Distributed Universality

Abstract

International audienceA notion of a universal construction suited to distributed computing has been introduced by M. Herlihy in his celebrated paper “Wait-free synchronization” (ACM TOPLAS, 1991). A universal construction is an algorithm that can be used to wait-free implement any object defined by a sequential specification. Herlihy’s paper shows that the basic system model, which supports only atomic read/write registers, has to be enriched with consensus objects to allow the design of universal constructions. The generalized notion of a k-universal construction has been recently introduced by Gafni and Guerraoui (CONCUR, 2011). A k-universal construction is an algorithm that can be used to simultaneously implement k objects (instead of just one object), with the guarantee that at least one of the k constructed objects progresses forever. While Herlihy’s universal construction relies on atomic registers and consensus objects, a k-universal construction relies on atomic registers and k-simultaneous consensus objects (which are wait-free equivalent to k-set agreement objects in the read/write system model).This paper significantly extends the universality results introduced by Herlihy and Gafni-Guerraoui. In particular, we present a k-universal construction which satisfies the following five desired properties, which are not satisfied by the previous k-universal construction: (1) among the k objects that are constructed, at least ℓ objects (and not just one) are guaranteed to progress forever; (2) the progress condition for processes is wait-freedom, which means that each correct process executes an infinite number of operations on each object that progresses forever; (3) if any of the k constructed objects stops progressing, all its copies (one at each process) stop in the same state; (4) the proposed construction is contention-aware, in the sense that it uses only read/write registers in the absence of contention; and (5) it is generous with respect to the obstruction-freedom progress condition, which means that each process is able to complete any one of its pending operations on the k objects if all the other processes hold still long enough. The proposed construction, which is based on new design principles, is called a (k,ℓ)-universal construction. It uses a natural extension of k-simultaneous consensus objects, called (k,ℓ)-simultaneous consensus objects ((k,ℓ)-SC). Together with atomic registers, (k,ℓ)-SC objects are shown to be necessary and sufficient for building a (k,ℓ)-universal construction, and, in that sense, (k,ℓ)-SC objects are (k,ℓ)-universal

Distributed Computability

“…A yet more general construction is described in [81], that considers the simultaneous construction of k objects such that the wait-freedom property is satisfied for at least ℓ of them, 1 ≤ ℓ ≤ k. Such a construction relies on the k-simultaneous consensus object defined in [4].…”

Mastering concurrent computing through sequential thinking

“…Distributed universality [23,31,63] Some of the previous papers were awarded the famous ACM-EATCS Dijkstra Award. Created in 2000, this award is given to outstanding papers on the principles of distributed computing, whose significance and impact on the theory and/or practice of distributed computing have been evident for at least a decade).…”

Read-Write Memory and k-Set Consensus as an Affine Task

“…Simulating a k-process shared memory system. We employ generalized state machines (proposed in [13] and extended in [28]) that allow for simulating a k-process read-write memory system in the k-set-consensus model. To ensure consistency of simulated read and write operations, we use commit-adopt objects [10] that can be implemented using reads and writes.…”

“…The third stage consists in checking whether pending operations can safely be terminated (lines [15][16][17][18][19][20], and if so, whether the process has completed its simulation (line 21) or if new operations can be initiated (line [21][22][23][24][25][26][27][28].…”

“…Indeed, the equality implies that the writes in the estimated snapshot have been observed by every process (line 17). Last, if a process did not terminate, it increments its write counter and, if there is a new operation available, the process selects the operation (see lines [22][23][24][25][26][27][28].…”