TY - GEN

T1 - Lower bound on wait-free counting

AU - Moran, Shlomo

AU - Taubenfeld, Gadi

N1 - Copyright:
Copyright 2004 Elsevier B.V., All rights reserved.

PY - 1993

Y1 - 1993

N2 - A counting protocol (mod m) consists of shared memory bits - referred to as the counter - and of a procedure for incrementing the counter value by 1 (mod m). The procedure may be executed by many processes concurrently. It is required to satisfy a very weak correctness requirement, namely: the counter is required to show a correct value only in quiescent states - states in which no process is incrementing the counter. Special cases of counting protocols are `counting networks' [AHS91] and `concurrent counters' [MTY92]. We consider the problem of implementing a wait-free counting protocol, assuming that the basic atomic operation of a process is a read-modify-write on a single bit. Let flip(Pr) be the maximum number of times a single increment operation changes the counter bits in a counting protocol Pr. Our main result is: In any wait-free counting protocol Pr which counts modulo m, m divides 2flip(Pr). Thus, flip(Pr)≥log m and m is a power of 2. This result provides interesting generalizations of lower bounds and impossibility results for counting and smoothing networks.

AB - A counting protocol (mod m) consists of shared memory bits - referred to as the counter - and of a procedure for incrementing the counter value by 1 (mod m). The procedure may be executed by many processes concurrently. It is required to satisfy a very weak correctness requirement, namely: the counter is required to show a correct value only in quiescent states - states in which no process is incrementing the counter. Special cases of counting protocols are `counting networks' [AHS91] and `concurrent counters' [MTY92]. We consider the problem of implementing a wait-free counting protocol, assuming that the basic atomic operation of a process is a read-modify-write on a single bit. Let flip(Pr) be the maximum number of times a single increment operation changes the counter bits in a counting protocol Pr. Our main result is: In any wait-free counting protocol Pr which counts modulo m, m divides 2flip(Pr). Thus, flip(Pr)≥log m and m is a power of 2. This result provides interesting generalizations of lower bounds and impossibility results for counting and smoothing networks.

UR - http://www.scopus.com/inward/record.url?scp=0027800206&partnerID=8YFLogxK

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AN - SCOPUS:0027800206

SN - 0897916131

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 251

EP - 259

BT - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

A2 - Anon, null

PB - Publ by ACM

T2 - Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing

Y2 - 15 August 1993 through 18 August 1993

ER -