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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">mais</journal-id><journal-title-group><journal-title xml:lang="ru">Моделирование и анализ информационных систем</journal-title><trans-title-group xml:lang="en"><trans-title>Modeling and Analysis of Information Systems</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1818-1015</issn><issn pub-type="epub">2313-5417</issn><publisher><publisher-name>Yaroslavl State University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.18255/1818-1015-2018-4-402-410</article-id><article-id custom-type="elpub" pub-id-type="custom">mais-732</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Оригинальные статьи</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Articles</subject></subj-group></article-categories><title-group><article-title>О некоторых подходах к решению задачи «Useful Proof-of-work for blockchains»</article-title><trans-title-group xml:lang="en"><trans-title>On Some Approaches to the Solution of the Problem «Useful Proof-of-work for Blockchains»</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дурнев</surname><given-names>Валерий Георгиевич</given-names></name><name name-style="western" xml:lang="en"><surname>Durnev</surname><given-names>Valeriy G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р физ.-мат. наук, профессор</p></bio><bio xml:lang="en"><p>Doctor, Professor</p></bio><email xlink:type="simple">Durnev@uniyar.ac.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8068-0784</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мурин</surname><given-names>Дмитрий Михайлович</given-names></name><name name-style="western" xml:lang="en"><surname>Murin</surname><given-names>Dmitry M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>канд. физ.-мат. наук, доцент</p></bio><bio xml:lang="en"><p>PhD, Docent</p></bio><email xlink:type="simple">nirum87@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1427-4937</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Соколов</surname><given-names>Валерий Анатольевич</given-names></name><name name-style="western" xml:lang="en"><surname>Sokolov</surname><given-names>Valery A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р физ.-мат. наук, профессор</p></bio><bio xml:lang="en"><p>Doctor, Professor</p></bio><email xlink:type="simple">valery-sokolov@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0553-7387</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Чалый</surname><given-names>Дмитрий Юрьевич</given-names></name><name name-style="western" xml:lang="en"><surname>Chalyy</surname><given-names>Dmitry Ju.</given-names></name></name-alternatives><bio xml:lang="ru"><p>канд. физ.-мат. наук, доцент</p></bio><bio xml:lang="en"><p>PhD, Docent</p></bio><email xlink:type="simple">chaly@uniyar.ac.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Ярославский государственный университет им. П.Г. Демидова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>P.G. Demidov Yaroslavl State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>27</day><month>08</month><year>2018</year></pub-date><volume>25</volume><issue>4</issue><fpage>402</fpage><lpage>410</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Дурнев В.Г., Мурин Д.М., Соколов В.А., Чалый Д.Ю., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Дурнев В.Г., Мурин Д.М., Соколов В.А., Чалый Д.Ю.</copyright-holder><copyright-holder xml:lang="en">Durnev V.G., Murin D.M., Sokolov V.A., Chalyy D.J.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.mais-journal.ru/jour/article/view/732">https://www.mais-journal.ru/jour/article/view/732</self-uri><abstract><p>Технология блокчейн основана на принципе доказательства работой «Proof-ofwork». Суть данного принципа состоит в том, что некоторое событие (например, перевод денежных средств с одного счета на другой) становится значимым только после того, как оно подтверждено определенным объемом вычислительной работы. Соответственно возникает потребность в вычислительных задачах, над которыми такую работу можно производить, причем на решение этих задач будет тратиться практически вся вычислительная мощность блокчейн-сети. На сегодня в качестве таких задач получили распространение «хэш-головоломки» – задачи поиска битовой строки с хэшем, удовлетворяющим определенным условиям. Существенным недостатком хэш-головоломок является отсутствие у них какого-либо полезного применения за пределами технологии блокчейн. В работе описываются подходы к решению задачи «Useful Proof-of-work for blockchains», а именно предлагается рассматривать в качестве вычислительных задач для доказательства работой возникающие на практике индивидуальные представители NP-полных задач, которые могут решаться, например, SAT- или LLL-решателями. Отдельной проработки требует вопрос об использовании FPT-задач. Предлагаемый подход позволяет обеспечить следующие свойства вычислительных задач для доказательства работой: полезность, управляемость сложностью задач (через изменение размерности, выбор задач определенного вида, указание точности необходимого решения), массовость. При этом допускается, что не каждая решенная задача может оказаться полезной, однако предоставляется возможность решать с помощью технологии блокчейн задачи, возникающие на практике. Кроме прочего, таким образом становится возможным сопоставить стоимость виртуальной криптовалюты через затраты электроэнергии при ее генерации с практическим результатом от решения вычислительных задач. Наиболее трудными вопросами в контексте рассматриваемого подхода являются реализация связи событий и задач, обеспечивающих эти события вычислительной работой, и реализация системы анализа сложности задач. Статью следует воспринимать как программу исследований, поскольку многие технические детали требуют отдельной проработки.</p></abstract><trans-abstract xml:lang="en"><p>The blockchain technology is based on the ”Proof-of-work” principles. The essence of this principle is that some event (for example the bill-to-bill money transaction) becomes significant after the confirmation by a certain computer work. So, a demand arose for such computational problems to work on, and we will spend on it about the whole blockchain system computing capacity. Now the main kind of such a problem is a hash-puzzle – the problem to find a bit string with a hash that satisfies some conditions. The important hash-puzzle weakness is the lack of the useful application outside of the blockchain technology. In this work, we offer some approaches to ”Useful Proof-of-work for blockchains” problem, namely, consider some practical variants of the NP-complete problems that could be solved with the help of SAT or LLL-solvers as the Proof-of-Work computational problems. The use of the FPTproblems requires special study. The offered approach allows to provide the following characteristics of the proof-of-work computational problems: usefulness, problems complexity management (through the dimension change, choosing problems of certain kind, the indication of necessary solution precision), mass character. Herewith we admit that not every solved problem can be useful but we consider the opportunity to solve some practical problems with the help of the blockchain technology. Among other things it is also possible to compare the virtual crypto-currency value (through the energy costs spent) and the effective result of the practical problems solution. The most complicated points of the described approach are the realization of the events-problems (providing the computer work for these events) relations and the realization of the problems complexity analysis system. This issue should be viewed as the study program because of many technical details that must be worked out further.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>доказательство работой</kwd><kwd>блокчейн</kwd><kwd>выполнимость</kwd><kwd>SAT-решатель</kwd><kwd>NP-полнота</kwd><kwd>FPT</kwd><kwd>алгоритм</kwd></kwd-group><kwd-group xml:lang="en"><kwd>proof-of-work</kwd><kwd>blockchain</kwd><kwd>satisfiability</kwd><kwd>SAT-solver</kwd><kwd>NP-complete</kwd><kwd>FPT</kwd><kwd>algorithm</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Nakamoto S., “Bitcoin: A Peer-to-Peer Electronic Cash System”, 2009, 1–9. https://bitcoin.org/bitcoin.pdf.</mixed-citation><mixed-citation xml:lang="en">Nakamoto S., “Bitcoin: A Peer-to-Peer Electronic Cash System”, 2009, 1–9. https://bitcoin.org/bitcoin.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Buterin V., “Ethereum White Paper: A next-generation smart contract and decentralized application platform”, 2014. https://github.com/ethereum/wiki/wiki/White-Paper.</mixed-citation><mixed-citation xml:lang="en">Buterin V., “Ethereum White Paper: A next-generation smart contract and decentralized application platform”, 2014. https://github.com/ethereum/wiki/wiki/White-Paper.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Marques-Silva J.P., Sakallah K. ˙ A., “GRASP: A new search algorithm for satisfiability”, ˙ ICCAD ’96 Proceedings of the 1996 IEEE/ACM international conference on Computeraided design, 1996, 220—227.</mixed-citation><mixed-citation xml:lang="en">Marques-Silva J.P., Sakallah K. ˙ A., “GRASP: A new search algorithm for satisfiability”, ˙ ICCAD ’96 Proceedings of the 1996 IEEE/ACM international conference on Computeraided design, 1996, 220—227.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Bayardo Jr.R., Schrag R., “Using CSP look-back techniques to solve real-world SAT ˙ instances”, AAAI’97/IAAI’97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence, 1997, 203—208.</mixed-citation><mixed-citation xml:lang="en">Bayardo Jr.R., Schrag R., “Using CSP look-back techniques to solve real-world SAT ˙ instances”, AAAI’97/IAAI’97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence, 1997, 203—208.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">“International Students’ Olympiad in Cryptography NSUCRYPTO. 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