TY - CHAP

T1 - Resilient consensus for infinitely many processes

T2 - (Extended abstract)

AU - Merritt, Michael

AU - Taubenfeld, Gadi

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2003

Y1 - 2003

N2 - We provide results for implementing resilient consensus for a (countably) infinite collection of processes. - For a known number of faults, we prove the following equivalence result: For every t ≥ 1, there is a t-resilient consensus object for infinitely many processes if and only if there is a t-resilient consensus object for t + 1 processes. - For an unknown or infinite number of faults, we consider whether an infinite set of wait-free consensus objects, capable of solving consensus for any finite collection of processes, suffice to solve wait-free consensus for infinitely many processes. We show that this implication holds under an assumption precluding runs in which the number of simultaneously active processes is not bounded, leaving the general question open. All the proofs are constructive and several of the constructions have adaptive time complexity. (Reduced to the finite domain, some improve on the time complexity of known results.) Furthermore, we prove that the constructions are optimal in some space parameters by providing tight simultaneous-access and space lower bounds. Finally, using known techniques, we draw new conclusions on the universality of resilient consensus objects in the infinite domain.

AB - We provide results for implementing resilient consensus for a (countably) infinite collection of processes. - For a known number of faults, we prove the following equivalence result: For every t ≥ 1, there is a t-resilient consensus object for infinitely many processes if and only if there is a t-resilient consensus object for t + 1 processes. - For an unknown or infinite number of faults, we consider whether an infinite set of wait-free consensus objects, capable of solving consensus for any finite collection of processes, suffice to solve wait-free consensus for infinitely many processes. We show that this implication holds under an assumption precluding runs in which the number of simultaneously active processes is not bounded, leaving the general question open. All the proofs are constructive and several of the constructions have adaptive time complexity. (Reduced to the finite domain, some improve on the time complexity of known results.) Furthermore, we prove that the constructions are optimal in some space parameters by providing tight simultaneous-access and space lower bounds. Finally, using known techniques, we draw new conclusions on the universality of resilient consensus objects in the infinite domain.

UR - http://www.scopus.com/inward/record.url?scp=35248813440&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-39989-6_1

DO - 10.1007/978-3-540-39989-6_1

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:35248813440

SN - 354020184X

SN - 9783540201847

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 15

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Fich, Faith Ellen

PB - Springer Verlag

ER -