Wait-free Hierarchy Research Articles

Extending the wait-free hierarchy to multi-threaded systems

In modern operating systems and programming languages adapted to multicore computer architectures, parallelism is abstracted by the notion of execution threads. Multi-threaded systems have two major specificities: on the one part, new threads can be created dynamically at runtime, so there is no bound on the number of threads participating in long-running executions. On the other part, threads have access to a memory allocation mechanism that cannot allocate infinite arrays. These specificities make it challenging to adapt some algorithms to multi-threaded systems, in particular those that need to assign one shared register per process. This paper explores the synchronization power of shared objects in multi-threaded systems by extending the famous Herlihy’s wait-free hierarchy to take these constraints into consideration. It proposes to subdivide the set of objects with an infinite consensus number into nine new degrees, depending on their ability to synchronize a bounded, finite or infinite number of processes, with or without the need to allocate an infinite array. To show the relevance of the proposed extension, for each new degree it is either proved that it is empty, or an object illustrating it is proposed.

All of Us Are Smarter than Any of Us: Nondeterministic Wait-Free Hierarchies Are Not Robust

A wait-free hierarchy ACM Transactions on Programming Languages and Systems, 11 (1991), pp. 124--149; Proceedings of the 12th ACM Symposium on Principles of Distributed Computing, 1993, pp. 145--158] classifies object types on the basis of their strength in supporting wait-free implementations of other types. Such a hierarchy is robust if it is impossible to implement objects of types that it classifies as "strong" by combining objects of types that it classifies as "weak." We prove that if nondeterministic types are allowed, the only wait-free hierarchy that is robust is the trivial one, which lumps all types into a single level. In particular, the consensus hierarchy (the most closely studied wait-free hierarchy) is not robust. Our result implies that, in general, it is not possible to determine the power of a concurrent system that supports a given set of primitive object types by reasoning about the power of each primitive type in isolation.

On the space complexity of randomized synchronization

The “waite-free hierarchy” provides a classification of multiprocessor synchronization primitives based on the values ofnfor which there are deterministic wait-free implementations ofn-process consensus using instances of these objects andread-writeregisters. In a randomized wait-free setting, this classification is degenerate, sincen-process consensus can be solved using onlyO(n) read-writeregisters.In this paper, we propose a classification of synchronization primitives based on thespace complexityof randomized solutions ton-process consensus. Ahistoryless object,such as aread-writeregister, aswapregister, or atest&setregister, is an object whose state depends only on the lost nontrivial operation thate was applied to it. We show that, usinghistorylessobjects, Ω(√n) object instances are necessary to solven-process consensus. This lower bound holds even if the objects have unbounded size and the termination requirement isnondeterministic solo termination, a property strictly weaker than randomized wait-freedom.We then use this result to related the randomized space complexity of basic multiprocessor synchronization primitives such asshared counters, fetch&addregisters, andcompare&swapregisters. Viewed collectively, our results imply that there is a separation based on space complexity for synchronization primitives in randomized computation, and that this separation differs from that implied by the deterministic “wait-free hierarchy.”