Space- and Time-Efficient Long-Lived Test-And-Set Objects

We provide several space-and time-efficient implementations of randomized long-lived Test-And-Set (TAS) objects from registers, in the standard asynchronous shared memory system with n processes. Our main construction uses O(n) registers, which is optimal, and TAS() and Reset() methods have expected step-complexity O(log log n) against the oblivious adversary. Prior to this work, no long-lived TAS implementation from O(n) registers was known, where all methods have sub-linear (expected) step complexity. Another construction achieves expected stepcomplexity O(log* n) for TAS() against the oblivious adversary, constant worst-case step-complexity for Reset(), but requires O(n 1.5) registers. These results are obtained from general transformations of randomized one-time TAS implementations (e.g., [3, 11, 13]) into long-lived ones.