{"title":"Gröbner基与Church-Rosser交换苏系统的超指数下界","authors":"Dung T. Huynh","doi":"10.1016/S0019-9958(86)80035-3","DOIUrl":null,"url":null,"abstract":"<div><p>The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a Church-Rosser system is presently unknown. In this paper we derive a double-exponential lower bound (2<sup>2<em>n</em>C</sup>) for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"68 1","pages":"Pages 196-206"},"PeriodicalIF":0.0000,"publicationDate":"1986-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80035-3","citationCount":"54","resultStr":"{\"title\":\"A superexponential lower bound for Gröbner bases and Church-Rosser commutative thue systems\",\"authors\":\"Dung T. Huynh\",\"doi\":\"10.1016/S0019-9958(86)80035-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a Church-Rosser system is presently unknown. In this paper we derive a double-exponential lower bound (2<sup>2<em>n</em>C</sup>) for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"68 1\",\"pages\":\"Pages 196-206\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80035-3\",\"citationCount\":\"54\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995886800353\",\"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":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
A superexponential lower bound for Gröbner bases and Church-Rosser commutative thue systems
The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a Church-Rosser system is presently unknown. In this paper we derive a double-exponential lower bound (22nC) for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases.
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