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These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"To learn the fundamental concepts of formal languages, automata theory and computation theory, such as deterministic and non-deterministic finite automata, regular expressions, context-free grammars, pushdown automata and Turing machines. To be able to compare their generative powers. To learn structural properties and pumping lemmas, basic closure properties and decision algorithms To understand the notion of undecidability, and to be able to prove algorithmic problems undecidable.","fi":"To learn the fundamental concepts of formal languages, automata theory and computation theory, such as deterministic and non-deterministic finite automata, regular expressions, context-free grammars, pushdown automata and Turing machines. To be able to compare their generative powers. To learn structural properties and pumping lemmas, basic closure properties and decision algorithms To understand the notion of undecidability, and to be able to prove algorithmic problems undecidable."},"tweetText":null,"content":{"en":"Automata theory constitutes a cornerstone of mathematical computer science, and in particular finite automata have turned out to be very useful tools in many areas of discrete mathematics. Different models of automata in classical Chomsky hierarchy as well as corresponding grammars are considered and their generating power is compared. Basic undecidability results are proved.","fi":"Automata theory constitutes a cornerstone of mathematical computer science, and in particular finite automata have turned out to be very useful tools in many areas of discrete mathematics. Different models of automata in classical Chomsky hierarchy as well as corresponding grammars are considered and their generating power is compared. Basic undecidability results are proved."},"additional":{"en":"Preceding studies\r\nmathematical maturity\r\n\r\nCourse will be given every other autumn (in even years).","fi":"Preceding studies\r\nmathematical maturity\r\n\r\nCourse will be given every other autumn (in even years)."},"prerequisites":{"en":"Mathematical maturity","fi":"Mathematical maturity"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Automata and Formal Languages","id":"otm-40ef607c-9c0d-3405-b824-9d72e270b343","code":"MATE5225","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-69f8ea31-de0c-3050-ab2a-e571fbab1f95"],"organisations":[],"attainmentLanguages":[],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}