In classical asynchronous distributed systems composed of a fixed number n of processes where some proportion may fail by crashing, many objects do not have a wait-free linearizable implementation (e.g. stacks, queues, etc.). It has been proved that consensus is universal in such systems, which means that this system augmented with consensus objects allows to implement any object that has a sequential specification. To this end, many universal constructions have been proposed in systems augmented with consensus objects or with different equivalent objects or special hardware instructions (compare&swap, fetch&add, etc.). In this paper, we consider a more general system model called infinite arrival model where infinitely many processes may arrive and leave or crash during a run. We prove that consensus is still universal in this more general model. For that, we propose a universal construction. As a first step we build a weak log for which we propose two implementations using consensus objects for the first and the compare&swap special instruction for the other.
The recent surge of blockchain systems has renewed the interest in traditional Byzantine fault-tolerant consensus protocols. Many such consensus protocols have a primary-backup design in which an assigned replica, the primary, is responsible for coordinating the consensus protocol. Although the primary-backup design leads to relatively simple and high performance consensus protocols, it places an unreasonable burden on a good primary and allows malicious primaries to substantially affect the system performance. In this paper, we propose a protocol-agnostic approach to improve the design of pri…
A natural way to measure the power of a distributed-computing model is to characterize the set of tasks that can be solved in it. %the model. In general, however, the question of whether a given task can be solved in a given model is undecidable, even if we only consider the wait-free shared-memory model. In this paper, we address this question for restricted classes of models and tasks. We show that the question of whether a collection $C$ of \emph{$(\ell,j)$-set consensus} objects, for various $\ell$ (the number of processes that can invoke the object) and $j$ (the number of distinct outputs…
The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC' 09) as a weakening of the classic consensus. When there is concurrency, the consensus output can be arbitrary, not even the input of any process. They showed that safe-consensus is equivalent to consensus, in a wait-free system. We study the solvability of consensus in three shared memory iterated models extended with the power of safe-consensus black boxes. In the first iterated model, for the $i$-th iteration, the processes write to memory, then they snapshot it and finally they invoke safe-consensus boxes. We prove that…
Proof-of-Stake systems randomly choose, on each round, one of the participants as a consensus leader that extends the chain with the next block such that the selection probability is proportional to the owned stake. However, distributed random number generation is notoriously difficult. Systems that derive randomness from the previous blocks are completely insecure; solutions that provide secure random selection are inefficient due to their high communication complexity; and approaches that balance security and performance exhibit selection bias. When block creation is rewarded with new stake,…
We study the ability of different shared object types to solve recoverable consensus using non-volatile shared memory in a system with crashes and recoveries. In particular, we compare the difficulty of solving recoverable consensus to the difficulty of solving the standard wait-free consensus problem in a system with halting failures. We focus on the model where individual processes may crash and recover and the large class of object types that are equipped with a read operation. We characterize the readable object types that can solve recoverable consensus among a given number of processes. …
The question of whether all shared objects with consensus number 2 belong to Common2, the set of objects that can be implemented in a wait-free manner by any type of consensus number 2, was first posed by Herlihy. In the absence of general results, several researchers have obtained implementations for restricted-concurrency versions of FIFO queues. We present the first Common2 algorithm for a queue with two enqueuers and any number of dequeuers.
The optimal space complexity of consensus in shared memory is a decades-old open problem. For a system of $n$ processes, no algorithm is known that uses a sublinear number of registers. However, the best known lower bound due to Fich, Herlihy, and Shavit requires $Ω(\sqrt{n})$ registers. The special symmetric case of the problem where processes are anonymous (run the same algorithm) has also attracted attention. Even in this case, the best lower and upper bounds are still $Ω(\sqrt{n})$ and $O(n)$. Moreover, Fich, Herlihy, and Shavit first proved their lower bound for anonymous processes, and t…
The consensus number of an object is the maximum number of processes among which binary consensus can be solved using any number of instances of the object and read-write registers. Herlihy [6] showed in his seminal work that if an object has a consensus number of n, then there is a universal construction for a wait-free and linearizable implementation of any non-trivial concurrent object or data structure that is shared among n processes. Thus, a synchronization object such as compare-and-swap with an infinite consensus number and the corresponding instruction can be viewed as "strong". On th…
Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that - all the outputs are within distance 1 of one another, and - each output value lies on a shortest path between two input values. From prior work, it is known that there is no wait-f…
We consider synchronous dynamic networks which like radio networks may have asymmetric communication links, and are affected by communication rather than processor failures. In this paper we investigate the minimal message survivability in a per round basis that allows for the minimal global cooperation, i.e., allows to solve any task that is wait-free read-write solvable. The paper completely characterizes this survivability requirement. Message survivability is formalized by considering adversaries that have a limited power to remove messages in a round. Removal of a message on a link in one…
The problem of Byzantine consensus has been key to designing secure distributed systems. However, it is particularly difficult, mainly due to the presence of Byzantine processes that act arbitrarily and the unknown message delays in general networks. Although it is well known that both safety and liveness are at risk as soon as $n/3$ Byzantine processes fail, very few works attempted to characterize precisely the faults that produce safety violations from the faults that produce termination violations. In this paper, we present a new lower bound on the solvability of the consensus problem by d…
Impossibility Results for Strong Linearizability: The Difficulty of Consistent Refereeing
Technion - Israel Institute of Technology（以色列理工学院）；Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学）；LIX, Ecole Polytechnique, CNRS and Institut Polytechnique de Paris（巴黎综合理工学院LIX实验室、法国国家科学研究中心和巴黎理工学院）
It is well known that the consensus problem cannot be solved deterministically in an asynchronous environment, but that randomized solutions are possible. We propose a new model, called noisy scheduling, in which an adversarial schedule is perturbed randomly, and show that in this model randomness in the environment can substitute for randomness in the algorithm. In particular, we show that a simplified, deterministic version of Chandra's wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves consensus in time at most logarithmic in the number of active processes. The pro…
We consider the problem of solving consensus using deterministic algorithms in a synchronous dynamic network with unreliable, directional point-to-point links, which are under the control of a message adversary. In contrast to a large body of existing work that focuses on oblivious message adversaries where the communication graphs are picked from a predefined set, we consider message adversaries where guarantees about stable periods that occur only eventually can be expressed. We reveal to what extent such eventual stability is necessary and sufficient, that is, we present the shortest period…
Laboratory investigations have shown that a formal theory of fault-tolerance will be essential to harness nanoscale self-assembly as a medium of computation. Several researchers have voiced an intuition that self-assembly phenomena are related to the field of distributed computing. This paper formalizes some of that intuition. We construct tile assembly systems that are able to simulate the solution of the wait-free consensus problem in some distributed systems. (For potential future work, this may allow binding errors in tile assembly to be analyzed, and managed, with positive results in dist…
