Nontrivial and Universal Helping for Wait-Free Queues and Stacks

This paper studies two approaches to formalize helping in wait-free implementations of shared objects. The first approach is based on operation valency, and it allows us to make the important distinction between trivial and nontrivial helping. We show that a wait-free implementation of a queue from common2 objects (e.g., Test&Set) requires nontrivial helping. In contrast, there is a wait-free implementation of a stack from Common2 objects with only trivial helping. This separation might shed light on the difficulty of implementing a queue from Common2 objects. The other approach formalizes the helping mechanism employed by Herlihy\u27s universal wait-free construction and is based on having an operation by one process restrict the possible linearizations of operations by other processes. We show that objects possessing such universal helping can be used to solve consensus

Relaxed Queues and Stacks from Read/Write Operations

Considering asynchronous shared memory systems in which any number of processes may crash, this work identifies and formally defines relaxations of queues and stacks that can be non-blocking or wait-free while being implemented using only read/write operations. Set-linearizability and Interval-linearizability are used to specify the relaxations formally, and precisely identify the subset of executions which preserve the original sequential behavior. The relaxations allow for an item to be returned more than once by different operations, but only in case of concurrency; we call such a property multiplicity. The stack implementation is wait-free, while the queue implementation is non-blocking. Interval-linearizability is used to describe a queue with multiplicity, with the additional relaxation that a dequeue operation can return weak-empty, which means that the queue might be empty. We present a read/write wait-free interval-linearizable algorithm of a concurrent queue. As far as we know, this work is the first that provides formalizations of the notions of multiplicity and weak-emptiness, which can be implemented on top of read/write registers only