{"title":"具有上下文无关丢番图问题的组","authors":"V. Yankovskiy","doi":"10.46298/jgcc.2021.13.1.7347","DOIUrl":null,"url":null,"abstract":"We find algebraic conditions on a group equivalent to the position of its\nDiophantine problem in the Chomsky Hierarchy. In particular, we prove that a\nfinitely generated group has a context-free Diophantine problem if and only if\nit is finite.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"21 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Groups with context-free Diophantine problem\",\"authors\":\"V. Yankovskiy\",\"doi\":\"10.46298/jgcc.2021.13.1.7347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find algebraic conditions on a group equivalent to the position of its\\nDiophantine problem in the Chomsky Hierarchy. In particular, we prove that a\\nfinitely generated group has a context-free Diophantine problem if and only if\\nit is finite.\",\"PeriodicalId\":41862,\"journal\":{\"name\":\"Groups Complexity Cryptology\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2021-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complexity Cryptology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/jgcc.2021.13.1.7347\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jgcc.2021.13.1.7347","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
We find algebraic conditions on a group equivalent to the position of its
Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a
finitely generated group has a context-free Diophantine problem if and only if
it is finite.
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