{"title":"计算复杂性问题的算术理论","authors":"Steve Homer , John Reif","doi":"10.1016/S0019-9958(86)80041-9","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers a number of arithmetic theories and shows how the strength of these theories relates to certain open problems in complexity theory concerning the polynomial-time hierarchy. These results are proved quite generally and hold for a wide class of subrecursive hierarchies. They can be used to characterize certain properties of functions provable in these theories.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"69 1","pages":"Pages 1-11"},"PeriodicalIF":0.0000,"publicationDate":"1986-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80041-9","citationCount":"3","resultStr":"{\"title\":\"Arithmetic theories for computational complexity problems\",\"authors\":\"Steve Homer , John Reif\",\"doi\":\"10.1016/S0019-9958(86)80041-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers a number of arithmetic theories and shows how the strength of these theories relates to certain open problems in complexity theory concerning the polynomial-time hierarchy. These results are proved quite generally and hold for a wide class of subrecursive hierarchies. They can be used to characterize certain properties of functions provable in these theories.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"69 1\",\"pages\":\"Pages 1-11\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80041-9\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995886800419\",\"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/S0019995886800419","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Arithmetic theories for computational complexity problems
This paper considers a number of arithmetic theories and shows how the strength of these theories relates to certain open problems in complexity theory concerning the polynomial-time hierarchy. These results are proved quite generally and hold for a wide class of subrecursive hierarchies. They can be used to characterize certain properties of functions provable in these theories.
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