{"title":"max-plus半环的最小实现问题和践踏问题是np - hard∗","authors":"Vincent D. Blondel , Natacha Portier","doi":"10.1016/S0764-4442(01)02192-9","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the <em>NP</em>-hardness of two problems. The first is the well-known minimal realization problem in the max-plus semiring. The second problem (Pisot's problem) is the problem of determining if a given integer linear recurrent sequence has a zero coefficient.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 12","pages":"Pages 1127-1130"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02192-9","citationCount":"0","resultStr":"{\"title\":\"Le problème de la réalisation minimale dans le demi-anneau max-plus et le problème de Pisot sont NP-durs∗\",\"authors\":\"Vincent D. Blondel , Natacha Portier\",\"doi\":\"10.1016/S0764-4442(01)02192-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the <em>NP</em>-hardness of two problems. The first is the well-known minimal realization problem in the max-plus semiring. The second problem (Pisot's problem) is the problem of determining if a given integer linear recurrent sequence has a zero coefficient.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 12\",\"pages\":\"Pages 1127-1130\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02192-9\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021929\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021929","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Le problème de la réalisation minimale dans le demi-anneau max-plus et le problème de Pisot sont NP-durs∗
We prove the NP-hardness of two problems. The first is the well-known minimal realization problem in the max-plus semiring. The second problem (Pisot's problem) is the problem of determining if a given integer linear recurrent sequence has a zero coefficient.
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