H. Attiya, A. Bar-Noy, D. Dolev, D. Koller, D. Peleg, R. Reischuk
{"title":"Achievable cases in an asynchronous environment","authors":"H. Attiya, A. Bar-Noy, D. Dolev, D. Koller, D. Peleg, R. Reischuk","doi":"10.1109/SFCS.1987.5","DOIUrl":null,"url":null,"abstract":"The paper deals with achievability of fault tolerant goals in a completely asynchronous distributed system. Fischer, Lynch, and Paterson [FLP] proved that in such a system \"nontrivial agreement\" cannot be achieved even in the (possible) presence of a single \"benign\" fault. In contrast, we exhibit two pairs of goals that are achievable even in the presence of up to t ≪ n/2 faulty processors, contradicting the widely held assumption that no nontrivial goals are attainable in such a system. The first pair deals with renaming processors so as to reduce the size of the initial name space. When only uniqueness is required of the new names, we present a lower bound of n + 1 on the size of the new name space, and a renaming algorithm which establishes an upper bound of n + t. In case the new names are required also to preserve the original order, a tight bound of 2t(n- t + 1) - 1 is obtained. The second pair of goals deals with the multi-slot critical section problem. We present algorithms for controlled access to a critical section. As for the number of slots required, a tight bound of t + 1 is proved in case the slots are identical. In the case of distinct slots the upper bound is 2t + 1.","PeriodicalId":153779,"journal":{"name":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"87","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1987.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 87
Abstract
The paper deals with achievability of fault tolerant goals in a completely asynchronous distributed system. Fischer, Lynch, and Paterson [FLP] proved that in such a system "nontrivial agreement" cannot be achieved even in the (possible) presence of a single "benign" fault. In contrast, we exhibit two pairs of goals that are achievable even in the presence of up to t ≪ n/2 faulty processors, contradicting the widely held assumption that no nontrivial goals are attainable in such a system. The first pair deals with renaming processors so as to reduce the size of the initial name space. When only uniqueness is required of the new names, we present a lower bound of n + 1 on the size of the new name space, and a renaming algorithm which establishes an upper bound of n + t. In case the new names are required also to preserve the original order, a tight bound of 2t(n- t + 1) - 1 is obtained. The second pair of goals deals with the multi-slot critical section problem. We present algorithms for controlled access to a critical section. As for the number of slots required, a tight bound of t + 1 is proved in case the slots are identical. In the case of distinct slots the upper bound is 2t + 1.