A Lower Bound on Wait-Free Counting

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, log m = f for some integer f ≤ flip(Pr). Thus, flip(Pr) ≥ log m and m is a power of 2. By...

• Type: Conference
• Year: 1993
• Where: PODC
• Authors: Shlomo Moran, Gadi Taubenfeld
• Keywords: Counting Protocol, Counting Protocol Pr, Distributed And Parallel Computing, PODC 1993, Wait-free Counting Protocol