A Characterization of Consensus Solvability for Closed Message Adversaries

Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns

Easy Consensus Algorithms for the Crash-Recovery Model

In the crash-recovery failure model of asynchronous distributed systems, processes can temporarily stop to execute steps and later restart their computation from a predefined local state. The crash-recovery model is much more realistic than the crash-stop failure model in which processes merely are allowed to stop executing steps. The additional complexity is reflected in the multitude of assumptions and the technical complexity of algorithms which have been developed for that model. We focus on the problem of consensus in the crash-recovery model, but instead of developing completely new algorithms from scratch, our approach aims at reusing existing crash-stop consensus algorithms in a modular way using the abstraction of failure detectors. As a result, we present three new and relatively simple consensus algorithms for the crash-recovery model for different types of assumptions

Global Data Computation in a Dedicated Chordal Ring

Existing Global Data Computation (GDC) protocols for asynchronous systems are designed for fully connected networks. In this paper, we discuss GDC in a dedicated asynchronous chordal ring, a type of un-fully connected networks. The virtual links approach, which constructs t+1 (t<n) process-disjoint paths for each pair of processes without direct connection to tolerate failures (where t is the maximum number of processes that may crash and n is the total number of processes), can be applied to solve the GDC problem in the chordal but the virtual links approach incurs high message complexity. To reduce the high communication cost, we propose a non round-based GDC protocol for the asynchronous chordal ring with perfect failure detectors. The main advantage of our approach is that there is no notion of round, processes only send messages via direct connections and the implementation of failure detectors does not require process-disjoint paths. Analysis and comparison with the virtual links approach shows that our protocol reduces the message complexity significantly.Singapore-MIT Alliance (SMA

State Machine Replication Is More Expensive Than Consensus

Consensus and State Machine Replication (SMR) are generally considered to be equivalent problems. In certain system models, indeed, the two problems are computationally equivalent: any solution to the former problem leads to a solution to the latter, and vice versa. In this paper, we study the relation between consensus and SMR from a complexity perspective. We find that, surprisingly, completing an SMR command can be more expensive than solving a consensus instance. Specifically, given a synchronous system model where every instance of consensus always terminates in constant time, completing an SMR command does not necessarily terminate in constant time. This result naturally extends to partially synchronous models. Besides theoretical interest, our result also corresponds to practical phenomena we identify empirically. We experiment with two well-known SMR implementations (Multi-Paxos and Raft) and show that, indeed, SMR is more expensive than consensus in practice. One important implication of our result is that - even under synchrony conditions - no SMR algorithm can ensure bounded response times

Dynamic group communication

Group communication is the basic infrastructure for implementing fault-tolerant replicated servers. While group communication is well understood in the context of static groups (in which the membership does not change), current specifications of dynamic group communication (in which processes can join and leave groups during the computation) have not yet reached the same level of maturity. The paper proposes new specifications - in the primary partition model - for dynamic reliable broadcast (simply called "reliable multicast”), dynamic atomic broadcast (simply called "atomic multicast”) and group membership. In the special case of a static system, the new specifications are identical to the well known static specifications. Interestingly, not only are these new specifications "syntactically” close to the static specifications, but they are also "semantically” close to the dynamic specifications proposed in the literature. We believe that this should contribute to clarify a topic that has always been difficult to understand by outsiders. Finally, the paper shows how to solve atomic multicast, group membership and reliable broadcast. The solution of atomic multicast is close to the (static) atomic broadcast solution based on reduction to consensus. Group membership is solved using atomic multicast. Reliable multicast can be efficiently solved by relying on a thrifty generic multicast algorith

On the Power of Rounds : Explorations of the Heard-Of Model

Distributed computing studies which problems can be solved by communicating processes -- computers, people,.... Because communication can take many shapes, and because of its uncertainty, lots of different models exist. So many that it's easy to get lost. One way to deal with this overabundance constrains processes to use rounds: they repeatedly broadcast a message tagged with their current round number, wait for messages with this same round number, and then use them to compute their next state and change round. The Heard-Of model leverages this idea through heard-of predicates, which constrain which messages is received at which round. Yet this model lacks the attention that it deserves from the research community. I believe the reason lies on the following three unsolved problems: how to find the heard-of predicate corresponding to a given model, is anything lost in this translation, and how to prove general results on heard-of predicates. This thesis addresses all three