνϡʔϦϯάܭࢉՄೳੑ ͱಉʹͳΔ ఆٛ2: νϡʔϦϯάϚγϯܭࢉՄೳੑ ɹؔ
f ʹର͠ɼͦΕΛܭࢉ͢Δ νϡʔϦϯάϚγϯ͕ଘࡏ͢Δͱ͖ɼf Λνϡʔ ϦϯάϚγϯܭࢉՄೳͱ͍͏.
.VOJW . . . .O ҙͷؔʹ͍ͭͯܭࢉՄೳ γϛϡϨʔτͰ͖Δ ສೳνϡʔϦϯάϚγϯ
ఆཧ1. ສೳνϡʔϦϯάϚγϯͷଘࡏఆཧ comp(p, x) = ( M(x) (p ͕͋ΔνϡʔϦϯάϚγϯ M
ͷίʔυͷͱ͖) 0 (p ͕νϡʔϦϯάϚγϯͷίʔυʹͳͬͯͳ͍ͱ͖) (ূ໌ུ֓) p ͱ x ͕༩͑ΒΕͨͱ͖ͷɼMuniv ͷܭࢉͷུ֓Λࣔ͢ɻ (1) p ͕νϡʔϦϯάػցͷ2ਐίʔυʹͳ͍ͬͯΔ͔Λௐɼ ͠ p ͕ਖ਼͍͠ίʔυͰͳ͚Εɼଈ࠲ʹ 0 Λग़ྗͯ͠ऴྃ (2) p ͕͋ΔνϡʔϦϯάػցMͷίʔυͩͬͨ߹ʹɼ M ͷ x ʹର͢Δ࣮ߦΛγϛϡϨʔτ͠ɼਖ਼ৗऴྃͨ͠߹ʹ ಉ͡ग़ྗΛग़ͯ͠ऴྃ͢Δ. * ҙͷνϡʔϦϯάϚγϯ͕2ਐͰදͤΔ͜ͱ͕ॏཁ
.VOJW Q Y Q͕ೋਐίʔυ͔ʁ :FT /P ਖ਼ৗऴྃ͢Δ͔ :FT .
Y /P ෦ؔ comp(p, x)
. Q Y Q͕ೋਐίʔυ͔ʁ :FT /P ਖ਼ৗऴྃ͢Δ͔ :FT .
Y /P શҬؔ t comp(p, x)
ఆཧ2. ܭࢉෆՄೳͳؔͷଘࡏఆཧ ͜͜Ͱɺɹɹɹɹɹɹ͕ܭࢉՄೳͰɺɹɹΛܭ ࢉ͢ΔνϡʔϦϯάϚγϯ͕ଘࡏͨ͠ͱͯ͠ɺ ͜ΕΛͱ͢Δɻ͢Δͱશͯͷɹʹରͯ͠ ɹɹɹɹɹɹɹɹɹɹͰ͋ΔɻҰํͰɺ͜ͷߦ ͷର֯ઢ͕ަΘΔॴͰɹɹͷఆٛΑΓɺ ɹɹɹɹɹɻΑͬͯɹɹɹɹɹɹɹɹɹɹɹ Ͱ͋Γɺໃ६͢Δɻ t
comp(p, x) = ( M(x) (p ͕͋Δ M ͷίʔυͰɺ͔͠ M(x) ͕ਖ਼ৗऴྃ͢Δͱ͖.) 0 (ͦͷଞͷͱ͖.) ূ໌ུ֓ νϡʔϦϯάϚγϯͷ̎ਐίʔυΛɹͱ͠ɺЄͷ ݩͷదͳೖྗΛɹͱ͢Δɻ ͜ͷΑ͏ʹͯ͠ɺؔΛӈͷΑ͏ʹఆٛ͢ Δɻ d(wi) wk t comp(p, x) d(wi) pk d(wi) = t comp(pk, wi) d(wi) d(wk) = z 6= y pi wi d(wk) 6= t comp(pk, wk)
ఆཧ3. ܭࢉෆՄೳͳؔ halt?(p, x) = ( 1 (p ͕͋Δ M
ͷίʔυͰɺ͔͠ M(x) ͕ਖ਼ৗऴྃ͢Δͱ͖) 0 (ͦͷଞͷͱ͖) f(p, x) = ( comp(p, x) (halt?(p, x) = 1) 0 (halt?(p, x) = 0) halt?(p, x) = ( 1 (p ͕͋Δ M ͷίʔυͰɺ͔͠ M(x) ͕ਖ਼ 0 (ͦͷଞͷͱ͖) ূ໌ུ֓ ɹɹɹɹɹ͕ܭࢉՄೳͩͱ͢ΔͱɺҎԼͷΑ͏ͳؔG͕ߏՄೳͰ͋Δɻ͔͠͠ɺ͜Εɺɹɹɹɹɹɹ γϡϛϨʔτՄೳͰ͋Δ͜ͱʹଞͳΒͳ͍ͷͰɺໃ६͢Δɻ halt?(p, x) = ( 1 (p ͕͋Δ M ͷίʔυͰɺ͔͠ M(x) ͕ਖ਼ৗऴྃ͢Δͱ͖) 0 (ͦͷଞͷͱ͖) t comp(p, x) લఏ ɹɹɹɹɹҙͷνϡʔϦϯάϚγϯʹରͯ͠ܭࢉՄೳ ఆཧ ɹɹɹɹɹɹܭࢉෆՄೳ ఆཧ ɹɹɹ comp(p, x) t comp(p, x)
ɹSolidity(ϓϩάϥϛϯάݴޠ)νϡʔϦϯάશ(≒ສೳ νϡʔϦϯάϚγϯ)Ͱ͋ΔΑ͏ʹ࡞ΒΕͨͷͰɺ͍͔ͳΔؔ (ΞϧΰϦζϜ)࣮ՄೳͰɺࣗ༝͕ඇৗʹߴ͍ɻ͔͠͠ɺͦ ͷΘΓʹࣄલʹఀࢭ͢Δ͔Ͳ͏͔༧ଌෆՄೳͳͷͰɺGas ͱGaslimitΛಋೖ͢Δ͜ͱʹΑͬͯɺແݶϧʔϓʹؕͬͨΓɺཞ ༻͞Εͳ͍Α͏ʹͨ͠ɻ
Reference • Wikipedia ΞϥϯɾνϡʔϦϯά • ܭࢉೖ ล ࣏ ถ࡚ थ
• ϓϩάϥϛϯάݴޠ 2012 # 1 — ݴޠͷجຊཁૉͱ֓೦ ٱ ༃