Wannan takarda ta magance wata muhimmiyar aibi a cikin daidaiton ƙarfafawa na Bitcoin, wanda Eyal da Sirer (2014) suka fara nuna. Duk da yake dabararsu ta SM1 ta nuna ma'adinan son kai mai riba, wannan aikin ya tabbatar da cewa ba ta fi dacewa ba. Muna gabatar da tsari na gaba ɗaya da algorithm don nemo manufofin ma'adinan son kai na ε-mafi kyau, kafa ƙaƙƙarfan iyaka akan riba da kuma bayyana ƙaramin ƙarfin lissafi don nasarar hare-hare fiye da yadda aka sani a baya.
Fahimtar ma'adinan son kai yana buƙatar tushe a cikin tsarin yarjejeniya na Bitcoin da kuma tsarin hare-hare na baya.
Bitcoin ya dogara da yarjejeniyar Tabbatar da Aiki (PoW) inda ma'adinai ke gasa don warware wasanin sirri na sirri. Na farko da ya warware wasan ya watsa sabon toshe, yana da'awar lada na toshe da kuɗin ma'amala. Ka'idojin ta ba da umarnin buga toshe nan da nan. Dokar mafi tsayin sarkar tana warware rassa.
Dabarar SM1 ta Eyal da Sirer ta ƙunshi ma'adinai da ke riƙe sabon toshe da aka haƙa, yana ƙirƙirar sarkar sirri. Mai kai hari yana bayyana tubalan da dabara don yin marayu ga tubalan gaskiya, yana da'awar rabon lada mara daidaituwa. Bincikensu ya nuna matakin riba na kusan 25% na rabon hash na cibiyar sadarwa don mai kai hari mai haɗin kai.
Muna faɗaɗa tsarin ma'adinan son kai zuwa cikin tsarin Tsarin Yanke Shawara na Markov (MDP), yana ba da damar bincika sararin dabarun cikakke.
An ayyana yanayin tsarin ta hanyar jagorancin sarkar sirri na mai kai hari akan sarkar jama'a. Ayyuka sun haɗa da: Karɓa (watsi da sarkar sirri), Ƙetare (buga don mamaye sarkar jama'a), Jira (ci gaba da haƙa a asirce), da Daidaita (buga isasshen don ɗaure). Tsarin ya haɗa da ƙarfin lissafi na mai kai hari α da kuma ma'aunin yaduwar cibiyar sadarwa γ.
Muna tsara matsalar a matsayin MDP mara iyaka mai rangwame. Ta amfani da algorithm na juzu'in ƙima ko manufa, muna ƙididdige manufa mai kyau ε π* wanda ke haɓaka kudaden shiga na mai kai hari R(α, γ, π). Sakamakon algorithm yana ba da umarnin aiki mafi kyau (Jira, Karɓa, Ƙetare, Daidaita) ga kowane yanayin da zai yiwu (jagora l).
~23%
Rabon hash da ake buƙata don riba (Tsarin Mu)
~25%
Rabon hash da ake buƙata don riba (SM1)
>0%
Yana ɓacewa ƙarƙashin tsarin jinkiri na zahiri
Dabarunmu masu kyau suna samar da ƙaramin matakin riba akai-akai fiye da SM1. Don ma'aunin yaduwa na yau da kullun (γ=0.5), matakin ya ragu daga kusan 25% zuwa kusan 23%. Wannan bambancin 2% yana da mahimmanci, yana kawo ƙarin masu yiwuwar kai hari cikin yankin riba.
Manufofin da aka samo suna rinjaye SM1 sosai. Babban ci gaban shine "janyewar kai hari" mai zurfi—sanin daidai lokacin da za a watsar da sarkar sirri (Karɓa) don yanke asara, maimakon dagewa kamar yadda SM1 ke yi akai-akai. Wannan hali na daidaitawa yana ƙara yawan kudaden shiga da ake tsammani a duk ƙimar α da γ.
Ƙarƙashin tsarin da ya haɗa da jinkirin yaduwar cibiyar sadarwa, matakin riba ya ɓace yadda ya kamata. Ko da ma'adinai masu ƙaramin ƙarfin hash (α → 0) suna da ƙarfafawar yuwuwar ɗan lokaci don riƙe tubalan, kamar yadda jinkiri ke haifar da rassa na halitta da za su iya amfani da su. Wannan yana bayyana ƙarin rashin daidaituwar ƙarfafawa a cikin yarjejeniyar Nakamoto.
Jigon binciken shine tsarin canjin yanayi da aikin kudaden shiga. Kudaden shiga na mai kai hari mai ƙarfin hash α yana bin manufa π shine:
$R(α, γ, π) = \frac{\text{Yawan tubalan da mai kai hari ya samu ake tsammani}}{\text{Yawan jimillar tubalan da aka ƙirƙira ake tsammani}}$
Yanayin shine jagora l. Yuwuwar canzawa ya dogara da α da ma'adinan gaskiya suna samun tubalan. Misali, daga yanayi l=1:
Jadawali Mai Muhimmanci 1: Kudaden Shiga na Dangantaka vs. Ƙarfin Hash (α)
Jadawali mai layi wanda ke kwatanta kudaden shiga na dangantaka R na manufa mafi kyau (daga algorithm ɗinmu) da manufar SM1 da ma'adinan gaskiya. Layin manufa mafi kyau yana sama da layin SM1 ga duk α > 0. Layukan suna ketare layin ma'adinan gaskiya (inda R = α) a wurare daban-daban, suna nuna ƙaramin mataki na manufa mafi kyau a zahiri.
Jadawali Mai Muhimmanci 2: Zanen Canjin Yanayi
Jadawali mai jagora wanda ke nuna yanayi (l=0,1,2,...) da ayyuka mafi kyau (wanda aka lakafta akan gefuna: Jira, Ƙetare, Karɓa, Daidaita) kamar yadda algorithm ya ƙaddara don takamaiman (α, γ). Wannan zanen yana nuna ainihin dabarar yanke shawara mara ban sha'awa, kamar karɓa daga jagora na 1 a ƙarƙashin wasu sharuɗɗa—wani motsi mara ma'ana wanda ba ya cikin SM1.
Yanayi: Tafkin ma'adinai "AlphaPool" yana sarrafa α = 0.24 na rabon hash na cibiyar sadarwa. Ma'aunin yaduwar cibiyar sadarwa shine γ=0.6 (ma'ana AlphaPool ya koyi 60% na tubalan gaskiya nan da nan).
Dabarar SM1: AlphaPool zai bi ƙa'ida mai tsauri: yi haƙa a asirce tare da jagora, buga don ƙetare lokacin da ya gabata da 2. Bincike ya nuna wannan yana samar da R_SM1 ≈ 0.239, wanda shine ƙasa da rabon hash ɗinsa (0.24), yana mai da shi mara riba idan aka kwatanta da ma'adinan gaskiya.
Manufa Mafi Kyau (daga algorithm ɗinmu): Manufar da aka ƙididdige π* na iya ba da umarni: Daga jagora na 1, idan an sami toshe na gaskiya, nan da nan Daidaita (buga) don ƙirƙirar daidaito da kuma gasa a zagaye na gaba, maimakon jira. Wannan canji mai sauƙi yana canza yuwuwar canzawa. Kudaden shiga da aka samu shine R_opt ≈ 0.242, wanda shine fiye da 0.24. Hare-haren ya zama mai riba.
Fahimta: Wannan yanayin yana nuna yadda yanke shawara mafi kyau, mai dogaro da yanayi zai iya juya rabon hash mara riba a ka'ida zuwa mai riba, kawai ta hanyar buga toshe na dabara.
Ƙirar Ka'idoji & Magungunan Rigakafi: Wannan aikin yana ba da kayan aiki don gwada ingantattun ingantattun Bitcoin (misali, GHOST, ka'idojin Blockchain masu haɗawa) akan ma'adinan son kai mafi kyau, ba kawai SM1 ba. Binciken shawarar rigakafin da Eyal da Sirer suka ba ya nuna ba shi da tasiri kamar yadda ake fata, yana jagorantar bincike na gaba zuwa ga gyare-gyare masu ƙarfi.
Bayan Bitcoin: Tsarin MDP yana aiki ga sauran sarƙoƙin Blockchain na Tabbatar da Aiki (misali, Litecoin, Bitcoin Cash) kuma ana iya daidaita shi don nazarin halayen dabara a cikin tsarin Tabbatar da Hannun jari (PoS), inda za a iya samun irin wannan "riƙe toshe" ko hare-haren "rashin daidaituwa".
Haɗe-haɗen Hare-hare: Aikin gaba dole ne ya ƙirƙira mu'amala tsakanin ma'adinan son kai da hare-haren kashe kuɗi sau biyu. Ma'adinan son kai mai sarkar sirri yana da dandali na halitta don ƙoƙarin kashe kuɗi sau biyu, wanda zai iya ƙara amfanin mai kai hari da kuma rage shingen duka hare-haren biyu.
Rarraba & Halayen Tafki: Ƙaramin mataki yana ƙara matsin lamba na tsakiya. Ana ƙarfafa manyan tafkuna su yi amfani da waɗannan dabarun masu kyau, kuma ana ƙarfafa ƙananan ma'adinai su shiga cikin su don samun kudaden shiga masu tsayi, suna haifar da madauki na amsa wanda ke lalata rarrabawa—tushen tsaro na Bitcoin.
Sapirshtein da sauransu sun ba da babban darasi a cikin gwajin matsin lamba na ka'idoji, suna matsawa bayan takamaiman amfani (SM1) don ƙirƙirar duk sararin na dabarun ma'adinan son kai. Bayyanarsu ta asali tana da tsauri: Tsarin ƙarfafawa na Bitcoin ba wai kawai ya karye a ƙarfin hash 25% ba—yana da rauni a cikinsa, tare da tsage-tsage da ke kusa da saman fiye da yadda Satoshi ya taɓa zato. "Matakin riba" ba katanga mai ƙarfi ba ne; gradient ne wanda dabarar mafi kyau za ta iya lalata shi zuwa kusan sifili a ƙarƙashin yanayin cibiyar sadarwa na zahiri. Wannan yana sake tsara ma'adinan son kai daga matsalar "babban mai kai hari" zuwa rashin daidaituwar ƙarfafawa na tsarin, mai kasancewa koyaushe.
Hankalin takardar ba shi da aibi kuma yana lalata. 1) Ƙirar Tsari: Sun gano SM1 daidai a matsayin maki ɗaya a cikin sararin dabarun da yawa. Ta hanyar tsara matsalar a matsayin Tsarin Yanke Shawara na Markov (MDP)—wata dabara mai daraja a cikin AI da ka'idar sarrafawa, kwatankwacin tsare-tsaren da aka yi amfani da su a cikin ayyukan ƙirƙira kamar takardar CycleGAN don bincika sararin fassarar hoto—sun buɗe damar bincika wannan sarari bisa tsari. 2) Magani na Algorithm: Algorithm na juzu'in ƙima ba kayan aiki kawai ba ne; hanyar tabbatarwa ce. Ba ta ɗauka dabarar; ta samo mafi kyau daga ka'idojin farko. 3) Matsawa Matsakaici: Sakamakon a bayyane yake: dabarun mafi kyau sun mamaye SM1, suna rage ma'auni don riba. 4) Kisan Jinkiri: Mataki na ƙarshe, haɗa da jinkirin cibiyar sadarwa, shine kisan gilla. Ya nuna cewa a cikin duniyar da ba ta nan take ba (ma'ana, gaskiya), ƙarfafawar tattalin arziki don ɗan lokaci karkata daga ka'idojin gabaɗaya ne, ba na musamman ba.
Ƙarfi: Ƙaƙƙarfan hanyar aiki yana saman matsayi. Tsarin MDP shine kayan aikin da ya dace don aikin, yana samar da tushe na yau da kullun, mai ƙididdigewa wanda binciken tunani na baya ya rasa. Yin la'akari da jinkirin cibiyar sadarwa yana haɗa mahimmin rata tsakanin ka'ida da aiki, yana daidaitawa da abubuwan lura daga binciken ma'aunin cibiyar sadarwa kamar waɗanda suka fito daga cibiyoyi kamar IC3 (Ƙaddamar da Kuɗin Kuɗi & Kwangila). Amfanin takardar a matsayin "mai nazarin tsaro" don gyare-gyaren ka'idoji babbar gudummawar aiki ce.
Aibobi & Makafin Gani: Binciken, duk da zurfinsa, har yanzu wasa ne na ɗan wasa biyu (mai kai hari vs. "sauran" gaskiya). Bai cika fuskantar daidaitattun tafki masu yawa, masu ƙarfi waɗanda ke siffanta Bitcoin a yau ba. Me zai faru idan manyan tafkuna da yawa duk suna gudanar da dabarun son kai mafi kyau (ko koyo) a kan juna? Tsarin kuma yana sauƙaƙa farashin janyewar kai hari (yin marayu ga tubalan ku), wanda zai iya samun farashi mara layi na tunani ko farin jini ga tafkuna. Bugu da ƙari, kamar yadda bincike na baya (misali, Gervais et al., 2016) ya lura, binciken ya ɗauka α mai tsayi; a zahiri, ƙarfin hash na iya gudu daga sarkar da ake ganin an kai masa hari, yana canza rabon mai kai hari da ƙarfi.
Ga Masu Haɓaka Ka'idoji: Dakatar da faci don SM1. Dole ne ku ƙirƙira don dabarar mafi kyau. Wannan takarda tana ba da ma'auni. Duk wani gyara da aka ba da shawara (misali, sabbin dokokin zaɓin rassa kamar GHOST) dole ne a tantance su akan wannan tsarin MDP. Manufar ya kamata ta zama sanya dabarar gaskiya ta zama daidaitattun Nash ga kowane α > 0, wata babbar hanya fiye da yadda ake riƙe a halin yanzu.
Ga Ma'adinai & Masu Gudanar da Tafki: Lissafin ya canza. Jagorar "tsaro" na 25% ta tsufa. Tafkuna masu ƙaramin ƙarfin hash kamar 20%, musamman waɗanda ke da haɗin kai mai kyau (babban γ), dole ne yanzu su yi la'akari da tursasawan tattalin arziki na riƙe da dabara. Abubuwan da'a da na ka'idar wasanni na rashin gudanar da manufa mafi kyau sun zama tattaunawar ɗakin zartarwa.
Ga Masu Zuba Jari & Masu Tsari: Ku fahimci cewa kasafin tsaro na Bitcoin (lada na ma'adinai) yana ƙarƙashin wani nau'i na hare-haren tattalin arziki mai zurfi fiye da yadda aka yarda da shi a baya. Haɗarin tsakiyar ma'adinai ba layi daya ba ne; yana ƙarƙashin mahimman mahimman wuraren da wannan bincike ya bayyana. Sa ido kan halayen tafki da lokutan yaduwar cibiyar sadarwa ya zama ma'auni mai mahimmanci na tsaro.
A ƙarshe, wannan takarda ba kawai ingantacciyar ilimi ba ce akan aikin baya; canjin tsari ne. Yana matsar da tattaunawar daga "Shin babban tafki zai iya yaudara?" zuwa "Ta yaya dabarar kowa mafi kyau, a cikin cibiyar sadarwa mara kyau, ke ci gaba da damun ƙarfafawar ka'idojin?" Amsar, abin takaici, ita ce "sosai". Burdin tabbatarwa yanzu yana kan masu karewa su nuna cewa yarjejeniyar Nakamoto, a sigarta ta yanzu, za a iya sanya ta zama daidaitaccen ƙarfafawa da gaske.