{"title":"算子对直线复杂度的影响","authors":"D. Boneh, R. Lipton","doi":"10.1109/ISTCS.1997.595151","DOIUrl":null,"url":null,"abstract":"This paper concerns lower bounds on the straight line complexity of multi-variate polynomials. We obtain a conditional result showing that certain explicit linear operators must greatly increase the complexity of some polynomials. We do so by showing that if these operators roughly preserve the complexity of all polynomials then, co-NP is in AM. We show that certain explicit operators must vastly increase the straight line complexity of certain polynomials.","PeriodicalId":367160,"journal":{"name":"Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Effect of operators on straight line complexity\",\"authors\":\"D. Boneh, R. Lipton\",\"doi\":\"10.1109/ISTCS.1997.595151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper concerns lower bounds on the straight line complexity of multi-variate polynomials. We obtain a conditional result showing that certain explicit linear operators must greatly increase the complexity of some polynomials. We do so by showing that if these operators roughly preserve the complexity of all polynomials then, co-NP is in AM. We show that certain explicit operators must vastly increase the straight line complexity of certain polynomials.\",\"PeriodicalId\":367160,\"journal\":{\"name\":\"Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISTCS.1997.595151\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISTCS.1997.595151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper concerns lower bounds on the straight line complexity of multi-variate polynomials. We obtain a conditional result showing that certain explicit linear operators must greatly increase the complexity of some polynomials. We do so by showing that if these operators roughly preserve the complexity of all polynomials then, co-NP is in AM. We show that certain explicit operators must vastly increase the straight line complexity of certain polynomials.
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