Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
二人単貧民の定理を Coqで証明する試み
Search
Katsuki Ohto
August 31, 2020
Research
0
210
二人単貧民の定理を Coqで証明する試み
単貧民をテーマに、Coqでゲームを扱うことについて検討する。
Katsuki Ohto
August 31, 2020
Tweet
Share
More Decks by Katsuki Ohto
See All by Katsuki Ohto
負け側の残り枚数を最大化する二人単貧民の解析
yuricat
0
98
二人単貧民の消費枚数に関する勝利条件の一般化とその解析
yuricat
0
200
ハンカチ落としの戦略最適化
yuricat
0
1.1k
Other Decks in Research
See All in Research
とあるSREの博士「過程」 / A Certain SRE’s Ph.D. Journey
yuukit
11
4.4k
単施設でできる臨床研究の考え方
shuntaros
0
3k
Adaptive Experimental Design for Efficient Average Treatment Effect Estimation and Treatment Choice
masakat0
0
120
問いを起点に、社会と共鳴する知を育む場へ
matsumoto_r
PRO
0
660
世界の人気アプリ100個を分析して見えたペイウォール設計の心得
akihiro_kokubo
PRO
62
32k
snlp2025_prevent_llm_spikes
takase
0
380
CVPR2025論文紹介:Unboxed
murakawatakuya
0
180
投資戦略202508
pw
0
570
EOGS: Gaussian Splatting for Efficient Satellite Image Photogrammetry
satai
4
670
Pythonでジオを使い倒そう! 〜それとFOSS4G Hiroshima 2026のご紹介を少し〜
wata909
0
980
J-RAGBench: 日本語RAGにおける Generator評価ベンチマークの構築
koki_itai
0
770
MetaEarth: A Generative Foundation Model for Global-Scale Remote Sensing Image Generation
satai
4
320
Featured
See All Featured
[Rails World 2023 - Day 1 Closing Keynote] - The Magic of Rails
eileencodes
37
2.6k
The Pragmatic Product Professional
lauravandoore
36
6.9k
Build your cross-platform service in a week with App Engine
jlugia
232
18k
Building Adaptive Systems
keathley
44
2.8k
Evolution of real-time – Irina Nazarova, EuRuKo, 2024
irinanazarova
9
980
Thoughts on Productivity
jonyablonski
70
4.9k
Improving Core Web Vitals using Speculation Rules API
sergeychernyshev
21
1.2k
Rails Girls Zürich Keynote
gr2m
95
14k
The Invisible Side of Design
smashingmag
302
51k
The World Runs on Bad Software
bkeepers
PRO
72
11k
Side Projects
sachag
455
43k
RailsConf 2023
tenderlove
30
1.3k
Transcript
ೋਓ୯ශຽͷఆཧΛ COQͰূ໌͢ΔࢼΈ େ উݾʢϑϦʔΤϯδχΞʣ 2020.8.31 ୈ4ճຊ߹ͤήʔϜཧݚڀूձ
ൃදɿCOQ୯ශຽ ➤ తɿ ఆཧূ໌ࢧԉܥCoqʹͯ ػցʹΑΔอূ͖ͷ ೋਓ୯ශຽͷূ໌Λॻ͘ ➤ ݁Ռɿ ݁·Ͱͷূ໌ͷྲྀΕ ࡉ͔͍ิΛશͯূ໌͢Δͷ
ਐߦதʢ͕͜͜ΩπΠʣ ➤ CoqʹΑΔήʔϜݕূͷ ՄೳੑΛհ
ೋਓ୯ශຽ
େ߽ܥήʔϜͷݚڀ ➤ ୩ɾখ (2017, 2018) ೋਓ୯ශຽͷউऀΛઢܗ࣌ؒͰٻΊΔΞϧΰϦζϜͷఏҊ ➤ ೋਓ୯ශຽʢ, 2007ʣͱ… τϥϯϓήʔϜେ߽ͷ؆ུԽ
ɾೋਓ ɾಛघϧʔϧͳ͠ ɾҰຕग़͠ͷΈ ➤ શใήʔϜ
ೋਓ୯ශຽͷఆࣜԽ ➤ ୯ශຽήʔϜͷҙͷঢ়ଶҎԼͷࡾͭͰදݱͰ͖Δ ɾख൪ଆͷखࡳɹ ɾඇख൪ଆͷखࡳ ɾͷࡳͷڧ͞ɹ ➤ ྫ
ʢಉ͡ڧ͞ͷࡳΛෳ࣋ͭ͜ͱ͋Δʣ X ¯ X r X = {1,3}, ¯ X = {2,2,4}, r = 0
ೋਓ୯ශຽͷఆࣜԽ ➤ ྫ ➤ ઌख͕̏Λग़ͨ͠߹ɹɹɹɹɹ {1} {2, 2, 4}
3 ޙख͕̐Λग़͢ɹɹɹɹɹɹɹɹ {1} {2, 2} 4 ઌखग़ͤͳ͍ͷͰύεɹɹɹɹ {1} {2, 2} 0 ޙख͕̎Λग़͢ɹɹɹɹɹɹɹɹ {1} {2} 2 ઌखύεɹɹɹɹɹɹɹɹɹɹ {1} {2} 0 ޙख͕̎Λग़ͯ͠ޙखউͪɹɹɹ {1} {} 2 X = {1,3}, ¯ X = {2,2,4}, r = 0
ೋਓ୯ශຽͷఆࣜԽ ➤ ྫ ➤ ઌख͕ Λग़͠ ˠ ޙख͕ Λग़ͨ͠߹ ˠ
ઌख͕ Λग़ͯ͠ઌखউͪ ➤ ઌख͕ Λग़͠ ˠ ޙख͕ Λग़ͨ͠߹ ˠ ઌखύεɺޙख͕ Λग़͢ ˠ ઌख͕ Λग़ͯ͠ઌखউͪ ➤ Ҏ্ͷ݁Ռ͔Βɹઌखউͪɹͷہ໘ X = {1,3}, ¯ X = {2,2,4}, r = 0 1 2 3 1 4 2 3
ೋਓ୯ශຽͷղ๏ ➤ ୩ɾখ (2018) ➤ ҎԼͷΞϧΰϦζϜʹΑΓखࡳͷϚονϯάΛܭࢉ 1 ڧ͞ 3 2
2 4 0 ख൪ଆ ඇख൪ଆ ࣗͷࡳ͔Βɺ ͦΕΑΓऑ͍૬खͷࡳʹ ϚονϯάลΛҾ͘ ख൪ଆ ࡳରʹ
ೋਓ୯ශຽͷղ๏ ➤ ୩ɾখ (2018) ➤ ҎԼͷΞϧΰϦζϜʹΑΓखࡳͷϚονϯάΛܭࢉ 1 ڧ͞ 3 2
2 4 0 ख൪ଆ ඇख൪ଆ ૬खͷ ࠷ऑࡳʹ Ҿ͚ͳ͍ʂ ࣗͷࡳ͔Βɺ ͦΕΑΓऑ͍૬खͷࡳʹ ϚονϯάลΛҾ͘
ೋਓ୯ශຽͷղ๏ ➤ ୩ɾখ (2018) ➤ ҎԼͷΞϧΰϦζϜʹΑΓखࡳͷϚονϯάΛܭࢉ 1 ڧ͞ 3 2
2 4 0 ख൪ଆ ඇख൪ଆ 2 1 ∨
ೋਓ୯ශຽͷղ๏ ➤ ہ໘ ʹ͓͍ͯ खࡳͦΕͧΕͷ࠷খࡳ ຕΛআ͍ͨखࡳΛ ➤ ऑ͍ࡳͷϚονϯάͷΛܭࢉ͢Δؔ ➤ ख൪ଆඞউ
⁶ (X, ¯ X, r) 1 X− , ¯ X− μ μ(X, ¯ X− + {r}) > μ( ¯ X, X− )
୯ශຽͷূ໌
ೋਓ୯ශຽͷΞϧΰϦζϜͷূ໌ ➤ ήʔϜʹଐ͢ΔԿΒ͔ͷʹର͢Δؼೲ๏Ͱূ໌Ͱ͖Δ ͜͜Ͱɺ྆ऀͷखࡳຕͷ߹ܭͱ͢Δ 1 ڧ͞ 3 2 2 4
0 ख൪ଆ ඇख൪ଆ 2 1 ∨
ೋਓ୯ශຽͷΞϧΰϦζϜͷূ໌ ➤ ূ໌͍ͨ͠ఆཧΛ࣍ͷ (a) (b) ʹׂ (a) ͳΒख൪ଆඞউ (b) ͳΒඇख൪ଆඞউ
➤ جૅεςοϓ खࡳ̍ຕͣͭʢ߹ܭ̎ຕʣͷͱ͖ (a) (b) ཱ͕ ➤ ؼೲεςοϓ खࡳ߹ܭ͕ ຕͷͱ͖ɺ ɾ(a)ہ໘ͳΒҰखͰউͪ or ૬खͷ(b)ہ໘ʹભҠ͢Δख͕͋Δ ɾ(b)ہ໘ͳΒ૬खͷ(a)ہ໘ʹඞͣભҠ͢Δ ͜ͱ͕ࣔͤͨͱ͢Δʢ͕͍͜͜͠ͷ͕ͩʣ μ(X, ¯ X− + {r}) > μ( ¯ X, X− ) μ(X, ¯ X− + {r}) ≤ μ( ¯ X, X− ) k
ೋਓ୯ශຽͷΞϧΰϦζϜͷূ໌ ➤ ূ໌͍ͨ͠ఆཧΛ࣍ͷ (a) (b) ʹׂ (a) ͳΒख൪ଆඞউ (b) ͳΒඇख൪ଆඞউ
➤ ؼೲεςοϓ खࡳ߹ܭ͕ ຕͷͱ͖ɺ ɾ(i) (a)ہ໘Ͱग़ͤΔࡳ͕͋Εؼೲ๏ͷԾఆͷ(b)Λద༻ ɾ(ii) (b)ہ໘Ͱग़ͤΔࡳ͕͋Εؼೲ๏ͷԾఆͷ(a)ɺ ɹɹɹग़ͤΔࡳ͕ͳ͚Ε (i) Λద༻ ɾ(i) (a)ہ໘Ͱग़ͤΔࡳ͕ͳ͚Ε (ii) Λద༻ Αͬͯखࡳ߹ܭ ຕͰ(a)(b)ཱ͕ μ(X, ¯ X− + {r}) > μ( ¯ X, X− ) μ(X, ¯ X− + {r}) ≤ μ( ¯ X, X− ) k + 1 k + 1
ఆཧূ໌ࢧԉܥ COQ
COQʹΑΔূ໌ͷྲྀΕ ➤ ఆཧূ໌ࢧԉܥ ূ໌Λهड़͢ΔͨΊͷϓϩάϥϛϯάݴޠ γεςϜ͕डཧͨ͠ূ໌ʢίʔυʣͨ͠ূ໌ͱͯ͠ Ҏ߱ͷূ໌ʹར༻Ͱ͖Δ ➤ CoqAgdaͳͲ͕༗໊ ➤ ʢຊൃදͷൣғͰʣ͍ΘΏΔʮࣗಈূ໌ʯͰͳ͍
➤ ྫɿࣗવ ʹରͯ͠ Λূ໌ͯ͠ΈΔ n n = 0 + n n = n + 0
None
None
ήʔϜ ON COQ
COQͰήʔϜΛѻ͏ख๏ ➤ ήʔϜ(ͷΈͳΒ༷ͣʑͳରʹʹڞ௨Ͱ͋Δ͕) CoqͰෳࡶͳରΛఆٛ͢Δ̎௨ΓͷΓํ ɾ࠶ؼؔʹΑΔఆٛ ɹ ɾؼೲతͳఆٛ ɹ ➤
ͲͪΒ͋Γ
࠶ؼؔʹΑΔήʔϜͷఆٛ ➤ ४උ
࠶ؼؔʹΑΔήʔϜͷఆٛ ➤ ࠶ؼؔͰશ୳ࡧΛఆٛ
࠶ؼؔʹΑΔήʔϜͷఆٛ ➤ Compute Ͱશ୳ࡧΛ࣮ߦ
࠶ؼؔʹΑΔήʔϜͷఆٛ ➤ ख੍ݶͳ͠ˠ࠶ؼؔͷఀࢭੑೳ͕CoqʹΘΒͣ×
ؼೲతͳήʔϜͷউഊఆٛ ➤ ҰྫɿউഊΛҾʹ໋Λฦؔ͢Λఆٛ͢Δ
ؼೲతͳήʔϜͷউഊఆٛ ➤ ۩ମྫʹର͢Δউഊͷܾఆ…ܭࢉͰ͖ͣɺূ໌Ͱߦ͏
COQͰήʔϜΛѻ͏ख๏ ➤ CoqͰήʔϜΛѻ͏߹ ɾ࠶ؼؔʹΑΔఆٛ ɹॴɿײʹ͍ۙఆٛɺܭࢉͰ͖Δ ɹॴɿఆٛ͢Δ࣌Ͱ੍ݶ͕େ͖͍ ɹ ɾؼೲతͳఆٛ ɹॴɿఆٛͰ͖Δൣғ͕͍ɺతͳূ໌
ɹॴɿײతͳήʔϜͱͷဃ