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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">10.18255/1818-1015-2020-4-412-427</article-id><article-id custom-type="elpub" pub-id-type="custom">mais-1433</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>Theory of Computing</subject></subj-group></article-categories><title-group><article-title>Темпоральная логика для программируемых логических контроллеров</article-title><trans-title-group xml:lang="en"><trans-title>Temporal Logic for Programmable Logic Controllers</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9734-3808</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гаранина</surname><given-names>Наталья Олеговна</given-names></name><name name-style="western" xml:lang="en"><surname>Garanina</surname><given-names>Natalia Olegovna</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат физико-математических наук, старший научный сотрудник</p></bio><bio xml:lang="en"><p>Ph.D. in Mathematics, senior research fellow</p></bio><email xlink:type="simple">garanina@iis.nsk.su</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9574-128X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ануреев</surname><given-names>Игорь Сергеевич</given-names></name><name name-style="western" xml:lang="en"><surname>Anureev</surname><given-names>Igor Sergeevich</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат физико-математических наук, старший научный сотрудник</p></bio><bio xml:lang="en"><p>Ph.D. in Mathematics, senior research fellow.6, Acad. Lavrentjev ave., Novosibirsk 630090.</p></bio><email xlink:type="simple">anureev@iis.nsk.su</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8198-3197</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Зюбин</surname><given-names>Владимир Евгеньевич</given-names></name><name name-style="western" xml:lang="en"><surname>Zyubin</surname><given-names>Vladimir Evgenyevich</given-names></name></name-alternatives><bio xml:lang="ru"><p>Доктор технических наук, заведующий лабораторией.пр. Акад. Коптюга, д. 1, Новосибирск, 630090.</p></bio><bio xml:lang="en"><p>Dr. Sci., head oflaboratory</p></bio><email xlink:type="simple">zyubin@iae.nsk.su</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5183-9736</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Старолетов</surname><given-names>Сергей Михайлович</given-names></name><name name-style="western" xml:lang="en"><surname>Staroletov</surname><given-names>Sergey Mikhailovich</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат физико-математических наук, доцент</p></bio><bio xml:lang="en"><p>Ph.D. in Mathematics, lecturer</p></bio><email xlink:type="simple">serg_soft@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9148-946X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лях</surname><given-names>Татьяна Викторовна</given-names></name><name name-style="western" xml:lang="en"><surname>Liakh</surname><given-names>Tatiana Victorovna</given-names></name></name-alternatives><bio xml:lang="ru"><p>Инженер-исследователь.пр. Акад. Коптюга, д. 1, Новосибирск, 630090.</p></bio><bio xml:lang="en"><p>Research engineer</p></bio><email xlink:type="simple">liakh@iae.nsk.su</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7468-0411</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Розов</surname><given-names>Андрей Сергеевич</given-names></name><name name-style="western" xml:lang="en"><surname>Rozov</surname><given-names>Andrey Sergeevich</given-names></name></name-alternatives><bio xml:lang="ru"><p>Младший научный сотрудник</p></bio><bio xml:lang="en"><p>Junior researcher</p></bio><email xlink:type="simple">rozov@iae.nsk.su</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3857-9380</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Горлач</surname><given-names>Сергей Петрович</given-names></name><name name-style="western" xml:lang="en"><surname>Gorlatch</surname><given-names>Sergei Petrovich</given-names></name></name-alternatives><bio xml:lang="ru"><p>Профессор, кандидат физико-математических наук.Шлосплац, д. 2, Мюнстер, 48149.</p></bio><bio xml:lang="en"><p>Prof. Dr. Habil</p></bio><email xlink:type="simple">gorlatch@uni-muenster.de</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт систем информатики имени А.П. Ершова СО РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>A.P. Ershov Institute of Informatics Systems (IIS), Siberian Branch of the Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Институт автоматики и электрометрии СО РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Institute of Automation and Electrometry SB RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Алтайский государственный технический университет им. И.И. Ползунова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Polzunov Altai State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Университет Мюнстера</institution><country>Германия</country></aff><aff xml:lang="en"><institution>University of Munster</institution><country>Germany</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>19</day><month>12</month><year>2020</year></pub-date><volume>27</volume><issue>4</issue><fpage>412</fpage><lpage>427</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Гаранина Н.О., Ануреев И.С., Зюбин В.Е., Старолетов С.М., Лях Т.В., Розов А.С., Горлач С.П., 2020</copyright-statement><copyright-year>2020</copyright-year><copyright-holder xml:lang="ru">Гаранина Н.О., Ануреев И.С., Зюбин В.Е., Старолетов С.М., Лях Т.В., Розов А.С., Горлач С.П.</copyright-holder><copyright-holder xml:lang="en">Garanina N.O., Anureev I.S., Zyubin V.E., Staroletov S.M., Liakh T.V., Rozov A.S., Gorlatch S.P.</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/1433">https://www.mais-journal.ru/jour/article/view/1433</self-uri><abstract><p>Мы исследуем формальную верификацию управляющего программного обеспечения критических систем, т. е. проверку соответствия функционирования проектируемой системы предъявленным требованиям. Важнейший класс управляющего программного обеспечения составляют программы для программируемых логических контроллеров (ПЛК). Особенностью программ ПЛК является цикл управления: 1) считываются входы, 2) изменяются состояния ПЛК и 3) записываются выходы. Поэтому для формальной верификации программ ПЛК нужна возможность описывать учитывающие эту специфику системы переходов, а также определять свойства систем, моделирующих программы ПЛК, как относительно переходов внутри цикла, так и относительно более крупных переходов в соответствии с семантикой цикла управления. Мы предлагаем формальную модель программы ПЛК как систему переходов гиперпроцессов и темпоральную логику cycle-LTL для формализации свойств ПЛК. Особенностью логики cycle-LTL является возможность рассматривать свойства систем управления двояким образом: воздействие окружения на систему управления и воздействие системы управления на окружение. Мы определяем модификации стандартных темпоральных операторов логики LTL для каждого из этих случаев, а также для свойств внутри цикла управления. Рассмотрены примеры требований, определенных в нашей логике. Описана трансляция формул cycle-LTL в формулы LTL и показана её корректность. Доказана возможность сведения задачи верификации методом проверки моделей для требований, определенных в логике cycle-LTL, к задаче верификации требований, определенных в стандартной логике LTL.</p></abstract><trans-abstract xml:lang="en"><p>We address the formal verification of the control software of critical systems, i.e., ensuring the absence of design errors in a system with respect to requirements. Control systems are usually based on industrial controllers, also known as Programmable Logic Controllers (PLCs). A specific feature of a PLC is a scan cycle: 1) the inputs are read, 2) the PLC states change, and 3) the outputs are written. Therefore, in order to formally verify PLC, e.g., by model checking, it is necessary to describe the transition system taking into account this specificity and reason both in terms of state transitions within a cycle and in terms of larger state transitions according to the scan-cyclic semantics. We propose a formal PLC model as a hyperprocess transition system and temporal cycle-LTL logic based on LTL logic for formulating PLC property. A feature of the cycle-LTL logic is the possibility of viewing the scan cycle in two ways: as the effect of the environment (in particular, the control object) on the control system and as the effect of the control system on the environment. For both cases we introduce modified LTL temporal operators. We also define special modified LTL temporal operators to specify inside properties of scan cycles. We describe the translation of formulas of cycle-LTL into formulas of LTL, and prove its correctness. This implies the possibility ofmodel checking requirements expressed in logic cycle-LTL, by using well-known model checking tools with LTL as specification logic, e.g., Spin. We give the illustrative examples of requirements expressed in the cycle-LTL logic.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>формальная верификация</kwd><kwd>темпоральная логика</kwd><kwd>системы переходов</kwd><kwd>программируемые логические контроллеры (ПЛК)</kwd></kwd-group><kwd-group xml:lang="en"><kwd>formal verification</kwd><kwd>temporal logics</kwd><kwd>transition systems</kwd><kwd>programmable logic controllers (PLC)</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено в рамках государственного задания № AAAA-A19-119120290056-0</funding-statement><funding-statement xml:lang="en">The reported study was funded by State assignment No AAAA-A19-119120290056-0.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">I. 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