Partial synchrony based on set timeliness

Abstract

We introduce a new model of partial synchrony for read-write shared memory systems. This model is based on the simple notion of set timeliness-a natural generalization of the seminal concept of timeliness in the partially synchrony model of Dwork et al. (J. ACM 35(2):288-323, 1988). Despite its simplicity, the concept of set timeliness is powerful enough to define a family of partially synchronous systems that closely match individual instances of the t-resilient k-set agreement problem among n processes, henceforth denoted (t, k, n)-agreement. In particular, we use it to give a partially synchronous system that is synchronous enough for solving (t, k, n)-agreement, but not enough for solving two incrementally stronger problems, namely, (t + 1, k, n)-agreement, which has a slightly stronger resiliency requirement, and (t, k − 1, n)-agreement, which has a slightly stronger agreement requirement. This is the first partially synchronous system that separates these sub-consensus problems. The above results show that set timeliness can be used to study and compare the partial synchrony requirements of problems that are strictly weaker than consensus.A preliminary version of this paper appeared in [3].

The Generalized Loneliness Detector and Weak System Models for k-Set Agreement

“…Links need not be FIFO but are assumed to be reliable. 1 Every process executes an instance of a distributed algorithm and is modeled as a deterministic state machine. Its execution consists of a sequence of instantaneous local steps, where a single process performs a state transition according to its transition function, in addition to either receiving a (possibly empty) set of previously sent messages or sending messages to an arbitrary set of processes (including itself).…”

“…Besides some time complexity results in systems where periods of synchrony and asynchrony alternate [5], we are only aware of one related approach (albeit for shared memory systems), namely, the set timeliness approach for k-set agreement in shared memory systems introduced in [1], [2]. Consult Section 3.3 for a more detailed relation of our models & results and existing ones.…”

Wait-freedom with advice

“…This gave many interesting insights on the nature of "wait-free unsolvable" tasks. For example, the celebrated result by Chandra et al [12] that the eventual leader failure detector is the weakest for solving for consensus 1 enabled a long line of research on characterizing the models in which can be implemented and, thus, consensus, can be solved (see, e.g., the related work section in [3]). A solution of a task using a failure detector guarantees that every correct process, i.e., a process that is predicted to take infinitely many steps by the failure pattern, eventually obtains an output.…”

“…We show finally that ( j, j + k − 1)-renaming can be solved kconcurrently, and, thus, using ¬ k . 3 Another interesting corollary of our characterization is that if a failure detector solves k-set agreement among an arbitrary given subset of k + 1 processes, then it is strong enough to solve k-set agreement among all processes. This is a generalization of the recent result of Delporte et al [16] that any failure detector allowing for solving consensus (1-set agreement) among each two processes, also allows for solving consensus among all processes.…”

“…2 Note that all tasks can be solved 1-concurrently. 3 For some values of j and k, however, the question of the maximal tolerated concurrency of ( j, j + k − 1)-renaming is still open [11]. One important feature inherited by our EFD framework from wait-free protocols is that it leverages simulation-based computing: processes can cooperate trying to bring all participating processes to their outputs.…”