The test-and-set object is a fundamental synchronization primitive for shared memory systems. This paper addresses the number of registers (supporting atomic reads and writes) required to implement a one-shot test-and-set object in the standard asynchronous shared memory model with n processes. The best lower bound is log n - 1 [12,21] for obstruction-free and deadlock-free implementations, and recently a deterministic obstruction-free implementation using O(√ n) registers was presented [11].

This article is concerned with the problem of implementing an unbounded timestamp object from multiwriter atomic registers, in an asynchronous distributed system of n processes with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen et al. [2008] showed that √ n /2 − O (1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processes can repeatedly get timestamps). We improve this existing lower bound in two ways. First we establish a lower bound of n /6 − 1 registers for the obstruction-free long-lived timestamp problem. Previous such linear lower bounds were only known for constrained versions of the timestamp problem. This bound is asymptotically tight; Ellen et al. [2008] constructed a wait-free algorithm that uses n − 1 registers. Second we show that √2 n − log n − O (1) registers are required for any obstruction-free implementation of one-shot timestamp systems (meaning each process can get a timestamp at most once). We show that this bound is also asymptotically tight by providing a wait-free one-shot timestamp system that uses at most ⌈2√ n ⌉ registers, thus establishing a space complexity gap between one-shot and long-lived timestamp systems.

Herlihy and Wing [11] established that the set of possible outcomes of a shared memory distributed algorithm remains unchanged when atomic objects are replaced by their linearizable implementations. Since then, linearizability has been the correctness condition of choice for distributed algorithm designers. In 2011, however, Golab, Higham and Woelfel [9] showed that, if an algorithm employs randomization, then the probability distribution over the set of possible outcomes can differ between the atomic and implemented versions. They also proved that a stronger condition, called strong linearizability, is necessary and sufficient to guarantee the same probability distributions for these two cases when the randomized algorithm is under the control of an adaptive adversary. Therefore, we are motivated to construct strongly linearizable implementations of common distributed objects whenever possible. In this paper we prove

This paper is concerned with the problem of implementing an unbounded timestamp object from multi-writer atomic registers, in an asynchronous distributed system of n processors with distinct identifiers where timestamps are taken from an arbitrary universe. Ellen, Fatourou and Ruppert [7] showed that √n/2-O(1) registers are required for any obstruction-free implementation of long-lived timestamp systems from atomic registers (meaning processors can repeatedly get timestamps).