Generalized FLP impossibility result for t-resilient asynchronous computations

Abstract

Demarcation of the border between solvable and unsolvable distributed tdis under various models is the holy grail of the theory of distributed computing. Oneof the most celebrated of theseresults is [6] (FLP) which established the impossibility of asynchronous consensus that can tolerate a single undetected fail-stop processor. This paper generalizes FLP to multiple faults. It establishes that k-set consensus proposed by Chaudhuri is impossible, if the protocol is to tolerate k failures, while there exists a protocol that tolerates k – 1 failures. Our proof technique is completely different than the one employed in [6]. We introduce a new model of computation, the im112ecliate-atoY12 ic-.s?2u~)shot. We fully characterize the graph of waitfree views within the model. Applying a variant of Sperner Lemma to this graph establishes the impossibility of k + 1 processors achieving waitfree k-set consensus. Finally, we introduce a new notion of nonblocking-busy-wait agreement protocol, With this ● Work supported by NSF Presiciential Young Iavest,igator Award under grant DCR84-51396 . Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direot commercial advantage, the ACM copyright notica and the title of the publication and its data appear, and notica is givan that copying is by permission of the Association for Computing Machinery. To copy otherwisa, or to republish, requiras a fea and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ 1993 ACM 0.89791.591-7/93/0005/0091 .,C$l .5(3 protocol we construct a read/write waitfree simulation techniclue by which k + 1 processors can produce a k-faulty execution of n processors protocol, {Tsing the simulation we establish the impossibility of n processors protocol that achieves k-set consensus and tolerates k failures, by reducing it to the waitfree case.